brainteasers

4 Hitting the Target problem solving and logical thinking .... 7 Could Be the Answer order of operations, problem solving, and logic .... 8 Finding the Answer order of operations, proble

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Grades 4–5

by Jillayne Prince Wallaker

illustrated by Vanessa Booth

Carson-Dellosa Publishing Company, Inc.

Greensboro, North Carolina

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© 2004, Carson-Dellosa Publishing Co., Inc., Greensboro, NC 27425 All rights reserved The purchase of this material entitles the buyer to reproduce worksheets and activities for classroom use only—not for commercial resale Reproductions of these materials for an entire school or district is strictly prohibited

No part of this book may be reproduced (except as noted above), stored in a retrieval system, or transmitted in any form or by any means (mechanically, electronically, recording, etc.) without the prior written consent of Carson-Dellosa Publishing Co., Inc.

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Credits:

Author: Jillayne Prince Wallaker

Cover Artist: Peggy Jackson

Inside Illustrations: Vanessa Booth

Project Director: Sherrill B Flora

Editors: Sharon Thompson and

Debra Olson Pressnall

Graphic Layout: Sharon Thompson

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Table of Contents

Introduction 4

Hitting the Target (problem solving and logical thinking) 5

Consecutive Number Add-Up (logic and problem solving) 6

Analyzing Consecutive Number Add-Up (logic and problem solving) 7

Could Be the Answer (order of operations, problem solving, and logic) 8

Finding the Answer (order of operations, problem solving, and logic) 9

Fill In the Digits (addition, subtraction, and problem solving) 10

Careful Placement (multiplication and puzzle logic) 11

Missing Digit (basic operations and problem solving) 12

Number Riddles (basic operations and logical thinking) 13

The Power of Zero through Nine (order of operations and problem solving) 14

Adding Words (addition with positive and negative addends and problem solving) 15

Fact Triangles (problem solving and logic) 16

Find the Numbers (basic operations and problem solving) 17

Hidden Numbers (basic operations and problem solving) 18

Working with Digits (multiplication and problem solving) 19

Whose Answer? (multiplication, division, and matrix logic) 20

Place Value Riddles (place value and logic) 21

Missing Steps (addition, problem solving, and logic) 22

More Missing Steps (addition, problem solving, and logic) 23

Puzzle It Out (problem solving and logic) 24

Soil Stuff (problem solving and logic) 25

Ages (problem solving and logic) 26

Pick Apart (fractions, logic, and problem solving) 27

My Money (money, problem solving, and matrix logic) 28

Break the Bank (money, problem solving, and logic) 29

Determining Money (money, problem solving, and logic) 30

Probability Two Ways (probability and logic) 31

How Probable? (fractions, probability, and logic) 32

New Pet (data organization, logic, and problem solving) 33

Hide and Seek (matrix logic) 34

It's Buggy (algebraic thinking and problem solving) 35

Label the Venn Diagram (problem solving and logic) 36

Let’s Measure (problem solving and matrix logic) 37

Polygons (geometry and logic) 38

Polygon Matrix (geometry and matrix logic) 39

Got the Area (area, problem solving, and logical thinking) 40

Order Up (sequencing and problem solving) 41

Keep Ordering (sequencing and problem solving) 42

Ordering Again (sequencing and problem solving) 43

The Total (number sense and matrix logic) 44

Review Test 45

Answer Key 47

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Introduction

Provide fun math practice that goes beyond the facts! With Brainteasers, students use

higher-level thinking and processing skills to solve problems Not only will students be expected

to make connections, analyze data, use deductive reasoning, and represent numbers in alternate ways, they will have opportunities to utilize skills that are prerequisites to other

learning—skills such as addition, subtraction, multiplication, division, fractions, geometry,

measurement, and money Students are encouraged to apply their understanding of those concepts in a new, unusual, or atypical manner Many students have memorized and

learned to use a skill in one or two given contexts With Brainteasers, students explore their

understanding of grade level concepts and picture and apply their skills to different situations.

Remediation and Extension Suggestions and Alternatives

Remediations

1 Allow students to work with partners or complete the pages on their own and conference with a partner to discuss problems on which they do not agree.

2 Let the student make a picture or sketch of the problem, or act it out.

3 Decrease the number of problems required for completion.

4 Represent the problems in a variety of ways.

5 Have students talk through or write their understanding of the process with partners Often, verbalizing assists understanding.

6 Many students cannot complete more than one or two higher-level thinking problems at

a time Have the student cut the page up, gluing the parts onto folded paper to make a booklet Alternatively, assign one or two problems a day until the page is complete.

Extensions

1 Ask students to use the page as a model and write their own problems The “write your own” activities allow students to demonstrate mastery of the concept while providing an avenue for self-expression and self-evaluation Placed on index cards with the answers on the back, the problems are great student-made additions to a math center.

2 Have students keep ongoing journals of where they encounter mathematics in real life

A goal of adding one experience a day is reasonable.

3 Ask students to solve problems using a variety of strategies

Have students evaluate which ones work best for them and

explain their preferences.

4 If appropriate, encourage students to do more than the

minimum requirements on the page For example, if two

additional examples are required, the student would create

five Set up a point system where students can earn bonus

points for additional examples.

5 Have students write clear directions to explain the process

for solving a problem and then share them with classmates.

6 Direct students to write explanations with proof for the

methods used to solve the problems.

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Choose 100 consecutive numbers Write the numbers in order in the balloons below

Write equations using the numbers in the table above Include addition, subtraction, multiplication, and division sentences Use whole numbers, fractions, and decimals Include multistep problems When a number is used as any part of a problem, shade its balloon Continue until each number has been used in an equation

Attribute checklist:

 Numbers in balloons are consecutive

 Each number in a balloon is used in an accurate problem

 Addition, subtraction, multiplication, and division problems are included

 Whole numbers, fractions, and decimals are used

 Multistep problems are used

Hitting the Target

problem solving and logical thinking

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Consecutive Number Add-Up

logic and problem solving

Place the numbers 1–9 in the first grid so that the sum of the numbers in each row and column are the same number Write the sum on the line after each row and under each column Use grid paper to practice Write your solution in the first grid Find other solutions by comparing with classmates Record them in the other 2 grids

Look with a partner for patterns

in the above grids Evaluate

how each number moves to

the next number

Take any set of consecutive

numbers Using the patterns

found above, place numbers

in the grids on the right Use

a different set of numbers for

each grid

Use multiples of 2, 3, and 4 in the grids Does the pattern still work?

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Analyzing Consecutive Number Add-Up

Solve Add the numbers in each column and row Write the answers in the blanks.Evaluate how each number moves to the next number Numbers move 4 different ways Write those ways here

37 43 44 25

39 45 26 32

Place consecutive numbers in the grids so that the sum of each row and column is equal Start each grid with a different number Share your results with a partner

On a separate sheet of grid paper, use the patterns to write other sets of numbers in

a grid Try numbers that are consecutive when counting by a number other than 1 For example, write the multiples of 2, 3, 5, 10, or 100 in the grid

logic and problem solving

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Could Be the Answer

order of operations, problem solving, and logic

Use the order of operations to make each problem correct Place parentheses to arrive at the given answer

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Finding the Answer

order of operations, problem solving, and logic

Think a bit harder about these problems Place function symbols and parentheses in each number sentence to arrive at the given answer

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Fill In the Digits

addition, subtraction, and problem solving

Add or subtract Find the missing digits

• Make your own problems

• Check for accuracy with a calculator

• Copy the problems into the boxes

on the right, but leave the shaded

boxes blank

• Fold the paper back along the line

• Trade problems with a partner

• Add or subtract

• Find the missing digits

• When you are done, unfold the page and check your work

+ 1

5

8 7

6 5 7

0

– 9

4

2 7

3

3 4

7 3

+ 3 5

4

3

5 6 4

1

– 7

1

3 8

8

3 4 9

– 8

5

5 4

3

4 8 2

2 7

5 5

5 8

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Careful Placement

multiplication and puzzle logic

Solve Write the answers in the puzzle so that the vertical and horizontal numbers interconnect If an answer does not fit in the puzzle, check your work

4 3

x 9 1

9 4

x 9 1

4 4

x 3 5

4 6

x 7 5

Write your own multiplication problems, using only 2-digit or 3-digit factors

Use another piece of paper to work the grid Rewrite your final answers here

4 6

x 8 4

5 0

x 9 2

9 8

x 9 7

1 9 5

x 3 1

x

A.

C.

E.

G.

B.

D.

F.

H.

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Missing Digit

basic operations and problem solving

Think carefully about each set of numbers Look for relationships and explain them on the lines below Complete the grids

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Number Riddles

Read carefully to solve each number

riddle Write your answer in the blank

1 Divide me by 6 and add 3 Divide

this by 3, then multiply by 4 to get

12 What number am I?

2 Multiply me by 3, then add 3 Divide by 5,

then subtract 4 The final answer is 2 What number am I?

3 Divide 24 by me, then multiply by 5

Subtract 7 and multiply by 7 You get 56 What number am I?

4 Divide me by 5, subtract 9, then multiply by 6

Subtract 2, then multiply by 4 to get 16 What number am I?

5 Add 2 to me, multiply by 3, then subtract 9

Divide by 6, then add 4 You get 6 What number am I?

6 Divide 18 by me, then subtract 9 before

adding 1 Triple the answer Add 6, then

7 Multiply me by 9, then subtract 104 Divide this

by 5 Subtract 2, then divide by 8 Multiply this

8 Add 34 to me, then divide by 4 Multiply this by 5

Add 1 more Multiply this by 2, then divide by 8

9 Divide me by 4, subtract 3, and then divide by 7

Multiply by 8, then add 4 Divide by 4 to get 9 What number am I?

Think of 5 riddles of your own Write them on another sheet of paper Check your problems for accuracy Copy each problem onto an index card Write the answer on the back Exchange your number riddles with a partner

basic operations and logical thinking

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Write 3 equations for each of the following answers Each equation must include the numbers 0–9 Use your knowledge of order of operations to help you Compare your answers with those of a partner Check for accuracy

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Adding Words

addition with positive and negative addends

Use the table Give each letter in the word a number value Add the numbers to find the total value of the word

Read and follow the directions

7 How many words can you write with a value of 0? _

8 Write 4 words with a value

9 Write 4 words with a value greater than 10

10 Find the value of this sentence: Math is fun

11 Write a sentence Find the total value of the words in your sentence

12 Write a sentence with a value greater than 25

13 Compare your sentence with the sentence of a partner

Who has the sentence with the greatest value?

14 Does the sentence with the most words have the greatest sum?

Explain

-52345

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Fact Triangles

problem solving and logic

Each letter in the addition/subtraction fact triangles represents a number 1–10 The letter R equals 3 Find the value of each of the other letters *Hint: The value of the letter at the top of each triangle equals the sum of the other two addends

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Find the Numbers

T

x R M

M

x M RM

M =

R =

T =

J+ S

B

B + BSJ

B =

J =

S =

G– KK

P – U = C + C P

P P P P P + P UP

C =

P =

U =

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Hidden Numbers

Each puzzle contains multiple ways to make a given answer Any squares that touch can work together Each number in the puzzle grid must be used at least once

1 At least 10 threes can be found in this puzzle Write 10 equations.

2 This puzzle contains at least 10 fives Write 10 equations.

3 At least 10 tens can be found in this puzzle Write 10 equations.

Compare your answers

with those of a partner

Star those only you found

( 8 ÷ 2 + 2 ) ÷ 2 = 3

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Working with Digits

The following sets of digits have been used to write multiplication problems Read the clues and use the digits to solve them Write the problems

multiplication and problem solving

1 2 3 4

1 Ian used these digits to make

a 1-digit x 3-digit problem

The answer to his problem is 1,236

2 Brandon used these digits to

make a 1-digit x 3-digit problem

with a product of 924

3 Madalen used the digits to

make a 2-digit x 2-digit problem

4 Judy took 1 digit out and used

the other 3 digits to make

a 1-digit x 2-digit problem

4 5 6 7

5 Paolo used the digits to make a

1-digit x 3-digit problem with a product of 3,282

6 Ruth used the digits to make a

2-digit x 2-digit number The answer to her problem is 3,450

7 Ernest used the digits to make a

2-digit x 2-digit number The answer to his problem is 3,618

8 Zoe used 1 digit twice She made

a 1-digit x 4-digit problem with a product of 33,292

Choose a different set of digits Write your own clues for someone else to solve

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Whose Answer?

multiplication, division, and matrix logic

Solve Write each answer above a column in the matrix Arrange the answers from smallest to largest Then use the clues and the matrix to identify the problem each student wrote

• Jade’s answer starts with an even digit

• The answer to Luis’s problem is even

• The sum of the digits in Will’s answer is 15

• Eloy has a 4-digit answer

• Gabe’s even answer has 3-odd digits

• Jade’s answer has fewer digits than Will’s answer

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Place Value Riddles

place value and logic

Read each riddle Write 4 possible answers on the lines

1 I am a 4-digit number that is a multiple of 2 Take half of me and you get

a multiple of 3

number: _ half is: _ number: _ half is: _

2 I am a 4-digit number whose digits add to 17 Each digit from left to right

is larger than the previous digit

_ _ _ _

3 I am a 6-digit number with all odd digits No more than 2 digits can be

the same I am not a multiple of 3 or 5

_ _ _ _

4 I am a 6-digit number I am a multiple of 2, 3, and 5.

_ _ _ _

5 I am a 5-digit even number Two digits are the same The other 3 digits

are different from each other and larger than the 2 like digits

_ _ _ _

6 I am a 4-digit odd number whose tens and hundreds digits are even

The sum of my digits is 16

_ _ _ _

Compare your numbers with those

of a partner Check for accuracy

Put a check mark next to each answer

that matches Star those that only you

have Make a group list of possible

answers for each riddle

Write your own place value riddle on

another sheet of paper Provide 4 possible

answers on the back Share your riddles

with a partner

I am

a

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Missing Steps

addition, problem solving, and logic

Add your way to the top Add adjacent numbers and write the sum in the box above them Use the numbers given to fill in the first row of steps

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Write your own Check your answers.

Copy the final sum on the top step of

the right pyramid Leave the other boxes

blank Write the numbers for the first row

of steps, in order from least to greatest,

on the lines Trade with a partner _

_

addition, problem solving, and logic

Add your way to the top

Add adjacent numbers

and write the sum in the

box above them Use the

numbers given to fill in the

first row of steps

Add your way to the top Use the numbers given to fill in the first row When finished, unfold the paper and check your work

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