Flexible Math Manipulatives

Making the Complex ConcreteMisty Wine and Elise Carter

Training Outcomes

Become familiar with the new ARRA Math manipulativesExplore uses of manipulatives for various grade levels and learnersMake connections to the Universal Design of Learning

Concrete, Pictorial, Abstract

For all studentsScaffold instruction for students to access grade level curriculumHow to use resources in instruction to bridge students from concrete to pictorial to abstract understanding of mathematics concepts

Capture Sheet

Remember to be mindful of the UDL Principals from ‘The Wheel’.

Content Area: 

My Current Practice:  Based on what I now know, I would add…..

Teaching Strategies Technology        

Representation (process)

Engagement

Expression (Product)

Ground Rules for Manipulatives

We know manipulatives are fun but REMEMBER- these are tools not toy!

Clip art will indicate when we will be working hands on or doing a demonstration

When using the manipulatives feel free to explore and think about ways to utilize them in your classroom. (Utilize the capture sheet!)

New Math Kit Contents

Weighted Numbers with a simple two pan balanceClear View Base Ten BlocksAngle Viewer 360 Degree Protractor Elapsed Time Line Fraction circle equivalent rings (time, percent, degree, decimal, fraction)Pattern Blocks (Standard Set and Expanded Set)Geared Mini-Clocks

http://www.enasco.com/product/TB15532(X)T

Angle Viewer 360 Degree Protractor

ProtractorMath Concept – measure anglesConfusing aspects/ misconceptions –traditional protractor is procedural and students don’t know what they’re measuringUse of the tool

Which angle is bigger?

Students frequently don’t know they are measuring the distance between 2 rays.

Clearview Base Ten Blocks

Groupable base ten modelsMath Concept – number and place valueConfusing aspects/ misconceptions –(including) misconceptions with operations – composing and decomposing a ten (regrouping)Use of the tool

Primary2‐digit addition with composing (27 + 35) (explore)

Upper GradesLCM 4 and 6 on 1‐100 chart (explore)

Place Value and Number Relationships

http://www.amblesideprimary.com/ambleweb/mentalmaths/countersquare.html

Elapsed Time Line and Geared Clock

Geared Clock – minute hand moves hour hand; Elapsed Time Line Strip including full day cycle p.m./a.m.Math Concept – Establishing start time given beginning time, determining time elapsed, reading informational text Confusing aspects/ misconceptions- Telling time, Elapsed timeUse of the tool

Relate times on a geared clock to those on a time number line to the nearest five minutes, using a.m. and p.m. (Model Integrated Day)Ask: How is a clock like a number line? How is it different? Provide each pair with a Student Elapsed Time Ruler™ (to be referred to as a time number line). Review that a day lasts 24 hours and explain that the time number line represents one day. Ask: Which numbers on the time number line represent hours and which represent minutes? How do you know (e.g., The big numbers are hours because they show counting to 12 twice, which equals 24. The small numbers are minutes because 30 is half way between the two hours, just like half past.)? Remind students that the day starts and ends at 12 midnight. Provide time for pairs to determine how a.m. and p.m. are marked on the time number line (e.g., a.m. times start at midnight and go to noon and include the red numbers). Ask pairs to mark the time school ends on the time ruler with an overhead marker and explain their answer (e.g., 3:05 is the first line after the blue 3 because I count the minutes by 5. It is 3:05 p.m. because it is after noon.). Provide time for pairs to represent additional times (to the nearest five minutes including a.m. and p.m.) on a time number line, on a geared clock, and in writing. Ask: How does relating a geared clock to a time number line help you tell time?

A movie ends at 3:05. It lasted an hour and 45 minutes. When did the movie start?

Elapsed Time Line and Geared Clock

Fraction Circle Equivalence Rings-time, percent, degree, decimal, fraction

Used with fraction circlesMath Concept - equivalentsConfusing aspects/ misconceptions –relating the whole to different parts of a wholeUse of the tool

Pattern Blocks: Expanded Set

Four new blocks that expand the set of pattern blocks to tenMath Concept – K-2 geometry concepts (composing and decomposing shapes in K-2); upper grades: geometry (congruence, area, perimeter), equivalent fractionsConfusing aspects/ misconceptions (upper grades) – spatial relationships between fractional parts, a whole must be defined – (no fixed whole)Use of the tool

Grade1 Marking Period 4 W5

Build composite rectangles using pattern blocksReview the defining attributes of a rectangle. Provide students time to construct rectangles from any combination of the ten pattern blocks. Conduct a Gallery Walk of students’ composite rectangles. Discuss: Which shapes can be composed to make a rectangle? Ask pairs to begin with a pink double hexagon and use any combination of the other nine types of pattern blocks to build a rectangle. While students complete the task, ask: How do you decide which pattern blocks to use? What is challenging about this task? What do you need to know about rectangles to complete this task? Conduct a Gallery Walk of students’ composite rectangles. Ask: How does rethinking about the attributes that define a rectangle help you build an original rectangle from smaller shapes?

Check for Student Understanding: Note the extent to which each student is able to build composite rectangles.

Composing and Decomposing Shapes

Composing and Decomposing Shapes

Equivalent Fractions

With traditional pattern block set (excluding square and tan parallelogram), the fractional parts were limited to halves, thirds, sixths.

Ask: What fractional relationships can be represented with the expanded set of pattern blocks?

(halves, thirds, fourths, sixths, eights, twelfths, twenty-fourths)

Math Monster!

Using the online pattern blocks, create a monster

that has the value of

327

100

10

1http://nlvm.usu.edu/en/nav/frames_asid_169_g_1_t_2.html?open=activities

Expressions with Parenthesis

Concept 5th Grade Unit 5 Write an expression using grouping symbols to find how many sides 6 triangles and 3 hexagons have.

(6 x 3) + (3 x 6)

Weighted Numbers

3 dimensional weighted numeralsMath Concept – balance/equal sign, equality/inequalityConfusing aspects/ misconceptions –meaning of equal, not equal, greater than, less than sign(s)Use of the tool

Conclude Training

ClosureWrap up/QuestionsEvaluation http://montgomeryschoolsmd.org/departments/hiat/training/collab_cycle.shtmVirtual Math Manipulatives

http://nlvm.usu.edu/en/nav/vlibrary.html