Manipulatives Can Help Adults Learn Math Too

Marcia TorgrudeK-12 Math Specialistmtorgrude@tie.net

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 Frameworkhttp://shell04.theworld.com/std/anpn//frame5.html

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 -

http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

– Cuisinaire Rods

Working with Fractions

• Equivalent Fractions– http://illuminations.nctm.org/ActivityDetail.as

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 TilesExpressions

• Build 3x +2 + (-4x) +(-5) • Simplify this. • Now try: • 5x-9-2-3x

Working with Algebra TilesAddition/Subtraction

• Build 2x2 + 3x + 5• Now add x2 – 2x• Solve• Now try: 2x2 +4x – 5 – (x2 +2x -3)

Working with Algebra TilesMultiplication

• Build (x+3) (x- 2)• Solve• Now try: (-2x + 2)(x – 3)

Working with Algebra TilesFactoring

• Create an array for x2 + 5x + 6• What are the factors?• Now try: x2 – 7x + 12

• http://mathbits.com/mathbits/AlgebraTiles/AlgebraTilesMathBitsNe

w07ImpFree.html

Open Discussion

• What understanding did you build today?• How might you use the manipulatives with

adult learners?• What questions do you have?