Manipulatives Can Help Adults Learn Math Too Marcia Torgrude K-12 Math Specialist

Number Sense “Being able to handle numbers comfortably and competently is important to adults as parents, workers and community members. This competence relies upon having developed a kind of "number sense" about whole numbers, money, fractions, decimals, and percentages. Number sense includes calculation skills with numbers as well as a sense of number and operation and an ability to appropriately use estimation, mental math, computation, calculators or other tools.” The Massachusetts Mathematics Curriculum Framework

Outcomes Mental Math – for daily life skills Using manipulatives at any age to gain an understanding of numbers Multiplication/Division strategies Develop Fraction sense Visualize decimals for understanding Build Algebraic understanding hands-on

Mental Math If I earn $415 per week. How much will I earn in 20 weeks? No paper or pencil – how could we solve this mentally? Estimation Breaking numbers apart Compensation

Manipulatives for Multiplication Base ten blocks Grid/Array model Compare to traditional algorithm What are your thoughts?

Manipulatives for Division Grid Friendly number or partial quotient division Compare to traditional algorithm What are your thoughts? Why is this important for adult learners?

Working with Fractions Parts of a whole – Pattern Blocks Hands on Patch Tool – Illuminations - D=27 D=27 – Cuisinaire Rods

Working with Fractions Equivalent Fractions – px?id=18 px?id=18

Working with Fractions Adding Fractions – Pattern Blocks – Cuisinaire rods

Working with Fractions Making Sense of Multiplying Fractions – You have two thirds of an enormous brownie and decide to eat one fourth of the two thirds. How much of the brownie are you eating? Making Sense of Dividing fractions – I have 3 ½ pounds of hamburger. I want to make quarter pound burgers. How many can I make?

Working with Decimals Base ten blocks to build decimal number sense Graph paper and decimals

Working with Integers Building understanding of positive and negative numbers Adding and Subtracting positive and negative Use of Charge Model Use of the linear model

Algebraic Equations Algebra Tiles to develop an understanding of algebraic expressions and equations Adding/Subtracting Multiplying Using the Array or Grid model Connecting to the traditional algorithms

Working with Algebra Tiles Expressions Build 3x +2 + (-4x) +(-5) Simplify this. Now try: 5x-9-2-3x

Working with Algebra Tiles Addition/Subtraction Build 2x 2 + 3x + 5 Now add x 2 – 2x Solve Now try: 2x 2 +4x – 5 – (x 2 +2x -3)

Working with Algebra Tiles Multiplication Build (x+3) (x- 2) Solve Now try: (-2x + 2)(x – 3)

Working with Algebra Tiles Factoring Create an array for x 2 + 5x + 6 What are the factors? Now try: x 2 – 7x w07ImpFree.html w07ImpFree.html

Open Discussion What understanding did you build today? How might you use the manipulatives with adult learners? What questions do you have?