Manipulatives Can Help
Adults Learn Math Too
Marcia Torgrude
K-12 Math Specialist
mtorgrude@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 Framework
http://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?I
D=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 Tiles
Expressions
• Build 3x +2 + (-4x) +(-5)
• Simplify this.
• Now try:
• 5x-9-2-3x
Working with Algebra Tiles
Addition/Subtraction
•
•
•
•
Build 2x2 + 3x + 5
Now add x2 – 2x
Solve
Now try: 2x2 +4x – 5 – (x2 +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 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?