Core Curriculum by MidSchoolMath - Sixth Grade

4/12/2021 Core Curriculum by MidSchoolMath (2021) - Sixth Grade Report

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Alignment: Overall Summary

Core Curriculum byMidSchoolMath - SixthGradeMidSchoolMath | Sixth Grade



The materials reviewed for Core Curriculum by MidSchoolMath Grade math 6 meet expectations for Alignment to the CCSSM. In

Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and

practice-content connections.

SEE RATING SCALE UNDERSTANDING GATEWAYS

Gateway 1: FOCUS & COHERENCE

12-14 Meets Expectations 8-11 Partially Meets Expectations 0-7 Does Not Meet Expectations

Gateway 2:

RIGOR & MATHEMATICAL PRACTICES


Gateway 3: USABILITY


Gateway OneFocus & CoherenceMeets ExpectationsThe materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for focusand coherence. For focus, the materials assess grade-level content, and partially give all studentsextensive work with grade-level problems to meet the full intent of grade-level standards. Forcoherence, each grade’s materials are coherent and consistent with the CCSSM.

ALIGNMENT Meets Expectations |

0 7 12 14

0 10 16 18

USABILITY Meets Expectations |

0 17 25 27

CRITERION 1A - 1B

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18

27



INDICATOR 1A

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forassessing grade-level content.

The materials are organized by the Domains and Clusters delineated by CCSS. Each Cluster has aMilestone Assessment, and all assessments include multiple choice and/or multiple select. Theassessments are aligned to grade-level standards, and examples include:

In Milestone Assessment 6.NS.C, Question 11, “Which number sentence is true? a) ; b) ; c) ; d) .”

In Milestone Assessment 6.EE.A, Question 16, “ and are equivalent expressionsbecause: a) they both have b as a variable; b) they both have four terms; c) they both produce thesame value no matter what number represents; d) they both equal 4 when .”

In Milestone Assessment 6.SP.B, Question 3, “Histograms, dot plots and box plots can all be usedto display data. Which statement is true? a) Histograms show the distribution and the actual valuesof the data set; b) Dot plots show the distribution and the actual values of the data set; c) Box plotsshow the distribution and the actual values of the data set; d) Not enough information.”

In Milestone Assessment 6.RP.A, Question 1, “Which statement correctly describes the image ofclouds and suns? Select all the apply. a) For every three clouds, there are two suns; b) For every sixclouds, there are nine suns; c) For every three suns, there are two clouds; d) For every two clouds,there are one sun.”

INDICATOR 1B

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for givingall students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level

standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for focusas they assess grade-level content and provide all students extensive work with grade-level problems tomeet the full intent of grade-level standards.

−16 > −13

3 < −3 −(−7) > 9 −18 < −14

b + b + b + b 4b

b b = 1

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Materials present opportunities for all students to meet the full intent of grade-level standards throughextensive work with grade-level problems. Each lesson addresses one grade-level standard with allstandards addressed over the course of the year. Lessons are three to four days long. There areopportunities within each lesson to practice the content of the standards including: Math Simulator,one to four questions; Practice Printable typically has six to ten questions; Additional Practice has fourto ten questions; Clicker Quizzes include six questions; and the teacher can assign a speci�c domain inTest Trainer Pro. Examples where the full intent is attended to include:

In 6.RP.A.3 Clone Wars, students make tables of equivalent ratios relating quantities with whole-number measurements, �nd missing values in the tables, and plot the pairs of values on thecoordinate plane. For example, Practice Printable Question 2, “Frankie is looking to add �sh to histank. He has done some research and found that di�erent �sh require a certain amount of space tothrive. Fill in the missing information in the ratio tables and then plot the ordered pairs on thecoordinate plane. (Be sure to clearly label which line represents which �sh.)”

In 6.NS.A.1 Mr. Mung’s Ice Cream, students solve real-world problems with division of fractions byfractions. For example, Practice Printable Question 2, “Create a story context for 6¼ ÷ 1¼. Draw avisual fraction model to show the quotient.”

In 6.EE.A.4 ...And a Tin of Rice, students identify when two expressions are equivalent. Forexample, Practice Printable Questions 1-4, “Decide whether each pair of equations are equivalent.Explain how you know. Question 3: “2x + 3y and 5xy.”

The Test Trainer Pro and Simulation Trainer are also designed to provide additional, grade-level work.

In Test Trainer Pro, primarily used as a daily warm-up, teachers can assign a speci�c domain, but notstandards. Teachers have access to the question bank in order to see what the questions are, butcannot edit them.

In Simulation Trainer, the content matches the lesson, but students can provide any number as ananswer, then watch the steps worked out (no words) in a solution video. They’re presented with thesame question again and can put in the correct answer, then watch the same solution again. If theyget it correct the �rst time, they also watch the solution video. The next questions are not novel,but the same situation with new numbers. If students miss one, it resets them to the beginning, nomatter where they were in the assignment. It is possible that some students would never complete aSimulation Trainer.

CRITERION 1C - 1G

Each grade’s materials are coherent and consistent with the Standards.

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INDICATOR 1C

When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations that, whenimplemented as designed, the majority of the materials address the major clusters of each grade.

The approximate number of days devoted to major work of the grade (including assessments andsupporting work connected to the major work) is 125 out of 183, which is approximately 68%.

The number of lessons devoted to major work of the grade (including assessments and supportingwork connected to the major work) is 26 out of 37 lessons, which is approximately 70%.

The number of weeks devoted to major work (including assessments and supporting workconnected to the major work) is 26 out of 36, which is approximately 72%.

A day-level analysis is most representative of the materials because this represents the class time that isdevoted to major work of the grade including reviews, domain intensives, and assessments. As a result,approximately 68% of the materials focus on major work of the grade.

INDICATOR 1D

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting content enhancing focus and coherence simultaneously by engaging students in the majorwork of the grade.

Examples of connections between supporting content and major work of the grade include:

6.NS.B.2 Which Way connects to 6.RP.3b as students divide multi-digit numbers to �nd unit rates.In the Practice Printable, Question 4, “Carlos and Doug went on a road trip. They recorded how farthey traveled each day in a travel journal. If they drove for a total of 30 hours, what was theiraverage speed?” The journal provides the data: Day 1, 450 miles; Day 2, 300 miles; Day 3, 350miles, Day 4, 400 miles. Additionally, the Immersion & Data and Computation portions of thelesson require students to use ratio reasoning to determine which route is fastest.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forcoherence. The majority of the materials: address the major clusters of the grade, have supportingcontent connected to major work, make connections between clusters and domains, and have contentfrom prior and future grades connected to grade-level work.

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6.G.A.2 River Rescue connects to 6.NS.A as students divide fractions by fractions to solve volume

problems. In the Practice Printable, Question 6, “A right rectangular prism has a volume of

cubic units. The width is cubic units, and the height is cubic units. What is the length?”

6.NS.B.4 The Castle Guard connects to 6.EE.3 as students use the Greatest Common Factor toproduce equivalent expressions. In the Practice Printable, Question 3, “For each sum or di�erence,factor out the GCF, and rewrite the sum or di�erence.”

INDICATOR 1E

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forincluding problems and activities that serve to connect two or more clusters in a domain or two or moredomains in a grade. Examples include:

6.RP.A.3a Clone Wars “connects 6.RP.A to 6.EE.C as students can use ratio reasoning as a meansto analyze the graph of the relationship between independent and dependent variables.” In thePractice Printable, Question 2 shows two types of �sh and the space required based on the numberof �sh. Question 3 states, “Using the tables and graph from Question 2 , write a few sentencescomparing the ratios of the amount of space needed for each �sh. How is this shown in the graph?”

6.SP.A.3 Periodontal Pockets connects 6.SP.A and 6.NS.B as students compute with multi-digitnumbers to “calculate and analyze the mean and the mean absolute deviation of a data set.” InPractice Printable, Question 2 states, “Tyrell is looking for a new place to keep his sailboat. He lovesto sail and is looking for a location that will provide great sailing conditions year round. Tyrell’s idealwind speed for optimal sailing conditions is around 10 knots. Below is some data he has gathered tohelp him make his �nal decision. (provided: a table with two di�erent rivers and the average windspeed for each month) a) What is the mean wind speed of each location? b) What is the medianwind speed of each location? c) Calculate the MAD for each set of data.”

INDICATOR 1F

Content from future grades is identi�ed and related to grade-level work, and materials relate grade-level concepts explicitly to prior

knowledge from earlier grades.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for clearlyidentifying content from future grades and relating it to grade-level work and explicitly relating grade-level concepts to prior knowledge from earlier grades.

Examples of clearly identifying content from future grades and relating it to grade-level work include:

6.RP.A.1 For Every Day states “This activity connects 6.RP to 7.RP.A and 8.EE.B, as unit rate isthe basis for work involving constant of proportionality and slope of linear equations.”

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The game “Ko’s Journey” addresses several standards across grade levels. The Grade 6 standardsinclude 6.RP.A.3a-c; 6.NS.B.3; 6.NS.C.6 and 8; and 6.G.A.2, though some of these have only onequestion. The game also addresses the Grade 4 concept of using a protractor and Grade 5 conceptsincluding fractions, coordinate plane, and converting measurement units. The game introduces theGrade 8 concept of slope, though students are given formulas and directed through each equation.

Examples of explicitly relating grade-level concepts to prior knowledge from earlier grades include:

6.EE.B.7 The Sign of Zero states, “This activity connects 6.EE to 5.NF as students write and solvereal-world problems involving multiplication of fractions and mixed numbers.”

6.G.A.4 Build a Better Box states, “This activity connects 6.G.A to 5.G.B in that students will drawnets and apply area formulas using their knowledge of classifying two-dimensional �gures.”

INDICATOR 1G

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modi�cation.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6, in order to foster coherencebetween grades, can be completed within a regular school year with little to no modi�cation. Asdesigned, the materials, with assessments, can be completed in 146-183 days.

There are �ve domains which contain a total of 37 lessons. Lessons are designed to take three tofour days each, leading to a total of 111-148 lesson days.

There are �ve days for Major Cluster Intensives.

There are 30 assessment days including 10 days for review, 10 spiral review days in the DistributedPractice Modules, and 10 milestone assessments.

The Scope and Sequence Chart in the Teacher Edition provides pacing information. A lesson is designedfor 60 minutes.

Gateway TwoRigor & the Mathematical PracticesMeets ExpectationsThe materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for rigorand balance and practice-content connections. The materials re�ect the balances in the Standards andhelp students develop conceptual understanding, procedural skill and �uency, and application. Thematerials make meaningful connections between the Standards for Mathematical Content and theStandards for Mathematical Practice (MPs).

CRITERION 2A - 2D



INDICATOR 2A

Materials develop conceptual understanding of key mathematical concepts, especially where called for in speci�c content standards or

cluster headings.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations fordeveloping conceptual understanding of key mathematical concepts, especially where called for inspeci�c standards or cluster headings.

Examples of problems and questions that develop conceptual understanding across the grade levelinclude:

In 6.EE.A.3 Provision Problem states, “How many equivalent expressions can we create from thisexpression? .” Suggested answers include: “Combine like terms. ; Factor outGCF. ; Factor out GCF & combine like terms ; Factor out common factor (notGCF) ; Factor out common factor (not GCF) & combine terms ”.

In 6.G.A.3 Fuel Factor, the teacher is prompted to ask students questions to further their thinkingsuch as, “What is the direction for the course? What do you notice about the coordinates of theendpoints of horizontal line segments? What do you notice about the coordinates of the endpointsof vertical line segments? Imagine the coordinates on a grid. How might you �nd the length of aline segment connecting them? Since there is no grid, how might you �nd the length of the linesegment anyway?”

In 6.NS.A.1 Mr. Mung’s Ice Cream, the teacher is prompted to complete this example using a bar

diagram. “ is divided by . What is the quotient? We could draw a visual fraction model. We start

by drawing a representation of . Then we separate the diagram into fourths because of the

denominator of the divisor. We then ask ourselves how many groups of are in ? Then separate

the diagram into groups of . We can see two groups of , so the quotient is 2.”

Examples where students independently demonstrate conceptual understanding throughout the gradeinclude:

Materials re�ect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate

attention to: developing students’ conceptual understanding; procedural skill and �uency; and engaging applications.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for rigor.The materials develop conceptual understanding of key mathematical concepts, give attentionthroughout the year to procedural skill and �uency, spend su�cient time working with engagingapplications of mathematics, and do not always treat the three aspects of rigor together or separately.

24n − 16n + 12 8n + 12

4(6n − 4n + 3) 4(2n + 3)

2(12n − 8n + 6) 2(4n + 6)

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In 6.EE.C.9 Sister Act, Practice Printable, Question 1 states, “A worker earns $17 per hour. a.Writean equation to show the relationship between the hours she works (h) and the amount she is paid(p). b. What is the independent variable? What is the dependent variable?”

In 6.RP.A.1 For Every Day, Practice Printable, Question 4 states, “To make a deep orange color,Regina mixed 8 drops of red paint and 2 drops of yellow paint. Describe the relationship betweenthe red paint and yellow paint in at least 4 di�erent ways.”

In 6.RP.A.2 Road Trip Ratios, Practice Printable, Questions 1-4 each provide a ratio and askstudents to produce two unit rates, “1) 8 cats eat 4 large cans of cat food. _ cans per cat _ cats percan.”

In 6.SP.A.1 Statistical Friends, Practice Printable, Question 1 states, “Determine whether eachquestion below is statistical or non-statistical.” In Question 9, students demonstrate conceptualunderstanding when they, “Write a statistical question that could be answered by collecting datafrom your classmates.”

INDICATOR 2B

Materials give attention throughout the year to individual standards that set an expectation for procedural skill and �uency.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forattending to the standards that set an expectation of procedural skill and �uency.

The materials develop procedural skill and �uency throughout the grade level in the Math Simulator,examples in Teacher Instruction, Cluster Intensives, domain speci�c Test Trainer Pro and the ClickerQuiz. Examples include:

In 6.NS.B.2 Which Way, the Teacher Instruction directs teachers to say, “perform long division andmake sure to line up columns.” Three di�erent example problems are provided. Steps for thedivision algorithm are shown three days in a row during the lesson. Students also see the completedalgorithm for at least 15 practice problems. 6.NS.2 is practiced in two other units and in the gameKo’s Journey.

In 6.NS.B.3 Enter the Dragon, the Teacher Instruction has the teacher walk through the steps forthe four operations, repeatedly asking, “What is the process to (add, subtract, multiply, divide)decimals?” The Math Simulator provides �ve sets of three problems for students to solve. Aftereach set, the correct answer and process is worked out for the student. There are decimalcalculations in eight other lessons.

In 6.EE.A.1 I Dream of Djinni, the Teacher Instruction supports students in procedural skills relatedto exponents. The terms base and exponent are introduced, and the teacher walks throughexamples where the base and exponent are unknown. Then, the teacher walks through evaluating anexpression that involves an exponent and requires using the order of operations.

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In 6.EE.A.2c Real Stories of the AIF (Accident Investigation Force), the teacher providesinstruction for using an expression for drag factor, a formula to convert between Farenheit andCelsius, and an expression with multiple variables. The teacher prompt states, “It’s important tosubstitute values carefully; many mathematicians put parentheses around each value to make surethey have substituted it correctly and in the right spot,” and later, “When substituting in forvariables in formulas or expressions, it’s often helpful to put the values in parentheses to help keepthem separated and to remain clear on the operations to be used on each value.”

Examples of students independently demonstrating procedural skills and �uencies include:

In 6.NS.B.2 Which Way, the Clicker Quiz contains six questions that involve long division, including�ve word problems and one problem that requires interpreting a quotient in multiple ways(remainder, fraction, decimal). In the Practice Printable, there are four problems in Question 1,“Find each quotient” and four word problems that require long division. For example, PracticePrintable Question 1a states, “ ”; Question 5 states, “The city of Vine View is building anew rectangular park for the townspeople. The park will have an area of 8,925 square yards. If thewidth of the park is to be 84 yards, how much fencing does the city need to surround the park?”

In 6.NS.B.3 Enter the Dragon, the Practice Printable contains four problems each for adding,subtracting, multiplying and dividing multi-digit decimal numbers. The Clicker Quiz contains sixproblems, one problem each for each of the four operations, and two word problems that requireusing multiple operations to solve. For example, Practice Printable, Question 2 states, “

”; Question 6 states “ ”; Question 10 states “ ”; Question 14 states“ ”.

In 6.EE.A.1 I Dream of Djinni, one question in the Clicker Quiz shows an image of a man thinking and a woman thinking and states, “ Ryan and Jane are thinking about writing thisexpression using an exponent. Who is correct?” In the Practice Printable, Question 4 states, “Fill inthe missing information for each row.” A three column table with the headings “exponential form,expanded form and standard form,” is provided.

In 6.EE.A.2c Real Stories of the AIF, Practice Printable, Question 1 states, “Complete the chart

using the formula for area of a triangle, ”; students are given a table with 5 pairs of base andheight values, and calculate the area. In Practice Printable, Question 2 states, “Evaluate eachexpression in the chart if and ”; the chart contains six expressions using thevariables.

INDICATOR 2C

Materials are designed so that teachers and students spend su�cient time working with engaging applications of the mathematics.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for beingdesigned so that teachers and students spend su�cient time working with engaging applications ofmathematics. Engaging applications include single and multi-step problems, routine and non-routine

40, 584 ÷ 76

70.64 + 0.0059 43.02 − 0.0078 48.5 ⋅ 1.604

0.5208 ÷ 6.2

76

67 7 × 7 × 7 × 7 × 7 × 7

A =

bh21

a = 2, b = 4, c = 6 d = 3

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problems, presented in a context in which mathematics is applied.

Examples of students engaging in routine application of skills and knowledge include:

In 6.RP.A.3c Stealing Home, an example states “Country music makes up 75% of Ashley’s musiccollection. If she has 33 albums that are by country artists, how many albums does she have in herentire music collection?

In 6.NS.A.1 Mr. Mung’s Ice Cream, Practice Printable, Question 6 states, “Milo bags groceries at alocal market. The plastic bags he uses are designed to hold 25 pounds. If a typical water bottle

weighs pounds, how many bottles could Milo put in a bag (assuming they all �t)?”

In 6.EE.7 The Sign of Zero, Practice Printable, Question 2 states, “The map at the right showspoints A, B, and C. Say the distance from point A to point C is three times the distance from pointA to point B, and the distance from point A to point C is 105 miles. What is the distance from pointA to point B?”

In 6.RP.A.3a Clone Wars, Practice Printable, Question 4 states, “Kennedy thinks the best orangejuice is made using 3 cups of water and 5 cups of juice concentrate. How many cups of water andjuice concentrate will she need to make 40 cups of juice? Create a table or diagram to show yourreasoning.”

Examples of students engaging in non-routine application of skills and knowledge include:

In 6.SP.B.4 & 5 Shoot for the Moon!, Practice Printable, students write a newspaper article basedon data from a survey including “a headline, graphical display, the number of observations, at leastone graphic, a description of how the survey was conducted, the measures of center includingmean, median and mode. Report all measures of variability and striking deviations.”

In 6.NS.C.7c Day by Day, the Practice Printable includes: At Wonder Toys, new employees receivea 30-day evaluation that ranks bad days and good days on a scale of -10 to 10. “Miss Brooks has anew assistant at Wonder Toys named Mary Smithson. The time has come for Mary’s 30-dayevaluation. Based on the number of bad days, Mary thinks she may lose her job. Miss Brooksexplains that, along with the number of good and bad days, she has to look at the magnitude of thegood and bad days to determine job performance. Use Mary Smithson’s evaluation to explain whatMiss Brooks is talking about and to determine whether Mary has a good evaluation or a poorevaluation.”

In 6.RP.A.2 Road Trip Ratios, Practice Printable, Question 7 states, “Pareesa bought two newaquariums, each holding exactly 200 gallons of water. One aquarium will hold only small �sh andthe other will hold large �sh. She will buy 5 small �sh for every 10 gallons of water in the aquarium.She will buy 8 large �sh for every 40 gallons of water in the aquarium. How many total �sh willParessa have? What will be the ratio of large �sh to small �sh?”

INDICATOR 2D

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The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of

rigor within the grade.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations that thethree aspects of rigor are not always treated together and are not always treated separately.

Examples of the three aspects of rigor being present independently throughout the materials include:

In 6.NS.C.5 Weather Bear, students develop conceptual understanding of the meaning of positiveand negative numbers. During Teacher Instruction, these examples are provided: “Let’s look at adi�erent example of walking forwards and backwards. What is the meaning of taking 5 stepsforward? What is the meaning of taking 2 steps backward? What is the meaning of zero in thiscase?; Now, let’s look at gaining and losing yards in football. What is the meaning of a gain of 6yards? What is the meaning of a loss of 4 yards? What is the meaning of zero in this case?”

In 6.NS.C.6c Special Intelligence, students develop procedural skill in plotting points. In thePractice Printable, Question 4, students “Plot each point on the coordinate plane, and label it with

the corresponding letter.” Students are given nine points to plot, including some with , to ensurethey have multiple opportunities to plot points on the coordinate plane.

In 6.EE.A.2c Real Stories of the AIF, students evaluate expressions at speci�c values of theirvariables that arise from formulas used in real-world problems. In the Practice Printable, Question3 states “The cost of a pass to the amusement park for 5 days or less is , where n is thenumber of days you are visiting. The cost for a pass to the amusement park for more than 5 days is

, where n is the number of days you are visiting. a) If you plan on visiting for 5 days, whatis the cost of the pass? b) What would be the cost for visiting for 6 days? c) Is it a better deal to visitfor 5 or 6 days? Explain. d) What would be the cost to visit for one week?”

Examples of multiple aspects of rigor being engaged simultaneously to develop students’ mathematicalunderstanding of a single topic/unit of study include:

In 6.G.A.1 The Lilliput Regatta, students use their conceptual understanding of area to �nd the areaof right triangles, other triangles, special quadrilaterals, and polygons in application problems bycomposing into rectangles or decomposing into triangles and other shapes. The teacher showsstudents how to decompose �gures, �nd missing dimensions, and calculate the area of each region.Students also practice procedural skills while �nding the areas of �gures throughout the lesson. Forexample, Practice Printable, Question 2 states, “What is the area of �gure ABCD, in squarecentimeters?” (�gure ABCD is a kite).

In 6.EE.B.6 Land in Lama, students use their understanding of variables to represent numbers asthey develop skill in writing equations that represent real-world problems. In the Practice Printable,Question 2 states, “David went into a �oral shop to buy his mother some �owers. Depending on

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the season, carnations cost c dollars; roses cost r dollars; and tulips cost t dollars. Vases are $12.Write an expression to represent David’s cost for 4 carnations, 5 roses, 3 tulips, and a vase.”

INDICATOR 2E

Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason

abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice

standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting the intentional development of MP1 and MP2 for students, in connection to the grade-levelcontent standards, as expected by the mathematical practice standards.

Examples of the intentional development of MP1 to meet its full intent in connection to grade-levelcontent include:

In 6.NS.C.8 The Mark of Zero, Detailed Lesson Plan, “During Immersion and Data &Computation, students receive information that initially seems vague. As they explore thestatements provided to them in conjunction with the ‘map’ (coordinate plane), they begin to seemore value in the statements, can infer more speci�c details, and consequently change course asneeded. The ‘Think-Pair-Share’ protocol aids students in making sense of the problem, as they lookfor entry points to its solution.”

CRITERION 2E - 2I

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forpractice-content connections. The materials meaningfully connect the Standards for MathematicalContent and the Standards for Mathematical Practice (MPs).

Each Detailed Lesson Plan, Lesson Plan Overview, includes one to three MPs and describes how thelesson connects to the MPs. In addition, each Detailed Lesson Plan includes a speci�c tip from JoBoaler that provides guidance about how to connect the MPs with the lesson. In the Teacher’s Guide,Protocols to Support Standards for Mathematical Practice includes, “To support the Standards forMathematical Practice, MidSchoolMath has compiled a ‘Top 10’ bank to include protocols (orinstructional moves) that teachers use to structure learning experiences to deepen the understanding ofthe SMP. Recommended protocols for each lesson are found in the Detailed Lesson Plans with teacherinstructions to implement.” The protocols are directly related to the MPs they best support.

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In 6.RP.A.3b Vacation Day, Lesson Plan Overview, Applying Standards for Mathematical Practice,“During Immersion, students use a ‘Think-Pair-Share’ protocol to determine what they need toknow and begin a solution pathway. In Data & Computation, students recognize that equivalentratios and the unit rate can give them important information about the guard’s wages. Students canuse ratio tables, double number lines, and other strategies to solve the problem, and have theopportunity to share their strategies.”


In 6.NS.C.5 Weather Bear, Detailed Lesson Plan states, “During Immersion and Data &Computation, students will recognize that a positive number, a negative number, and zero havespeci�c meanings within a context. Students will make sense of real-world quantities and theirrelationships when looking at altitudes. Students will also recognize that numbers, such as 7 and -7,are opposite values and are in opposite direction from zero on a number line.”

In 6.RP.A.1 For Every Day, Lesson Plan Overview, Applying Standards for Mathematical Practice,“During Data & Computation, students compute the quantitative ratio of two quantities,contextualize it to make meaning of a ‘real-world’ situation, then express it using ratio language.”

In 6.EE.B.7 The Sign Of Zero, Lesson Plan Overview, Applying Standards for MathematicalPractice, “During Immersion, students have the opportunity to make initial sense of what is beingasked, by talking with a partner about what was presented in the video, speci�cally a diagram that isshown a second time. The ‘Think-Pair-Share’ protocol allows students to gain a perspective otherthan their own. During Data & Computation, students receive additional quantitative informationwhose meaning must be attended to when building symbolic equations of the mathematicalrelationship. After solving the equation, students must attend fully to its meaning in the situation,as it's not the �nal answer; an additional operation must be performed to get the intended value.”

INDICATOR 2F

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in

connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting the intentional development of MP3 for students, in connection to the grade-level contentstandards, as expected by the mathematical practice standards.

The materials include 10 protocols to support Mathematical Practices. Several of these protocolsengage students in constructing arguments and analyzing the arguments of others. When they areincluded in a lesson, the materials provide directions or prompts for the teacher to support engagingstudents in MP3. Examples include:

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“Lawyer Up! (12-17 min): When a task has the classroom divided between two answers or ideas,divide students into groups of four with two attorneys on each side. Tell each attorney team toprepare a defense for their ‘case’ (≈ 4 min). Instruct students to present their argument. Eachattorney is given one minute to present their view, alternating sides (≈ 4 min). Together, theattorneys must decide which case is more defendable (≈ 1 min). Tally results of each group todetermine which case wins (≈ 1-2 min). Complete the protocol with a ‘popcorn-style’ casesummary (≈ 2-3 min).”

“Math Circles (15-28 min): Prior to class, create 5 to 7 engaging questions at grade level, place ondi�erent table-tops. For example, Why does a circle have 360 degrees and a triangle 180 degrees?Assign groups to take turns at each table to discuss concepts (≈ 3-4 min each table).”

“Quick Write (8-10 min): After showing an Immersion video, provide students with a uniqueprompt, such as: ‘I believe that the store owner should…’, or ‘The person on Mars should make thedecision to…’ and include the prompt, ‘because…’ with blank space above and below. Quick writesare excellent for new concepts (≈ 8-10 min).”

“Sketch It! (11-13 min): Tell students to draw a picture that includes both the story and mathcomponents that create a visual representation of the math concept (≈ 5-7 min). Choose twostudents with varying approaches to present their work (≈ 1 min each) to the class (viaMidSchoolMath software platform or other method) and prepare the entire class to discuss theadvantages of each model (≈ 5 min).”

The materials include examples of prompting students to construct viable arguments and critique thearguments of others.

In 6.EE.A.2c Real Stories of the AIF, Practice Printable, Question 3c, “The cost of a pass to theamusement park for 5 days or less is , where n is the number of days you are visiting. Thecost for a pass to the amusement park for more than 5 days is , where n is the number ofdays you are visiting. Is it a better deal to visit for 5 or 6 days? Explain.”

In 6.SP.B.4 & 5 Shoot for the Moon!, Practice Printable, Introduction Problem, “What could thenewspaper article look like? Be sure to include a headline, graphical display, the number ofobservations, a description of how the survey was conducted, the measures of center includingmean, median and mode. Report all measures of variability and striking deviations. Choose the mostappropriate measure of center and measure of variability and defend your choices; include a closingcomment.” In the Simulator question, “Choose the most appropriate measure of center andmeasure of variability and defend your choices.”, and in Practice Printable, Questions 2c-d states,“What is the better measure of center for this data set? Why? Which is the better measure ofvariation of this data set? Why?”

In 6.RP.A.3c Stealing Home, Practice Printable, Question 3, “Tyrell took a history test. Heanswered 21 of the 25 questions correctly. In order to get an ‘A’ on the test he needs to get at leasta 90%. Did Tyrell get an ‘A’ on his history test? Explain your reasoning.”

50 + 10n

45 + 10(n − 1)



In 6.SP.A.3 Periodontal Pockets, Practice Printable, Question 1, “All sixth graders at MadisonMiddle School were given a math and reading placement test at the beginning of the year. a) If youwanted to know on average if sixth grade students scored better on the math test or reading test,would you consider the measure of center of the data or the measure of variability of the data?Explain your reasoning. b) If you wanted to see how consistent (or similar to each other) the scoreson the respective tests were, would you focus on the measure of center of the data or the measureof variability of the data? Explain your reasoning.”

In 6.NS.C.7c Day by Day, Practice Printable, Introduction Problem, “Use Mary Smithson’sevaluation to explain what Miss Brooks is talking about and to determine whether Mary has a goodevaluation or a poor evaluation.”

The materials provide guidance for teachers on how to engage students with MP3. In several lessons,the Detailed Lesson Plan identi�es MP3 and provides prompts that support teachers in engagingstudents with MP3. Examples include:

In 6.NS.C.7d Co�ee Accounting, “In Data & Computation, students take the practice test bythemselves, then work with another student to justify their conclusions in the ‘Study Hall’ protocol.Because the order of the wording impacts the meaning of the statements, students practice alogical progression of statements. Paired students explore the truth of their partner’s conjectures,and ask rich questions and critique the reasoning of other students. The following Teacher Promptsencourage students to explain their reasoning and examine their partner’s reasoning and logic. Didyour study hall partners present a logical argument? Can you repeat what another student’s logicis? Did you notice any �aws in their logic? Can you draw a picture to explain your reasoning? Isthere another way to explain your own logic?”

In 6.NS.C.7c Day by Day, Data & Computation “includes prompts that support students indeveloping their own arguments and critiquing those of others: 2. Use the ‘Quick Write’ protocol,where students are prompted to write down ideas about whether Rob is having good days or baddays, and prompted to make a conclusion with supporting evidence. It is important that studentsare not given too much information, or prompted with guiding questions at this stage. 3. Havestudents join with two other students. Each student has 2 minutes to present their ‘Quick Write.’During which the other two students act as supervisors, and are there to provide feedback they feelwould be helpful in strengthening the conclusion. Use the following prompts with students toencourage the critique process: ‘I was confused when you ____. ‘It might be more clear if you said________. ‘Can you re-state that in a di�erent way?’"

INDICATOR 2G

Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in

connection to the grade-level content standards, as expected by the mathematical practice standards.

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The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting the intentional development of MP4 and MP5 for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.


In 6.EE.A.2c Real Stories of the AIF, Lesson Plan Overview, “MP4: Model with mathematics. OnDay 1, during the Data & Computation phase, the students will decide how fast the driver wasdriving using the ‘ ’ formula. The students will use the formula to identify the rate of speed on aspeci�c road surface.”

In 6.EE.B.6 Land in Lama, the Detailed Lesson Plan states, “MP4: Model with mathematics. InLand in Lama, students are tasked with representing the cost of the land through an expression,which is, in essence, a modeling task. Further supporting the practice, during Immersion, theproblem is relatively unstructured, requiring students to determine what they need to know, andanalyzing how the problem might be solved while making assumptions about the relationshipsbetween unknown quantities. Visual representation the students develop supports clarity ofthinking about their model and assumptions. Students re�ne their model as more information isgiven during Data & Computation. The full intent of the practice occurs as students create theirown variables and include them as part of the expression.”

In 6.G.A.2 River Rescue, the Detailed Lesson Plan states, “MP4: Model with mathematics. RiverRescue opens with a unique protocol that leads students to begin modeling with mathematics rightaway in Immersion. Students imagine a �owing river and must try to think of a way to determinethe amount of water that is �owing per second. They team in small groups, using their intuition toguide them in an early attempt to model the situation. They draw pictures and discuss ideas in anattempt to �nd an entry point into the upcoming task. In Data & Computation, students calculatethe �ow rate of the river (modeled as volume of a rectangular prism with fractional side lengths). InResolution, students revise their thinking, comparing not only their answer, but their originalconceptual ideas of how to calculate �ow rate.”


In 6.RP.A.3c Stealing Home, the Detailed Lesson Plan states, “MP5: Use appropriate toolsstrategically. During Data & Computation and Practice Printable, students discover that two partsof a percent problem are given (whole, part, or percent) and a third unknown part must bedetermined. Students can use di�erent tools that help them see that 100% splits up into parts(double number lines, tape diagrams, ratio tables, etc.).” In the Practice Printable, Question 5states, “Solve each problem below by using a table of equivalent ratios, a tape diagram, a doublenumber line or an equation. a) 75 is 15% of what number? b) What is 60% of 210? c) 120 is 30% ofwhat number? d) 160 is 20% of what number?”

30df



In 6.SP.B.4&5 Shoot for the Moon!, the Detailed Lesson Plan states, “MP5: Use appropriate toolsstrategically. In Data & Computation, students are asked "What could the newspaper article looklike?" This general question requires students to consider the tools available to them and to makepersonal choices as to how to use them. These include mathematical tools (graphs, tables,mathematical graphics, etc.) and also physical tools ( rulers, graph paper, pencils, etc.). Technologytools (computers, tablets, calculators, spreadsheets, and graphical display software) may also beconsidered.”

INDICATOR 2H

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for

students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting the intentional development of MP6 for students, in connection to the grade-level contentstandards, as expected by the mathematical practice standards.

The materials use precise and accurate terminology and de�nitions when describing mathematics, andthe materials provide instruction in how to communicate mathematical thinking using words, diagrams,and symbols. Examples include:

Each Detailed Lesson Plan provides teachers with a list of vocabulary words and de�nitions thatcorrespond to the language of the standard that is attached to the lesson; usually speci�c tocontent, but sometimes more general. For example, 6.NS.3 states “Fluently add, subtract,multiply, and divide multi-digit decimals using the standard algorithm for each operation.” Thevocabulary provided to the teacher in 6.NS.B.3, Enter the Dragon is, “Decimal number: A numberthat can show place value less than 1; represents values such as tenths, hundredths, thousandths,etc.”

The vocabulary provided for the teacher is highlighted in red in the student materials on thePractice Printable.

Each Detailed Lesson Plan prompts teachers to “Look for opportunities to clarify vocabulary” whilestudents work on the Immersion problem which includes, “As students explain their reasoning toyou and to classmates, look for opportunities to clarify their vocabulary. Allow students to ‘get theiridea out’ using their own language but when possible, make clarifying statements using precisevocabulary to say the same thing. This allows students to hear the vocabulary in context, which isamong the strongest methods for learning vocabulary.”

Each Detailed Lesson Plan includes this reminder, “Vocabulary Protocols: In your math classroom,make a Word Wall to hang and refer to vocabulary words throughout the lesson. As a whole-classexercise, create a visual representation and de�nition once students have had time to use their newwords throughout a lesson. In the Practice Printable, remind students that key vocabulary wordsare highlighted. De�nitions are available at the upper right in their student account. In the Student

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Re�ection, the rubric lists the key vocabulary words for the lesson. Students are required to usethese vocabulary words to explain, in narrative form, the math experienced in this lesson. During‘Gallery Walks,’ vocabulary can be a focus of the ‘I Wonder..., I Notice…’ protocol.”

Each lesson includes student re�ection. Students are provided with a list of vocabulary words fromthe lesson to help them include appropriate math vocabulary in the re�ection. The rubric for there�ection includes, “I clearly described how the math is used in the story and used appropriatemath vocabulary.”

Vocabulary for students is provided in the Glossary in the student workbook. “This glossary containsterms and de�nitions used in MidSchoolMath Comprehensive Curriculum, including 5th to 8thgrades.”

The Teacher Instruction portion of each detailed lesson plan begins with, “Here are examples ofstatements you might make to the class:” which often, though not always, includes the vocabularywith a brief de�nition or used in context. For example, the vocabulary provided for 6.RP.A.3c,Stealing Home is “Part”, “Whole”, and “Percent.” The sample statements provided are, “Rememberthere are always two parts of the percent problem given from the part, whole, or percent;Remember that the percent of a quantity is per 100; In Stealing Home, we had to help �nd thenumber of runs Jackie Robinson would score during the 1948 season; We can convert the percent

to a rate per 100, so 52% is ; A ratio table can be created using the percent as a rate of 100, andthen other helpful equivalent ratios can be identi�ed.”

INDICATOR 2I

Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in

repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forsupporting the intentional development of MP7 and MP8 for students, in connection to the grade-levelcontent standards, as expected by the mathematical practice standards.


In 6.NS.B.4 The Castle Guard, the materials state, “MP7: Look for and make use of structure. OnDay 1, during both the Immersion and Data & Computation phases, students will understand thedi�erences on how to calculate the greatest common factor and least common multiple betweentwo numbers.” Optional teacher prompts include, “What do we know about the number of daysthat each guard works? How can we use a number line as a tool to show when the guards work?Does the LCM or GCF need to be found when the guards work together again? How do we �ndthe LCM? What are the multiples of 2? What are the multiples of 4? What are the multiples of 5?What is the LCM of 2, 4, and 5? When will the guards work together again?”

10052

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In 6.RP.A.3d Sa�ron Shu�e, Lesson Plan Overview, “MP7: Look for and make use of structure.During Data & Computation, students work together to notice that ratios can be used to convert ameasurement from one unit to another. By using ratios written in fraction form as conversionfactors, students recognize the structure of the fraction, where a common numerator anddenominator make 1 (cancel each other out).Students use this structure repeatedly to keep track ofunits during conversion and to cancel them out as needed to end with the appropriate unit.”

In 6.G.A.3 Fuel Factor, the Detailed Lesson Plan states, “MP7: Look for and make use of structure.During Immersion and Data & Computation, students will recognize that endpoints for horizontalline segments have the same y-coordinate, and the length of such segments can be found bysubtracting the x-coordinates because the grid structure shows the lengths to be the distancebetween x-coordinates. Similarly, endpoints for vertical line segments have the same x-coordinate,and the length of such segments can be found by subtracting the y-coordinates because the gridstructure shows the lengths to be the distance between y-coordinates. Students are able to makeuse of these structures for the practical purpose of determining the length of the race course.” Theprompts provided for teachers include: “What is the direction for the course? What do you noticeabout the coordinates of the endpoints of horizontal line segments? What do you notice about thecoordinates of the endpoints of vertical line segments? Imagine the coordinates on a grid. Howmight you �nd the length of a line segment connecting them? Since there is no grid, how mightyou �nd the length of the line segment anyway? What is the total distance of the course? For howmany megaspans do the sisters think the ship will last?”


In 6.NS.C.6b Treasure Trail, the Detailed Lesson Plan states, “MP8: Look for and make use ofstructure. During Data & Computation, students have opportunity to recognize the coordinateplane as a structure that aids them in seeing a repeated pattern for coordinates that are re�ected.During Resolution, teacher prompts during the ‘Number Talk’ ask students to identify the constantpattern of how coordinates are a�ected by re�ection and to explain how the grid lines in thecoordinate plane aided them in realizing the general rule.”

In 6.EE.A.1 I Dream of Djinni, the Detailed Lesson Plan states, “MP8: Look for and expressregularity in repeated reasoning. On Day 1, during the Data & Computation phase, students will tryto determine which prize (option 1 or 2) will have the greatest number value. The students willcreate a chart to write down the information they already know about options 1 & 2 and then movetowards using repeated multiplication to trigger other tools or strategies that will produce thecorrect solution.”

In 6.G.A.1 The Lilliput Regatta, Lesson Plan Overview, “MP8: Look for and express regularity inrepeated reasoning. During Data & Computation and Practice Printable, as students repeatedlycalculate the area for each geometrical shape, they are able to see that they can manipulate theshape to �nd faster and easier ways to determine the area. They can repeatedly cut and re-form the



shape into parts, or can double its size and divide by two, or use other methods to determine thearea. The regularity in the repeated reasoning is that the area is always the same, no matter howthey manipulate the shape so long as its size is not changed.”

Gateway ThreeUsabilityMeets ExpectationsThe materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forUsability. The materials meet expectations for Criterion 1, Teacher Supports, for Criterion 2,Assessment, and for Criterion 3, Student Supports.

INDICATOR 3A

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials,

with speci�c attention to engaging students in order to guide their mathematical development.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding teacher guidance with useful annotations and suggestions for how to enact the studentmaterials and ancillary materials, with speci�c attention to engaging students in order to guide theirmathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student andancillary materials.

CRITERION 3A - 3F

The program includes opportunities for teachers to e�ectively plan and utilize materials with integrity and to further develop their own

understanding of the content.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for TeacherSupports. The materials: provide teacher guidance with useful annotations and suggestions for enactingthe materials, contain adult-level explanations and examples of the more complex grade-level conceptsand concepts beyond the current grade so that teachers can improve their own knowledge of thesubject, include standards correlation information that explains the role of the standards in the contextof the overall series, provide explanations of the instructional approaches of the program andidenti�cation of the research-based strategies, and provide a comprehensive list of supplies needed tosupport instructional activities.

9/9

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A Curriculum Overview provides a chart of the components and description for the lessons,assessments, and Domain Review. The curriculum components are described brie�y in theOverview section.

A Practical Approach to Using Assessments, Rubrics & Scoring Guidelines helps the teacherunderstand rubrics for the assessments.

In the Teacher Guide, there is instruction on planning a lesson with a sample sequence for lessonsand assessments. The materials provide pacing for the year.

In the Teacher Guide, the instructional protocols used throughout the series are described andconnected to the Mathematical Practices they support.

In the Detailed Lesson Plan, there is a section to help support Diverse Learners with a chart ofAccommodations, Modi�cations, and Extensions, as well as Language Routines.

Common Misconceptions are listed in each Detailed Lesson Plan.

Teachers are given suggestions for vocabulary incorporation such as, “In your math classroom, makea Word Wall to hang and refer to vocabulary words throughout the lesson. As a whole-classexercise, create a visual representation and de�nition once students have had time to use their newwords throughout a lesson.”

Guidance is given to teachers for applying and reinforcing math practices in the Teacher Guide andin Detailed Lesson Plans. For example, MP8: “This practice is reinforced by having the studentswatch a complimentary video in which Jo Boaler has students modeling how to look for and identifypatterns in real-life scenarios.” Guidance shared directly from Jo Boaler states, “Students needtime and space to develop their capacity to ‘look for and express regularity in repeated reasoning.’When you provide tasks that are speci�c to supporting MP8, explicitly tell students that it’s ok toslow down, and to think deeply.” Several “tips” to address the MP are also shared.

“Detailed Lesson Plans provide a step-by-step guide with speci�c learning objectives for the mathstandard, lesson summary, prerequisite standards, vocabulary and vocabulary protocols, applyingStandards for Mathematical Practice, Jo Boaler's SMP Tips, cluster connection, commonmisconceptions, instruction at a glance, and day-by-day teaching instructions with time allotments.Also included are suggestions for di�erentiation, and instructional moves as well as tips for theEnglish Language Learner student.”

Materials include su�cient and useful annotations and suggestions that are presented within thecontext of the speci�c learning objectives. Throughout each lesson’s Detailed Lesson Plan, there isnarrative information to assist the teacher in presenting student material throughout all phases.Examples include:



6.RP.A.2 Road Trip Ratios, Common Misconceptions: “Students may use additive reasoning versusmultiplicative reasoning to scale or simplify ratios. Encourage students to draw visuals to representthe ratios to concretely see the multiplicative reasoning.”

6.SP.A.2 Build a Better Forest, Cluster Connection: “This activity connects 6.SP.A and 6.SP.B asstudents calculate simple variation calculations, such as range (referred to here as ‘spread’).”

6.NS.C.6c Special Intelligence, Teacher Instruction: “Here are some examples you might make tothe class. Before plotting any points on the coordinate plane, review the scale for each axis. Theinterval may or may not be one and may or may not be the same for each axis; Remember thatwhen plotting on a coordinate plane, we �rst move horizontally and then vertically; In SpecialIntelligence, we plotted points on a coordinate plane that had a scale of 6 rather than 1. The largerscale allowed for the larger coordinate values to �t on the image of the map.”

6.EE.C.9 Sister Act, Part 3 Resolution: “1. Play Resolution video to the whole class, and have thestudents compare their solutions as they watch. 2. After the video, prompt students with thefollowing questions: What did you do that was the same? What was di�erent? What strategy doyou think was more e�cient to �nd the equation? Why? Students may respond aloud or in ajournal.”

INDICATOR 3B

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the

current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forcontaining adult-level explanations and examples of the more complex grade/course-level concepts andconcepts beyond the current course so that teachers can improve their own knowledge of the subject.

Under the Resources Tab, there is a section dedicated to Adult-Level Resources. These contain adult-level explanations including examples of the more complex grade/course-level concepts so that teacherscan improve their own knowledge of the subject. There are also professional articles provided on topicssuch as mathematical growth mindset, cultural diversity in math, and mathematical language routines.

The Teacher Guide contains a page at the beginning of each cluster section titled, “Cluster Refresherfor the Teacher - Adult Level Explanation”. This provides a page of basic background information for theteacher including strategies to develop understanding. For example,

“6.EE.B develops an understanding of the relationship between an equation and the arithmeticprocess. The algebraic approach becomes a more e�cient path to the solution for more complexproblems. By seeing the relationship of inverse operations, we can use an algebraic approach tosolving problems rather than work backward arithmetically. We build an understanding of solvingreal-world and mathematical problems by writing and solving equations. ... These number line

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diagrams provide information such as which numbers are part of the solution through the inclusiveclosed dot and the exclusive open circle. This visual reinforces an understanding of the number lineand the possible in�nite answers that make the inequality true.”

The Adult-Level Explanations booklet under the Resources tab includes a progression through eachdomain from Grade 5 through High School. The last section is Beyond Grade 8, which explains how themiddle grades learning connects to high school standards. For example: Beyond Grade 8: Expressions &Equations:

“Beginning in the early years of school, expressions are an integral part of the math curriculum. Anexpression is a statement that can include numbers, variables, operations, exponents and radicals, ora multitude of combinations of such. In the early years, arithmetic expressions were explored andmastered. In the middle grades, algebraic expressions are introduced, �rst with whole numbers,then whole numbers with exponents, and then integers with exponents. Following the practice withthese, radical and trigonometric expressions are introduced and explored. ... The concepts offunctions are vast and will be studied throughout high school and beyond. Having a strongfoundation in properties of operations, writing and manipulating expressions, solving for equationswith one or more variables, and understanding what answers are part of the solution(s) will allow fordeeper understanding of functions and math beyond middle school.”

INDICATOR 3C

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forincluding standards correlation information that explains the role of the standards in the context of theoverall series.

Correlation information is present for the mathematics standards addressed throughout the gradelevel/series.

Each course in this series includes a document called Planning the Year that provides the standardsand pacing for each lesson.

There are standards correlations in the Scope and Sequence Chart that lists each Lesson, DomainReview, and Major Cluster Lessons throughout a year.

Each lesson is designed to address a single standard.

Explanations of the role of the speci�c grade-level/course-level mathematics are present in the contextof the series.

The Teacher Guide contains a page at the beginning of each cluster section titled “Role ofMathematics” which clearly identi�es the grade-level clusters and standards within a domain anddescribes the intent of the cluster. The Cluster Role Across Grade Levels describes the grade-level

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content in context of the domain progression from when the initial related skills were introduced tohow the skills progress through high school. For example, “The 6.EE.A cluster involves applying andextending previous understandings of arithmetic to algebraic expressions. Students write andevaluate numerical and algebraic expressions, some of which involve whole-number exponents. Thebasic skills for this understanding begin in Grade 3, where students �uently multiply and dividewithin 100, using strategies such as the relationship between multiplication and division(3.OA.C.7). In Grade 4, students gain familiarity with factors and multiples, recognizing that awhole number is a multiple of each of its factors (4.OA.B.4). In Grade 5, students explain patternsin the number of zeros of the product when multiplying a number by powers of 10, and explainpatterns in the placement of the decimal point when a decimal is multiplied or divided by a power of10 (5.NBT.A.2). In Grade 6, students further apply skills in this cluster as they transition to workingwith equations and inequalities in 6.EE.B. In Grade 8, students extend their knowledge ofexponents in numerical expressions when they create equivalent expressions when working withinteger exponents (8.EE.A.1) and while performing operations with numbers expressed in scienti�cnotation (8.EE.A.4). In Algebra these will prove to be essential when students work withpolynomials, understanding that they form a system analogous to the integers (HSA.APR.A.1), andwhen they begin work with logarithms (HSF.BF.B.5).”

The Detailed Lesson Plan for each lesson lists the Prerequisite Standards required for students tobe successful in the lesson. For example, in 6.NS.A.1 Mr. Mung’s Ice Cream, the PrerequisiteStandards listed are 3.OA.B.6 and 5.NF.B.7.

The Detailed Lesson Plan for each lesson includes Cluster Connections that identify connectionsbetween clusters and coherence across grade levels. For example, in 6.RP.A.1 For Every Day,Cross-Cluster Connection, “This activity connects 6.RP to 7.RP.A and 8.EE.B, as unit rate is thebasis for work involving constant of proportionality and slope of linear equations.”

INDICATOR 3D

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for

how they can help support student progress and achievement.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide some strategies forinforming all stakeholders, including students, parents, or caregivers about the program, and thematerials provide minimal suggestions for how they can help support student progress and achievement.

In the Resources, the Letter to Parents addresses the structure and philosophy of the series as a wholebut does not provide speci�c curricular support. Suggestions for how parents or caregivers can helpsupport student progress and achievement are included in the Parent Letter: “We invite you tocontribute to your student’s learning by facilitating discussions at home about what they are learning inmath class. Ask your student to log in to their MidSchoolMath account and show you their math work.Try your best to listen and not be critique. Expect that math problems and solutions may be presenteddi�erently than how you were taught.” The program does not provide any other suggestions for howstakeholders can help support student progress and achievement throughout the remainder of thematerials.



INDICATOR 3E

Materials provide explanations of the instructional approaches of the program and identi�cation of the research-based strategies.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding explanations of the instructional approaches of the program and identi�cation of theresearch-based strategies.

Materials explain the instructional approaches of the program.

The Curriculum Overview in the Teacher's Guide states that the curriculum is designed to “STOPTHE DROP.” The materials state, “Core Curriculum by MidSchoolMath is developed to �x thisproblem through a fundamentally di�erent approach... MidSchoolMath emphasizes structured,conceptual learning to prepare students for Algebra I... MidSchoolMath is speci�cally designed toaddress the ‘The Mid School Math Cli�’.”

In the Teacher Guide, the overview on Scoring Guidelines states, “In coordination with Dr. JoBoaler, MidSchoolMath has developed an approach to using rubrics and scoring with an emphasison making them useful and practical for helping teachers support student learning. This is incontrast to the use of scoring guidelines for the primary purpose of giving grades.”

In the Letter to the Parent, the instructional approaches are summarized, “MidSchoolMath strivesto help students see that math is relevant and holds value and meaning in the world. The curriculumis designed not only to enhance student engagement, but also to provide stronger visualrepresentation of concepts with focus on logic structures and mathematical thinking for long-termcomprehension. ... Peer Teaching: Students learning from other students is a powerful mechanism,wherein both the ‘teachers’ and the ‘learners’' receive learning bene�ts.”

Materials reference relevant research sources:

“Hattie, J. (2017) Visible Learning

Cooney, J.B., Laidlaw, J. (2019) A curriculum structure with potential for higher than average gainsin middle school math

Tomlinson (2003) Di�erentiated Instruction

Dweck (2016) Growth Mindset

Carrier & Pashler (1992) The in�uence of retrieval on retention: the testing e�ect

Boaler, J. (2016) Mathematical MindSets

Rohrer, D., & Pashler, H. (2007) Increasing retention without increasing study time

Kibble, J (2017) Best practices in summative assessment

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Laidlaw, J. (2019) Ongoing research in simulators and contextualized math

Lave, J. (1988) Cognition in practice: Mind, mathematics and culture in everyday life

Schmidt and Houang (2005) Lack of focus in mathematics curriculum: symptom or cause.”

Materials include research-based strategies. Examples include:

“Detailed Lesson Plans (Research Indicator: Teacher pedagogy and e�cacy remains the highestoverall factor impacting student achievement. Multiple instructional models show greater gainsthan ‘stand and deliver’.)

The Math Simulator (Research Indicator: On randomized controlled trials, The Math SimulatorTMelicited high e�ect sizes for achievement gains across educational interventions. Contextuallearning and Productive Failure are likely in�uences contributing to the large achievement gains.)

Teacher Instruction (Research Indicator: Clarity of teacher instruction shows a large e�ect onstudent achievement.)

Practice Printable (Research Indicator: Di�erentiation of instruction leads to higher e�ect sizescompared to full-time ‘whole-group’ instruction. Varied instructional approaches support a growthmindset, an indicator for student success.)”

INDICATOR 3F

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding a comprehensive list of supplies needed to support instructional activities.

The Teacher Guide includes Planning the Year, Comprehensive Supply List which provides a supply listof both required and recommended supplies for the grade. For example: “Required: Markers, Chart,Paper, Colored Pencils, Dry-erase Markers, Graph Paper, Ruler, Protractor; Recommended: Individualwhite boards/laminated alternative, Calculator, Algebra tiles.”

Each Detailed Lesson Plan includes a Materials List for each component of the lesson. For example in6.NS.B.3 Enter the Dragon:

“Immersion: Materials - Enter the Dragon Immersion video; Poster paper/butcher paper;Markers/colored pencils

Data & Computation: Materials - Copies of Enter the Dragon Data Artifact, one per pair

Resolution: Materials - Enter the Dragon Resolution video

Math Simulator: Materials - Enter the Dragon Simulation Trainer; Student Devices; Paper andPencil; Student Headphones

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Practice Printable: Materials - Copies of Enter the Dragon Practice Printable, 1 per student

Student Re�ection: Materials - Copies of Student Re�ection rubric, 1 per student; White Paper;Colored Pencils; Sticky Notes

Clicker Quiz: Materials - Enter the Dragon Clicker Quiz; Student Devices; Paper and Pencil”

INDICATOR 3I

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations for havingassessment information included in the materials to indicate which standards are assessed. The materialsconsistently identify the standards and Mathematical Practices addressed by formal assessments.

In the Teacher Guide, Curriculum Components lists several assessments: Clicker Quiz, Test TrainerPro, and the summative Milestone Assessment. Each cluster has a Pre-assessment and a Post-assessment (Milestone Assessment) which clearly identi�es the standard(s) being assessed. Thestandard is part of the title, for example, “Milestone Post-Assessment 6.NS.A.”; individual tasksand items are not identi�ed on the actual assessment. However, each problem is identi�ed with thestandard being assessed in the teacher answer key.

Standards are identi�ed accurately and are from the appropriate grade level.

Assessment problems are presented in the same order as the lessons. They are sequential accordingto Domain and Cluster headings.

The Milestone Assessments include a chart that aligns Mathematical Practices to each question onthe assessment, including identifying if the assessment is online, print, or both.

CRITERION 3I - 3L

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect,

interpret, and act on data about student progress towards the standards.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forAssessment. The materials: have assessment information included in the materials to indicate whichstandards are assessed, include an assessment system that provides multiple opportunities throughoutthe grade to determine students' learning and su�cient guidance to teachers for interpreting studentperformance and suggestions for follow-up, and provide assessments that include opportunities forstudents to demonstrate the full intent of grade-level standards and practices.

10/10

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The end of each lesson includes a student self-assessment rubric that has students evaluate theirunderstanding of the content standard and the mathematical practices that align with the lesson.

INDICATOR 3J

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and

su�cient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forincluding an assessment system that provides multiple opportunities throughout the grade to determinestudents' learning and su�cient guidance to teachers for interpreting student performance andsuggestions for follow-up. There is guidance provided to help interpret student performance andspeci�c suggestions for following-up.

The assessment system provides multiple opportunities to determine students' learning and su�cientguidance to teachers for interpreting student performance.

In the Teacher Guide, the Domain Curriculum Components lists two assessments: Test Trainer Pro(formative) and Milestone Assessment (summative).

“Milestone Assessment is a summative evaluation following each cluster per grade. They areautomatically graded, yielding the percentage of items answered correctly. The math items arecrafted to include items of varying di�culty.” “Please note: Milestone Assessments should notbe used to determine student growth. As summative assessments, they are not as sensitive noras accurate as the adaptive tool, Test Trainer Pro, for providing individual student data forachievement gains over time.”

“Test Trainer Pro acts as a low-stakes, formative learning tool for students to practice testingunder more relaxed and stress-free conditions. It is an adaptive tool and is designed to elicit thelargest gains in student achievement possible in the shortest period of time.”

The Teacher Guide contains a section titled “A Practical Approach to Using Assessments, Rubrics& Scoring Guidelines.” This section provides several assessment rubrics:

The MidSchoolMath Rubric and Scoring Framework aligns a percentage “raw score” with a 4-point rubric and pro�ciency levels.

The Milestone Assessment Rubric aligns a percentage “raw score” with a 4-point rubric and hassuggestions for follow-up.

The Student Self Assessment has students re�ect and identify understanding for each lessoncomponent.

An article by Jo Boaler, “Assessing Students in a Growth Mindset Paradigm with Jo Boaler”provides “recommendations for assessment and grading practices to encourage growth mindsets.”

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Each Curricular cluster contains a tab for Assessments which has a Milestone AssessmentOverview & Rubric. There is a rubric from 0 to 3 provided for the open response section of theassessment. To earn all 3 points, students must demonstrate accuracy, show work, and may onlyhave minor mistakes.

“Recommended Scoring for Milestone Assessments: A 3-point response includes the correctsolution(s) to the question and demonstrates a thorough understanding of the mathematicalconcepts and/or procedures in the task. This response: Indicates that the student hascompleted the task correctly, using mathematically sound procedures; Contains su�cient workto demonstrate a thorough understanding of the mathematical concepts and/or procedures;May contain inconsequential errors that to not detract from the correct solution(s) and thedemonstration of a thorough understanding.”

The Overview states, “All items in Milestone Assessments are at grade level and evaluate studentunderstanding of the content at the ‘cluster’ level. Milestone Assessments should only beadministered to students after all lessons are completed within the cluster, following recommendedsequence and pacing.”

The answer key for each Milestone Assessment provides examples of correct responses for eachproblem. There is a sample response for the open-ended questions.

Several of the other lesson components could be used as formative assessments or for progressmonitoring such as the Clicker Quiz.

The assessment system provides task-speci�c suggestions for following-up with students. There aresuggestions for follow-up that are generic strategies, and there are some that direct students to reviewspeci�c content.

The Milestone Assessment Rubric includes Recommendations for Follow Up. These are found inthe front matter of the Teacher Guide. They are generic to all assessments and align with the 4points of the rubric:

“Review and correct any mistakes that were made. Participate in reteaching session led byteacher.

Review and correct any mistakes that were made. Identify common mistakes and create a ‘Top-3 Tips’ sheet for classmates.

Review and correct any mistakes that were made. Participate in the tutorial session.

Review and correct any mistakes that were made. Plan and host a tutorial session for theNearing Pro�cient group.”



The Milestone Assessment also includes suggestions based on which problems are missed. Theguidance directs students to review the worked example and Clicker Quiz in the lessons that alignto the missed problems and then revise the problems they missed in the assessment. This providesspeci�c feedback to review the content of the lesson.

The Student Self-Assessment provides a generic strategy for follow-up: “Recommended follow-up:When students self-identify as ‘Don’t get it!’ Or ‘Getting there!’ on an assignment, is it essentialfor teachers to attempt to provide support for these students as soon as possible. Additionally, it ishelpful for teachers to use scoring on Practice Printables and Clicker Quizzes to gauge studentcomprehension. Use the general scoring guidelines to determine approximate pro�ciency. It ishighly recommended that all assignments may be revised by students, even those which arescored.”

The Student Self-Assessment provides suggestions based on where the students rate themselves.Students are directed to review speci�c parts of the lesson to reinforce the parts they do not feelsuccessful with. There are also more generic strategies suggested that go across lessons and gradelevels.

The materials state that “Test Trainer Pro automates assessment and recommendations for follow-up under the score. As an assessment, Test Trainer Pro is the most speci�c, and most accuratemeasure available in MidSchoolMath to determine how students are performing in terms of gradeand domain level performance.” A teacher can view the Test Trainer Pro question bank; however,there is no way to review the speci�c follow-up recommendations provided since they are adaptedto each student.

Exit Ticket results are sometimes used to suggest grouping for instructional activities the followingday.

INDICATOR 3K

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across

the series.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. Assessments include opportunities for students todemonstrate the full intent of grade-level standards and the mathematical practices across the series.

Assessments are speci�c to each standard, so there is opportunity for students to demonstrate tothe full intent of grade-level standards.

Considering both formative and summative assessments, there are a variety of item types o�eredincluding Exit Tickets, Clicker Quizzes, Test Trainer Pro, Lesson Re�ection, Self-Re�ection, andMilestone Assessments.

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Most assessments are online and multiple choice in format, though there is a print option formilestone assessments that includes open response.

Students have the opportunity to demonstrate the full intent of the practices in assessments;practices are aligned in Milestone assessments and addressed in the student self-assessments foreach lesson.

INDICATOR 3L

Assessments o�er accommodations that allow students to demonstrate their knowledge and skills without changing the content of the

assessment.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide few accommodationsfor assessments that allow students to demonstrate their knowledge and skills without changing thecontent of the assessment.

For Milestone Post Assessments, the materials state, “Guidance for follow-up is provided in themilestone rubric. It is highly recommended that even Milestone Post Assessments may be revisedby students to achieve a higher score.”

The Clicker Quizzes sometimes provide speci�c suggestions such as, “Provide students with alaminated number line, and fraction tiles.” or “Allow students to use vocabulary cards.”

In the Teacher Guide, “Assessing Students in a Growth Mindset Paradigm with Jo Boaler” suggests,“If a grade is required and there is no additional time available due to school schedule constraints, Irecommend having a conversation with that student to negotiate the grade, with the studentindicating what they have learned, while collaborating on next steps to make progress on un�nishedlearning.” The article also states, “Current assessment practices can undermine the growth mindsetmessages students receive in other areas of the teaching and learning process. For example, ateacher may allow students to revise work to encourage a growth mindset during a low-stakesassignment, yet when it comes to a test, no revision is allowed.”

Test Trainer Pro is used for Progress Monitoring. “Test Trainer Pro automatically adapts to studentability level as students move through questions. Instruct students to work in a lower grade level orCore Skills (Grades 1-4) as needed or in a higher grade level or Algebra I as needed.” “Test TrainerPro meets students where they are and works alongside challenging grade level content. Studentshave the opportunity to practice items needed to complete learning, while the emphasis remainsfocused on mastering the current grade level.”

CRITERION 3M - 3V

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

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INDICATOR 3M

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning

grade-level/series mathematics.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding strategies and supports for students in special populations to support their regular and activeparticipation in learning grade-level/series mathematics.

Materials regularly provide strategies, supports, and resources for students in special populations to helpthem access grade-level mathematics. In each Detailed Lesson Plan, Supporting Diverse Learners,there is a chart titled Accommodations, Modi�cations, and Extensions for English Learners (EL) andSpecial Populations that provides accommodations for each component of the lesson. Many of theseare generic, but some are speci�c to the content of the lesson. For example, the components of6.EE.A.3, Provision Problem, include:

The Math Simulator Immersion: “Reinforce lesson vocabulary and ensure students understand themeaning and function of each word.”

The Math Simulator Data & Computation: “Create vocabulary �ash cards with each measure ofcenter or variability with its de�nition, how to �nd it, and an example..”

Simulation Trainer: “Pair students to allow for peer teaching and support. Allow students to usevocabulary �ash cards.”

Practice Printable: “Upon completion of the �rst page (Procedure #1), consider following the ExitTicket Di�erentiation Plan. Allow students to use vocabulary �ash cards and calculators. Considerdecoding the word problems together, circling the important numbers, and identifying importantwords.” The Practice Printable also has interactive buttons that allow students to complete workonline through draw and text tools as well as a work pad that includes an opportunity to chat withthe teacher.

Student Re�ection: “Pair students to allow for peer teaching and support.”

INDICATOR 3N

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forStudent Supports. The materials provide: strategies and supports for students in special populations tosupport their regular and active participation in learning grade-level mathematics, extensions and/oropportunities for students to engage with grade-level mathematics at higher levels of complexity,strategies and supports for students who read, write, and/or speak in a language other than English toregularly participate in learning grade-level mathematics, and manipulatives, both virtual and physical,that are accurate representations of the mathematical objects they represent and, when appropriate,are connected to written methods.

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Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of

complexity.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding extensions and/or opportunities for students to engage with grade-level mathematics athigher levels of complexity.

Materials provide multiple opportunities for advanced students to investigate the grade-level content ata higher level of complexity. The Exit Ticket in each lesson provides a di�erentiation plan that includesextension. While some strategies are the same across lessons, there are a variety of tasks o�ered.Examples include:

6.RP.A.3 Vacation Day Trails, “Bring in and distribute multiple local grocery store ads, and givestudents a shopping list of common items likely to be found in those ads. Tell students they eachhave $200 to spend on groceries. The goal is to pay the least for the most groceries. (They willjustify their spending by calculating unit prices.)”

6.RP.A.2 Road Trip Ratios, “Research the distance to travel from your cities to other cities.Estimate the number of hours that the trip would take. Then �nd the unit rate to get to each city.”

6.G.A.2 River Rescue, “Have students create their own shipping boxes that are right rectangularprisms. Find the volume of each box.”

In each Detailed Lesson Plan under Supporting Diverse Learners, there is a chart titledAccommodations, Modi�cations and Extensions for English Learners (EL) and Special Populations thatprovides extensions for each component of the lesson. Many of these are generic, but some are speci�cto the content of the lesson. For example, the components of 6.SP.A.3 Periodontal Pockets include:

The Math Simulator Data & Computation: “Task the students with answering this follow upquestion: ‘The mean of Mr. Novak’s pockets is 3.2. If they measure them again after a month, andthe mean is now 3.5, describe what happened with the data. What could be a possible data set nowto have a mean of 3.4?’”

Practice Printable: “Upon completion of the �rst page (Procedure #1), consider following the ExitTicket Di�erentiation Plan. Task the students with comparing measures of center and variability of2 similar data sets. They must explain the similarities and di�erences in each of the measures ofcenter and variability.”

Clicker Quiz: “Task students with writing and solving their own ‘clicker quiz’ question.”

Extensions are optional; there are no instances of advanced students doing more assignments thantheir classmates.

INDICATOR 3O

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Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning

with opportunities for students to monitor their learning.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide opportunities forvaried approaches to learning tasks over time and variety in how students are expected to demonstratetheir learning with opportunities for students to monitor their learning.

Many of the protocols used throughout the materials provide multi-modal opportunities for students toshare their thinking such as Sketch It, I Wonder I Notice, Gallery Walk, Lawyer Up!, and Make Up YourOwn. The Math Simulator Immersion Video that introduces each lesson provides a large variety ofsituations and “artifacts” for students to investigate. Within the components of the lesson, studentshave the opportunity to work online using Clicker Quizzes and the Simulation Trainer. They also havethe option to work online or use paper/pencil with the artifacts during Data & Computation andPractice Printables.

The Math Simulator process engages students with problem solving and interacting with each other tostart each lesson. Examples include:

6.RP.A.1 For Every Day, “What are the rest of the lyrics? During For Every Day, Delta TeamGeologist Kim O’Hara is on Mars at the home base, and she is rationing her food supply until herteam returns from their supply mission. Aside from determining how much of each item she canhave per day, she decides to write a rap song, to help her remember the quantities so she doesn’tovereat. The data provided is O’Hara’s notes: a reminder that she has to ration for 80 days, herfood inventory, and the �rst few lyrics of the song which begins with the phrase: For Every Day.” Inthe Detailed Lesson Plan, Day 1 Immersion, students use the QuickWrite protocol to brainstorm,“What do we need to know?”

6.SP.A.1 Statistical Friends, “Which questions are statistical questions? During Statistical Friends,Ayla has an upcoming quiz and is having trouble understanding what types of questions arestatistical. Her friend David steps in to help and creates a list of questions to help Ayla learn thedi�erence between statistical and non-statistical questions. The data provided is the page fromDavid’s notebook with ten sample questions.” In the Detailed Lesson Plan in Day 1 in Immersionand Data & Computation, “students analyze the questions given and make plausible arguments asto why they are either statistical or non-statistical. Students will justify their conclusions with asupporting logical statement while other students have the opportunity to present opposingarguments.”

In the Teacher Guide, under Curriculum Components & Research Indicators, the student re�ection atthe end of each lesson is described, “Student Re�ection warrants special attention as the culminatingassignment designed to trigger a ‘memory cascade’ of the math concept. Students create a visualrepresentation and supporting narrative to demonstrate their mastery of the standard.”



In the Teacher Guide, under a Practical Approach to Using Assessments, Rubrics & Scoring Guidelines,materials state, “Self-assessments are an excellent, and very quick way, for teachers to gauge studentlearning.” Students have the opportunity to self-assess throughout the lesson using a rating scale andalso on many of the exit tickets.

INDICATOR 3P

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide opportunities forteachers to use a variety of grouping strategies.

There are grouping strategies included for many of the protocols used throughout the materialssuch as Think-Pair-Share, Lawyer Up!, and Gallery Walk.

In each lesson, students complete an Exit Ticket “with the option of using the results to group thestudents for work the next day.”

The materials refer to grouping or regrouping students, but they don’t provide speci�c guidance toteachers on how to group the students. For example, “Gather necessary materials, make anynecessary student groupings, and plan any protocols that you deem helpful.”

INDICATOR 3Q

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly

participate in learning grade-level mathematics.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding strategies and supports for students who read, write, and/or speak in a language other thanEnglish to regularly participate in learning grade-level mathematics.

Materials consistently provide strategies and supports for students who read, write, and/or speak in alanguage other than English to meet or exceed grade-level standards through regular and activeparticipation in grade-level mathematics. Examples include:

In the Detailed Lesson Plan for every lesson, the same two strategies are suggested: “AccessClosed Caption and Spanish Subtitles within the video.” and “Pair students to allow for peerteaching and support. Consider allowing EL students to write the narrative in their native language,then use a digital translator to help them transcribe it into English.”

Each Detailed Lesson Plan makes a connection with one of the eight identi�ed Math LanguageRoutines (MLR), listed and described in the Teacher Guide. The MLRs include: Stronger andClearer Each Time, Collect and Display, Critique, Correct, and Clarify, Information Gap, Co-CraftQuestions and Problems, Three Reads, Compare and Connect, Discussion Supports.

All materials are available in Spanish.

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The use of protocols such as Think-Pair-Share, Quick Write, and I Wonder I Notice providesopportunities for developing skills with speaking, reading, and writing.

Vocabulary is provided at the beginning of each lesson and reinforced during practice and lessonre�ection, “In the Practice Printable, remind students that key vocabulary words are highlighted.”In the Student Re�ection, the rubric lists the key vocabulary words for the lesson. Students arerequired to use these vocabulary words to explain, in narrative form, the math experienced in thelesson.

There is teacher guidance under the Resources tab - Math Language Routines. “Principles for theDesign of Mathematics Curricula: Promoting Language and Content Development”, from theStanford University Graduate School of Education, provides background information, philosophy,four design principles, and eight math language routines with examples.

There are no strategies provided to di�erentiate the levels of student progress in languagedevelopment.

INDICATOR 3R

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide a balance of images orinformation about people, representing various demographic and physical characteristics.

The actors in the videos are from di�erent races and portray people from many ethnicities in a positive,respectful manner, and there is no demographic bias for who achieves success in the problem situationthat starts each lesson. Names in the problems include multi-cultural references such as Mario, Jalil,Misha, and Sonia. There are some colloquialisms such as “dude”. The settings span a wide rangeincluding rural, urban, international, and space.

INDICATOR 3S

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 do not provide speci�cguidance to encourage teachers to draw upon student home language to facilitate learning.

While there are supports in place to help students who read, write, and/or speak in a language otherthan English, there is no evidence of promoting home language and knowledge as an asset to engagestudents in the content material or purposefully utilizing student home language in context with thematerials.

INDICATOR 3T

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide some guidance toencourage teachers to draw upon student cultural and social backgrounds to facilitate learning.



Under the Resources tab, “Cultural Diversity in Math Moving from Shallow Notions of Culture toStudent-Centered Mathematics Tasks”, written by Toya J. Frank, Ph.D., discusses how to “maketasks more accessible for students across diverse backgrounds and cultures.” The article recognizesthat “our primary goal is to build common languages for mathematical discourse, while stillremaining aware that these diverse perspectives exist.” “It is often recommended that the solutionis to create tasks that may be more locally relevant.”

Materials for all stakeholders are available in Spanish, including video subtitles and communicationwith parents.

INDICATOR 3U

Materials provide supports for di�erent reading levels to ensure accessibility for students.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide some supports fordi�erent reading levels to ensure accessibility for students. Examples include:

In the Detailed Lesson Plan Overview, a frequent suggestion is, “In your math classroom, make aWord Wall to hang and refer to vocabulary words throughout the lesson. As a whole-class exercise,create a visual representation and de�nition once students have had time to use their new wordsthroughout a lesson.”

In the Teacher Guide under Math Language Routines, the introduction states, “A 'math languageroutine' (MLR) refers to a structured but adaptable format for amplifying, assessing, and developingstudents' language. The routines emphasize the use of language that is meaningful and purposeful,not inauthentic or simply answer-based. These routines can be adapted and incorporated acrosslessons in each unit to �t the mathematical work wherever there are productive opportunities tosupport students in using and improving their English and disciplinary language.” These routines areincluded in each lesson.

Other supports that promote accessibility for students include:

The mathematical practices support students in accessing grade-level content. In the TeacherGuide under Practices and Protocols, Jo Boaler explains each practice and provides suggestions forincorporating them to help students engage with the content. For example, MP1 Make sense andpersevere in solving problems: “1. Let students know that it is good to slow down, and take timeformulating the problem. 2. Help students understand that mistakes and struggle create braingrowth, that mistakes and struggling are central to learning and building perseverance. 3. Open upany mathematical question or task to encourage students to discuss possible methods, and toencourage opportunities for students to see and solve in di�erent ways. 4. Research has shown thatstudents are more successful when they are shown a problem before being given a method to solveit - give students questions and ask them - use your intuition, what do you think you could do? Trysome di�erent approaches. Later have students share their thinking.”



For Grades 6-8, the Major Cluster Intensive, Teacher-created Intensive includes Dan Meyer 3-ActTasks. These tasks are designed to provide multiple entry points and multiple strategies to �ndsolutions.

INDICATOR 3V

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate,

are connected to written methods.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 meet expectations forproviding manipulatives, both virtual and physical, that are accurate representations of themathematical objects they represent and, when appropriate, are connected to written methods.

Examples where manipulatives are accurate representations of mathematical objects include:

The students have access to virtual manipulatives on the Work Pad which is available online in theirSimulator Trainer, Practice Printable, Assessments, and Clicker Quiz. These include shapes, 2-colorcounters, base 10 blocks, algebra tiles, protractor, and ruler. In addition, there are di�erent styles ofdigital graph paper and dot paper on the digital whiteboard.

Throughout the materials, there are visual models with number lines, graphs, or bars, though thesecannot be manipulated.

During the Immersion and Resolution videos, items from the real world are used to representmathematical concepts.

The Teacher Guide has a section titled “Guidance on the Use of Virtual Manipulatives.” This sectionincludes sub-sections titled: Overview, General Guidance, During Lessons, Manipulative Tools, andExamples of their Use & Connecting to Written Methods. The “Examples of their Use &Connecting to Written Methods” provides teachers with guidance about how to use and makeconnections with the manipulatives.

In the Detailed Lesson Plan, Practice Printable, there is a “Manipulative Task!” where students usethe virtual tools in the Work Pad and speci�cally connect manipulatives to written methods. Forexample, in 6.NS.C.6b Treasure Trail, Manipulative Task for Digital WorkPad: “Have studentsreturn to Problem #4a-c on the Practice Printable and use the WorkPad to graph and re�ect thegiven point. Encourage students to experiment with the di�erent manipulatives provided in theWorkPad to complete the exercise. For example, students could use the grid background and theLine tool to create and label the coordinate plane. They could then use the 2-Color Counters toplot the original point. Students could then use any strategy to re�ect the point according to eachquestion prompt, labeling/indicating the re�ection method and the new coordinates using the Texttool. The physical act of re�ecting on the graph may help students to more clearly see theconnection between the type of re�ection and the corresponding change in the sign of thecoordinates.”

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INDICATOR 3W

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that

engage students in the grade-level/series standards, when applicable.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 integrate technology such asinteractive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways thatengage students in the grade-level standards, when applicable.

All aspects of the materials can be accessed digitally. Some components are only digital such as theSimulation Trainer, the Clicker Quizzes, and Test Trainer Pro.

The Math Simulator is the introduction video for each lesson which automatically guides studentsthrough the stages of Immersion, Data & Computation, and Resolution. The Simulator engagesstudents and adds real-world context to the lesson.

Every lesson includes an interactive Workpad which provides access to virtual manipulatives as wellas text and draw tools and options for virtual paper, such as graph paper and dot paper, to showwork virtually.

Teachers can assign parts of the lessons for independent work or choose Live Classroom where theyhost an electronic session with students and can share student work with the whole class.

Test Trainer Pro allows for Progress Monitoring which teachers can track by clicking on individualstudent dots to see their progress.

The digital materials do not allow for customizing or editing existing lessons for local use, butteachers can upload their own materials.

INDICATOR 3X

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other,

when applicable.

CRITERION 3W - 3Z

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for

teachers.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 include a visual design that isengaging and integrates digital technology, when applicable, with guidance for teachers. The materials:integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamicmathematics software in ways that engage students in the grade-level standards, include or referencedigital technology that provides opportunities for teachers and/or students to collaborate with eachother, have a visual design that supports students in engaging thoughtfully with the subject, and providesome teacher guidance for the use of embedded technology to support and enhance student learning.



The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 include or reference digitaltechnology that provides opportunities for teachers and/or students to collaborate with each other,when applicable.

In the Live Classroom option, there is a chat feature so students can comment with each other andre�ect on each others’ work.

There is a chat feature in each Practice Printable on the Workpad where students can send amessage directly to the teacher.

In the Math Simulator, after the Immersion video, a text box states, “What do you need to know?What are your ideas?” that allows anyone to share thinking with the whole class.

Teachers can assign the Math Simulator to students and let the system automatically guide themthrough each step, including several places where they collaborate and share their ideas within achat.

In the Progress Monitoring section, students and teachers can send messages back and forth ormessages can be sent to the whole class.

INDICATOR 3Y

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor

chaotic.

The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 have a visual design (whetherin print or digital) that supports students in engaging thoughtfully with the subject, and is neitherdistracting nor chaotic.

Graphics are visually appealing and connect with the lesson. Images are realistic and colorful; theyare not distracting, and they support student learning.

The Immersion videos are produced with various actors representing events in current and historicaltimes. Students are engaged without being distracted from the math concept being presented.

Digital artifacts are provided to help students understand the problem presented in the Immersionvideos. Each lesson includes artifacts speci�c to the simulation task; some examples are: tax bills,acre lots, receipts for merchandise, boxes.

The format is consistent from grade to grade and lesson to lesson. Every lesson has �ve sections:the Math Simulator, the Simulation Trainer, Practice Printable, Clicker Quiz, and StudentRe�ection, with the same organizational structure and clear routines.

INDICATOR 3Z

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.



The materials reviewed for Core Curriculum by MidSchoolMath Grade 6 provide some teacherguidance for the use of embedded technology to support and enhance student learning, whenapplicable.

Under the Resources tab, “Software Instructions” provides step-by-step guidance to setting up andimplementing the materials.

On the landing page of the website, the publishers post notices about upcoming changes.Currently, there is a video that shares the updates of their Simulator software and that professionaldevelopment will be o�ered on this as well.

In the Teacher Guide under Curriculum Overview, Manipulatives and the Workpad, “...the Workpadincludes a set of manipulatives that aide students in transitioning to more abstract understandings,For example, the Algebra Tiles can be used to understand abstract equations in a visual format.Base 10 Blocks allow a deeper understanding of the decimal system in symbol format.” However,there is little guidance within any lesson about using these tools.

Core Curriculum by MidSchoolMath - Sixth Grade

Documents

Transcript of Core Curriculum by MidSchoolMath - Sixth Grade