Strategies for Whole Number Computation

February 2013 Coaches Meeting

Three Types of Computational Strategies

• Counts by ones• Use of base-ten models

Direct Modeling

• Supported by written recordings

• Mental methods

Invented Strategie

s• Usually requires guided

development

Traditional

Algorithms

Direct Modeling- Problem Types

Identify the problem typeMatch the problem with the problem type.

Mental Strategies

Addition and subtraction strategies Adding On136 + 143

136 +100 = 236236 + 40 = 276276 + 3= 279

136 + 143= 279

Partial Subtraction

387- 146

387 - 100= 287287 – 40 = 247247 – 6 = 241

387 – 146 = 241

Addition and Subtraction Strategies Compensation236 + 297

236 + 300 = 536Subtract 3536 – 3 = 533

236 + 297 = 533

Adding more than is required , and then subtracting the extra amount.

Compensation547-296

547 – 300 = 247Add 4247 + 4 = 251

547 – 296 = 251

Subtracting more thn is required, then adding back the extra amout

Addition and Subtraction Strategies Moving153 + 598

Move 2 from 153 to 598151 + 600 = 751

153 + 598 = 751

Constant Difference

146 – 38

Add 2 to both numbers to create expression with friendly numbers148 – 40 = 108

146 – 38 = 108

Use and explain your StrategyYesterday there were 57 penguins sitting on the iceberg. Later 34 penguins joined them. How many penguins are now on the iceberg?

There were 72 penguins sitting on the iceberg. 49 penguins jumped into the icy water. How many penguins are still on the iceberg?

Perfect 500Number of Players: 2 or 3 Materials: One deck of 40 cards (4 each of the numbers 0-9)

Directions: The goal of the game is to have a sum as close to but not over 500 at the end of five rounds.

To begin, shuffle the deck of cards.

Deal 5 cards to each player. Use four of the cards to make 2, two-digit numbers, saving the fifth card for the next round.

Try to get as close as possible to 100. Record your addition problem and sum on the recording sheet, keeping a running total as you play.

For the second round, each player gets four cards to which they add the unused card from the first round.

After five rounds, the winner is the player who is closest to 500 without going over.

Representations:Models for Thinking

Strengthening the ability to move between and among representations improves the growth of children’s conceptual understanding.

Vandewalle, J. Elementary and Middle School Mathematics Teaching Developmentally. Pearson Education, 2007.

.

pictures

manipulativemodels

Real-worldsituations

writtensymbols

oral language

Models for thinking

A model for thinking about a mathematical concept refers to any object, picture, or drawing that represents the concept.

To see a concept in a model you must have some relationship in your mind to impose on the model.

Models give children something to think about, explore with, talk about, and reason with.

Open Number Line

Addition (2 digit + 2 digit)A sunflower is 47 cm tall. It grows another 25cm.

How tall is it?

Open Number Line

Subtraction (2 digit – 2 digit)I need 72 dollars to buy a skateboard. I have 39

dollars already. How many more dollars do I need to save?

1000 - 647

1000-647

1000-647