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Session 4 Pulling it All Together

Building a Solid Number FoundationStrategies for Education Assistants

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Player A

Player B

Player C

Player D

Playing board for the game Crooked Rules

Hundreds Tens Ones

Note: die = singular, dice = plural

No die? Why not number some blank playing cards. Then you could go 0 to 9.

Anyone got Spin To Win? Primary Games volume 1, (www.primarygames.co.uk)

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Math is right up there with snakes, public speaking, and

heights.

Burns, M. (1998). Math: Facing an American phobia. New York: Math Solutions Publications.

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Math Difficulties

• Memory• Language and communication disorders• Processing Difficulties• Poor self-esteem; passive learners• Attention• Organizational Skills• Math anxiety

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Curriculum Issues

• Spiraling curriculum• Too rapid introduction of new concepts• Insufficiently supported explanations and

activities• Insufficient practice (Carnine, Jones, & Dixon,

1994).

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Interventions Found Effective for Students with Disabilities

• Reinforcement and corrective feedback for fluency• Concrete-Representational-Abstract Instruction• Direct/Explicit Instruction• Demonstration Plus Permanent Model• Verbalization while problem solving• Big Ideas• Metacognitive strategies: Self-monitoring, Self-Instruction• Computer-Assisted Instruction• Monitoring student progress• Teaching skills to mastery

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The Trouble with Algebra

• Students have difficulty with Algebra for one of the same reasons they have difficulty with arithmetic – an inability to translate word problems into mathematical symbols (equations) that they can solve.

• Students with mild disabilities are unable to distinguish between relevant and irrelevant information; difficulty paraphrasing and imaging problem situation

• Algebraic translation involves assigning variables, noting constants, and representing relationships among variables.

• Abstract – using symbols to represent numbers and other values. Hard to use manipulatives (concrete) to show linear equations

• Erroneous assumption that many students are familiar with basic vocabulary and operations; many still are not fluent in number sense

• Attention to detail is crucial• All work must be shown

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Findings on Algebra Interventions

• Results – students with mild disabilities can successfully learn to represent and solve algebraic word problems when appropriate instruction is provided.

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Accommodations

• Use vertical lines or graph paper in math to help the student keep math problems in correct order

• Highlight symbols, different colors• Use different colors for rules, relationships• Use a model to help students deconstruct

word problems

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DRAW

• Discover the sign• Read the problem• Answer or DRAW a conceptual representation of the

problem using lines and tallies and check• Write the answer and check

• The first three steps address problem representation, the last = problem solution

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• When students cannot construct knowledge for themselves, they need some instruction.

Making Meaning…

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How would you tackle these calculations?

1). 23 – 9

2). 127 x 6

3). 4358 + 843 + 276

4). 98 ÷ 6

5). 5 + 8 + 5

6). 4 + 7 + 8 + 6 + 3

7). 24 + 17 + 16 + 12 + 33

8). $2.54 + $2.67 + $1.46

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Comparing methods

• Were you surprised by any of the methods others used?• Were you taught to use any of these methods at school?• Why do you think you use them now?• Did having to explain your method help you in any way?• Did hearing any other person’s method help you in any way?

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A Few more strategies….

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Subtraction

Expanded Subtraction

“What is 5271 take away 2638?”

5000 200 70 1

2000 600 30 8

5000 200 70 1

2000 600 30 8

30 3

601

Step 1 Step 2

5000 200 70 1

2000 600 30 8

2000 6000 30 3

6011

4000Step 3

Sometimes 4 steps needed. Answer here is 2633

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Multiplication

Multiplication

Begin with rapid tables recall.

Then informal partitioning or use of a grid:

To solve 47 x 6:

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40 7

6

40 7

240 42

Answer = 282

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Multiplication

Classic Error

Then when faced with a question like this: 37 x 25

Children will do 30 x 20 and 7 x 5

This is WRONG. (but they often cannot see why)

The sum 37 x 25 would need a grid like this:

Can you see why this proves 30 x 20 and 7 x 5 is incorrect?

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Multiplication

Proof30 7

20

5

600 140

150 35

Adding these four values gives the answer 925

It is within this type of question that the ‘add zero’ rule can pop up.

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And What About Those Formulas?

• Graffiti Activity:

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Your Turn….

• Using the formula sheets provided (or use formulas that you have seen but don’t necessarily understand totally), create mini graffiti information cards to explain what the formula is used for, how it “works”, examples of when/how it is used. These are for use with your students.

• Use your colleagues and instructor as resources. • Take an Internet Field Trip to gather more

information

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Reflection

• What did you find most interesting in this course?

• What do you wonder about?

Share with your table group.

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Evaluation

• Complete the evaluation sheet and give it to your instructor

• Summative Assessment – Complete and hand in before you leave.

• Thank You.