Kliman, M. Investigations in Number, Data, and Space:

Building on Numbers You Know. Dale Seymour, 1998.

Building on

Computation and

Estimation Strategies

Unit Goals:

•

Explore a wide range of strategies for

computation and estimation, especially

with multiplication and division

•

Use what the student already knows

about number relationships and the

meaning of operations.

•

Use estimation both before and after

computation to check the reasonableness

of their results.

Materials:

◊

Paper for score sheet, calculator or watch,

Numeral Cards

Players

: 3 - 4

Procedure:

1. Choose a problem template.

Example: __ __ __ x __ __

2. Take turns being the leader. The leader deals

one card for each slot in the template and

records the digits in order without showing

anyone.

Example: Deal 7,4,1,0,3 Write 741 x 03

3. The leader uncovers the problem and starts

timing. You have exactly 30 seconds to esti-

mate the answer mentally, without paper and

pencil. The leader finds the actual answer

with a calculator.

4. Record your estimate and the actual answer

on your score sheet. The difference between

them is your score.

5. The leader deals new Numeral Cards for

Rounds 2 and 3. Use the same problem tem-

plate.

6. After three rounds, total your scores. Low-

est score wins.

Score Sheet:

Game 1

Difference

Round 1: ______ - _______ = __________

Round 2: ______ - _______ = __________

Round 3: ______ - _______ = __________

Total Score: ___________

Math Game

Investigations in

Schools

Web Resources

You will find web resources at:

http://www.everett.k12.wa.us/math

www.illuminations.nctm.org - select

Activities

http://www.rainforestmaths.com/

Glossary

Multiple:The product of a given whole

number and another whole number

Factor: A number that is multiplied by an-

other number to find a product

Estimate: (To make) an approximate or

rough calculation, usually based on round-

ing

Equation: A number sentence which

shows that two quantities are equal

Example: 5 x 6 = 30

On-Line Glossary

http://www.amathsdictionaryforkids.com/

The Estimation Game

---

Listed below are questions to

Getting Started

∗

What is it that you don’t under-

stand? (Have your child be

specific.)

∗

What do you need to find out?

∗

What do you need to know?

∗

What terms do you understand

or not understand?

While Working

∗

How can you organize the in-

formation?

∗

Do you see any patterns or re-

lationships that will help solve

this?

∗

What would happen if…?

Reflecting about the Solution

∗

How do you know your answer

is reasonable?

∗

Has the question been an-

swered?

∗

Can you explain it another

way?

About Cluster Problems

Cluster problems are sets of problems that help

students think about using what they know to

solve harder problems. The cluster problems in

this unit are designed to help students make

sense of multiplying 2- and 3-digit numbers.

They build an understanding of the process by

pulling apart multiplication problems into man-

ageable sub-problems, solving each of the

smaller problems, then putting the parts back

together.

Cluster problems are intended to help students

learn how to look at a problem and build a strat-

egy to solve it based on the number relation-

ships they know. When working on cluster

problems with your child, encourage them to

add to the clusters any problems they think of

that they use to solve the final problem in the

cluster.

Kliman, M. Investigations in Number, Data, and Space:

Building on Numbers You Know. Dale Seymour, 1998.

Mathematics in

Investigations

Investigation 1:

∗

Skip counting between 2-, 3-, and 4-digit numbers

between any two 4- or 5-digit numbers

∗

Relating repeated addition to multiplication

∗

Using skip counting patterns to help solve multiplica-

tion and division problems

∗

Developing, explaining, and comparing strategies for

subtracting 4- and 5-digit numbers

∗

Recording computation strategies using words, num-

bers, and arithmetic symbols.

∗

Reading, writing, and sequencing 4-and 5-digit num-

bers

Investigation 2:

∗

Developing, recording, and comparing strategies for

solving multiplication and division problems

∗

Making sense of remainders

∗

Understanding relationships between multiplication

and division

∗

Modeling situations with multiplication, division and

other operations

Investigation 3:

∗

Developing, explaining, and comparing strategies for

estimating and finding exact answers to multiplica-

tion and division problems.

∗

Recording strategies for solving problems

∗

Solving problems in more than one way

∗

Using relationships between multiplication and divi-

sion to help solve problems