math blaster ages 9 12 - knowledge adventure

© Vivendi Universal Publishing and/or Math Blaster® Ages 9–12its subsidiaries. All Rights Reserved.

Teacher’s Guide

Math Blaster ®

Ages 9–12

0361501

AuthorJulia Hernandez

Design and Layout Pam WissingerTony Gervase

Editor Rosalind Emmett

Reproduction of these pages by the classroom teacher for use in the classroom is permissible. The reproduction of any part of this book for an entire school or school system or for commercial use is strictly prohibited.

© Vivendi Universal Publishing and/or its subsidiaries. All Rights Reserved. Math Blaster is a registered trademark of Vivendi Universal Publishing and/or its subsidiaries.

All trademarks referenced herein are the property of their respective owners. Math Blaster® Ages 9–12

3© Vivendi Universal Publishing and/or Math Blaster® Ages 9–12its subsidiaries. All Rights Reserved.

Program Overview . . . . . . . . . . . . . .4

Welcome . . . . . . . . . . . . . . . . . . . .5

Unit 1: Addition and Subtraction . . . .7Lesson A – Football FunLesson B – Weather ForecastingLesson C – Addition of Integers

Using + and – Tiles

Unit 2: Multiplication . . . . . . . . . . . .21Lesson A – A Community Garden Lesson B – Two-Dice BingoLesson C – Wild Numbers

Unit 3: Division . . . . . . . . . . . . . . . .41Lesson A – Easy as Apple PieLesson B – Division of FractionsLesson C – Finding Averages

Unit 4: Fractions . . . . . . . . . . . . . . .53Lesson A – Fraction QuiltLesson B – Fraction WarLesson C – Elapsed Time

Unit 5: Decimals with Percents . . . . . .67Lesson A – Decimal and Percent WarLesson B – Honey, I Shrank the Elephant!Lesson C – Making the Grade

Unit 6: Operations with Integers . . . .77Lesson A – Good Guys and Bad GuysLesson B – Song SurveyLesson C – Jeopardy!

Unit 7: Logic . . . . . . . . . . . . . . . . . .95Lesson A – Tangram PuzzlesLesson B – The Attribute GameLesson C – Logic Puzzles

Math Blaster® Ages 9–12Table of Contents


Math Blaster® Ages 9–12

Activity Components

Banana Splat

Throw bananas at the right monkeys to

solve equations with a missing number.

Crater Crossing

Estimate answers within a target range

as you navigate across moving pods and

avoid rogue monkeys.

Bridge Builder

Build bridges to get monkeys across the

jungle, using fractions, decimals, and

percents.

Monkey Maker

Create a series of monkeys with different

attributes using the logic clues in the puzzle.

Cube Quest

Use mental math and place value hints to

collect all the cubes and solve the equations.

Features• Covers important math skills grades 3–6

• Over 50,000 different problems

• Three levels of game play and 10 levels

of learning

• Five different activities in 17 unique

environments

• On-line help and math tips

• Cruncher Blaster, a fun, easy-to-use

spreadsheet and graphing program

Skill Development• Reinforces addition, subtraction, multiplica-

tion, and division of 2- to 6-digit numbers

• Covers positive and negative numbers

• Builds the connection between fractions,

decimals, and percents

• Strengthens estimation skills

• Sharpens logical thinking and complex

problem-solving skills


Welcome

Welcome to Math Blaster® Ages 9–12, an exciting and challenging way to improve yourstudents’ math skills and problem-solving strate-gies. These lessons were designed to help students achieve mathematical power with motivational activities both on and off the computer. Students will have many variedopportunities to work independently as well as collaboratively in small or large groups.

Students will develop their mathematical power through a variety of activities such as:• improving proficiency at mental math in

motivating game environments• comparing fractions, decimals, and

percents• using positive and negative numbers

in realistic settings• using logic and critical thinking• classifying and sorting by attributes• developing strategies based on

probabilities

Students will reinforce their math skills andproblem-solving strategies through:• mental math• probability• operations with integers• operations with fractions, decimals,

and percents• logic

Your students will be motivated to reinforce their basic math skills and develop new strategies as they complete the lessons in each of the seven units. These lessons aredesigned to be interwoven with the softwareadventures of Galactic Commander, Blasternaut, and Spot. Encourage your students to see connections between the computer software, the lessons in the sevenunits, and the mathematics used elsewhere in the classroom and in their lives.

Good luck on all your galactic adventures.Enjoy the challenging mathematics that MathBlaster brings from our galaxy to your class-room. Have a blast!


UNIT 1: ADDITION AND SUBTRACTION

Addition and subtraction are two of the most basic skills in mathematics. Addition andsubtraction are closely linked, and an understanding of these operations provides stu-dents with a foundation for other mathematical relationships. In the following activities,students will explore addition and subtraction of integers using manipulatives and men-tal math skills. Solutions will include positive numbers and negative numbers (integers).Students will also compare solutions using the concepts of greater than and less than.Mental math calculation is encouraged in all three activities.

LESSON A – FOOTBALL FUN

Curriculum Focus: Addition and Subtraction of IntegersRecommended Grade Levels: Grades 3–5Lesson Duration: 30 minutesObjectives: Students will work with adding and subtracting one- and

two-digit integers.

LESSON B – WEATHER FORECASTING

Curriculum Focus: Analyzing DataRecommended Grade Levels: Grades 4–5Lesson Duration: 10 minutes per day for 10 daysObjectives: Students will add, subtract, and compare integers in a

realistic context and graph and analyze real-world data.

LESSON C – ADDITION OF INTEGERS

USING + AND – TILES

Curriculum Focus: Addition and Subtraction of IntegersRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutesObjectives: Students will develop a concrete understanding of

addition and subtraction of integers and how the two operations are linked.


MATERIALS

• Football field game board• Gain or Loss? spinner• Large paper clips, one per pair• Pencil (with sharp point), one per pair• Dice, one die per pair of players • 9" x 12" box or cardboard border

(optional)• Football helmet game pieces, one per

player• Yardage tracking sheet• Copies of Football Fun activity sheets,

pgs. 10–11

VOCABULARY

first down touchdown

BEFORE THE COMPUTER

• Make two copies of the football field gameboard Football Fun activity sheet, pg. 10,and have the students tape the two pagestogether with the 50-yard line in the mid-dle. Using Football Fun activity sheet,pg. 11, color each football helmet gamepiece a different team color, or write eachplayer’s name on his or her own gamepiece. Color the spinnerin two colors, one colorfor gain and another for loss of yardage. Youmay wish to laminate thegame boards, the gamepieces, and the yardage spinners.

• To make a spinner,unbend a large paperclip until it looks like thediagram. Place a pencilpoint through the bentend of the paper cliponto the center point of the spinner. Practicespinning the paper clip a few times untilstudents are proficient at using the spinner.You may wish to laminate some spinners forextended use.

• Divide students into pairs or threesomes, ifnecessary.

• To start the game, each player rolls a die.The highest positive number goes first. Ifmore than two players are using one gameboard, the next highest positive numbergoes second. Start all game pieces on the50-yard line.

• Roll the die to determine how many yardsto move on the football game board. Spinthe Gain or Loss spinner. You will movefrom one to six yards on each play in eithera positive or a negative direction. Keeptrack of your yardage and field position onthe yardage tracking sheet. You may con-tinue to advance if you continue to gain 10yards or more in four tries.

• If the spinner should land directly on top ofthe border between Gain and Loss, theplayer may respin. If the spinner is slightly

Unit 1 – Addition and Subtraction Lesson A

FOOTBALL FUN


more in one area, then that’s the directionyou should move.

• If you fail to gain at least 10 yards in four tries, the next player begins at the 50-yard line and moves in the oppositedirection.

• If you land on or over the goal line, youscore a touchdown. A touchdown is worthseven points. After scoring a touchdown,the game piece returns to the 50-yard line,and the next player gets to toss the die.

• If you do not score a touchdown, you maybegin your next turn where you last left offor at the 50-yard line, whichever is closestto your goal line.

• Optional: The player with the most totalyardage when time is up gets a bonus 10 points.

AT THE COMPUTER

• Students can explore the use of adding andsubtracting more than one number to com-plete a three-operator equation. They’llneed to use a two-step process.1. Establish what missing value will

complete the equation.2. Explore what combination of integers

can be used to add or subtract to equal the missing value with either 1, 2, or 3 integers.

• Have students sign in and choose PracticeMath Skills.

• Choose Banana Splat, Level 1 or 2, viewingthe sample problems for appropriateness.

AFTER THE COMPUTER• Access an on-line sports source or look up

the NFL statistics in your local paper.

• Discuss what passing and rushing meanand how total and average yardage arecalculated.

OVERVIEW

Football Fun is a board game involving addi-tion and subtraction. Twenty to thirty minutesare usually sufficient, although the game canbe played again at different sittings as long aschildren need reinforcement of addition, sub-traction, and mental math skills. It is also a game of chance.

Unit 1 – Addition and Subtraction Lesson A

FOOTBALL FUN (CONTINUED)


Unit 1 Lesson A

FOOTBALL FUN

1020

3040

5010

2030

4050

TouchdownTouchdown

START


Unit 1 Lesson A

FOOTBALL FUN

Gain

Gain

Loss

LossPlayer:

YardsGain/Loss

Field PositionYard LineTurn

Touchdowns:

BONUS POINTS

1234123412341234

Total


MATERIALS

• Weather section of local newspaper for 10consecutive days

• Option: Watch and record data from TVweather broadcasts for 10 consecutive days

• Centimeter grid paper• Chart paper (optional)• Copies of Weather Forecasting activity

sheets, pgs. 14–15

VOCABULARY

prediction precipitation variationhigh low

BEFORE THE COMPUTER

• Read or watch the weather forecast for ten consecutive days. Using WeatherForecasting activity sheet, pg. 14, recordthe daily high and low predictions in yourlocal area.

• Record the actual high and low tempera-tures in your area for each day.

• Using Weather Forecasting activity sheet,pg. 15, graph the predictions and the actu-al temperatures. Write a paragraphdescribing your graph. Mention data suchas the highest high and the lowest low tem-peratures, the range of temperatures, andthe variation between predictions and actu-al temperatures.

• Make a chart to record the variation in thehigh temperature from day to day as a

positive or negative number. Also, recordthe variation in the low temperature fromday to day as a positive or negative num-ber. For example, if the high temperaturesfor Monday, Tuesday, and Wednesdaywere 75°, 78°, and 74°, respectively, thevariation would be +3 and -4, showing anincrease of 3° followed by a decrease of4°.

• Make a chart or a graph to record the difference between the actual tempera-turesand the predicted temperatures as a positive or negative number.

AT THE COMPUTER

• Students can explore adding and subtract-ing more than one number to complete athree-operator equation using positive andnegative integers. They’ll need to use a two-step process:1) Establish what missing value will

complete the equation.2) Explore which combination of 1, 2, or3 integers can be used to add or subtract

to equal the missing value.


• Choose Banana Splat, Level 5 or 6. Both involve adding or subtracting withnegative integers.

• Use The Cruncher Blaster program to make

Unit 1 – Addition and Subtraction Lesson B

WEATHER FORECASTING


a spreadsheet. Record all the actual tem-peratures and predicted temperatures onthe spreadsheet in rows labeled with thedays of the week.

• Set up a column for actual temperaturesand a column for predicted temperatures.Set up a third column for the difference orvariation by using a formula between thepair of actual and predicted temperatures.For example, if the actual high was 70degrees and the predicted high was 68degrees, then the difference is +2, meaningthat the actual temperature was twodegrees higher than the prediction.

• You can then select the area in yourspreadsheet to create and display a bar orline graph of your findings.

Unit 1 – Addition and Subtraction Lesson B

WEATHER FORECASTING (CONTINUED)


Unit 1 Lesson B

WEATHER FORECASTING

SAMPLE CHARTS

Day 1

Day 2

Day 3

Day 4

Day 5

Day 6

Day 7

Day 8

Day 9

Day 10

ActualHigh

Predicted

High Variance

Actual Low

Predicted

Low Variance or - or -

Day 1 - Day 2

Day 2 - Day 3

Day 3 - Day 4

Day 4 - Day 5

Day 5 - Day 6

Day 6 - Day 7

Day 7 - Day 8

Day 8 - Day 9

Day 9 - Day 10

LowHigh

=

Change in Temperature From One Day to the Next

HIGH AND LOW

IN ONE DAY

CHANGE IN

TEMPERATURE

FROM ONE DAY

TO THE NEXT


Unit 1 Lesson B

WEATHER FORECASTING

GRAPH PAPER


MATERIALS

• 16-part spinner• Recording sheet• 32 paper tiles in two colors; 16 of each

color• Large paper clip• Pencil• Copies of Addition of Integers Using + and

– Tiles activity sheets, pgs.18–20

VOCABULARY

positive integer negative integer

BEFORE THE COMPUTER

• Explain to the students that each one of thepaper tiles represent a 1. One color repre-sents +1 and the other color represents –1.Ask the class how they could show the num-ber zero using their counters. Elicit multipleresponses.For example:

• one red and one yellow tile• two red and two yellow tiles• three red and three yellow tiles

• Have students work in pairs using theAddition of Integers Using + and – Tilesactivity sheets, pgs. 18–20. Each studentspins the spinner once and records a posi-tive and a negative number. They will addthese numbers in two ways: (1) pencil andpaper addition using their own strategy,and (2) using the manipulative counters.

• When working with the paper tiles, haveone student be positive and the other nega-tive. Each student counts out the corre-sponding number of positive tiles and nega-tive tiles. Put all the tiles together in a pile.Remove all the zeroes until only one colorof tiles remains. Count the remaining tilesand determine if the tile color is positive ornegative. Note: It is also possible that notiles will remain if the two numbers wereexact opposites.

• Have students record the sum of the positiveand negative numbers on their recordingsheet. Continue until each student has com-pleted nine sums.

• Discuss different strategies for adding positive and negative numbers.

• This game can be repeated until studentsare comfortable doing addition of integerswithout manipulatives.

AT THE COMPUTER• Using positive and negative integers,

students can also explore adding and subtracting more than one number to complete a three-operator equation. They’ll need to use a two-step process:1) Establish which missing value will

complete the equation.2) Explore which combination of two or

three integers equals the missing value.

Unit 1 – Addition and Subtraction Lesson C

ADDITION OF INTEGERS USING + AND – TILES



• Choose Banana Splat, Level 8 or 9. Bothlevels involve adding and subtracting withnegative integers.

AFTER THE COMPUTER

• Here is a method to help students remember how to add positive and negative numbers using a concrete example from history.

Allies and Enemies• Explain that allies are friends. They have

something in common. Two positive num-bers would be allies. Two negative numberswould also be allies. Give examples ofallies, teammates on a team versus theopposing team.

• When allies join forces, they become bigger, stronger, and more powerful togeth-er. When number allies are added together,the resulting sum is a larger number of thesame sign.

• Explain that opponents have different view-points—both teams want to win. A positivenumber and a negative number would beopponents.

• Give an example of nations that were ene-mies during World War II or another war.Link this game to a current history lesson.

• When enemies engage in battle, theybecome weakened and smaller. When inte-ger enemies are added together, the result-ing sum is a smaller number. As the twonumbers engage in battle, an equal num-ber of positives and negatives are killed,until only one type of number remains(either positive or negative). The numbersthat are not lost in battle have the of the larger original force.

Unit 1 – Addition and Subtraction Lesson C

ADDITION OF INTEGERS USING + AND – TILES (CONTINUED)


Unit 1 Lesson C


1 23

45

67

8910

11

1213

1415

16


19

Unit 1 Lesson C


PLAYER NAME:

1. ________ + ________ = ________

2. ________ + ________ = ________

3. ________ + ________ = ________

4. ________ + ________ = ________

5. ________ + ________ = ________

6. ________ + ________ = ________

7. ________ + ________ = ________

8. ________ + ________ = ________

9. ________ + ________ = ________

PLAYER NAME:

1. ________ + ________ = ________

2. ________ + ________ = ________

3. ________ + ________ = ________

4. ________ + ________ = ________

5. ________ + ________ = ________

6. ________ + ________ = ________

7. ________ + ________ = ________

8. ________ + ________ = ________

9. ________ + ________ = ________


Unit 1 Lesson C


+ + + +

+ + + +

+ +

+ +

+

+

+

+

– – –

–

–

––

–

––

–

––

–

–

–


Unit 2: Multiplication

Multiplication is a mathematical shortcut for repeated addition. Multiplication is also a function that links numeric math facts with the geometric concept of area.Multiplication facts using factors up to ten can readily be modeled using a rectangu-lar (multiplication) grid. This can help students understand multiplication tables andbegin to memorize multiplication facts. It can also help them understand the commu-tative property and other patterns in multiplication.

LESSON A – A COMMUNITY GARDEN

Curriculum Focus: Multiplication and Areas of RectanglesRecommended Grade Levels: Grades 3–4Lesson Duration: 45 minutes (approximate time)Objectives: Students will investigate length, width, area, and perimeter

in this multiplication array game.

LESSON B – TWO-DICE BINGO

Curriculum Focus: MultiplicationRecommended Grade Levels: Grade 5Lesson Duration: 45 minutes Objectives: Students will multiply single-digit integers in this game of

chance.

LESSON C – WILD NUMBERS

Curriculum Focus: MultiplicationRecommended Grade Levels: Grades 3–5Lesson Duration: 45 minutes (approximate time)Objectives: Students will multiply one- and two-digit numbers and

look for patterns on a hundreds chart in this game of strategy and luck.


MATERIALS

• Number cards, two each, 3–10• Quarter-inch grid paper• Crayons, assorted colors• Data recording sheet• Pencil and paper• Calculator• Copies of A Community Garden

activity sheets, pgs. 24–26

VOCABULARY

length width perimeter areagrid square rectangle

BEFORE THE COMPUTER

• Using A Community Garden activity sheets,pgs. 24–26, cut apart a set of 16 numbercards, two each, of numbers 3–10, foreach pair of students. Laminate the cards,if you wish.

• Explain to students that the object of thegame is to plant a garden consisting ofeight crops on the smallest possible squareplot of land. The winner is the gardenerwho comes closest to planting the entirearea of a perfectly square garden.

• Have each player decide on eight differentcrops to grow in their own garden.Distribute quarter-inch grid paper to repre-sent the land available for their garden.Also distribute crayons and the datarecording sheet.

• Instruct students to shuffle all the numbercards and place them facedown in one pile.

• Demonstrate several rounds of the game onan overhead projector.

• The first player draws two cards, one repre-senting the length and one representing thewidth. The player then decides where to putthis rectangle in the garden. The player col-ors the rectangle and labels what will begrown in this region. Have players recordthe length, width, perimeter, and area ofeach region on the data recording sheet.

• Repeat the process until each player hashad eight turns.

• Have each student draw a square fencesurrounding their crop areas. Ask them tofind the total area used by the crops andthe total area of the square fenced region.Ask students to subtract the area of thecrops from the area of the square fencedregion. The gardener with the smallest dif-ference is the winner. In the case of a tie,the gardener with the greatest crop area isthe winner.

AT THE COMPUTER

• Reinforce basic multiplication facts by finding the matches in a given target rangewith Crater Crossing.

Unit 2 – Multiplication Lesson A

A COMMUNITY GARDEN



• Choose Crater Crossing, level 3 or 4.

AFTER THE COMPUTER

• Vary the number of crops to be grown inthe garden from 9 to 16.

• Find the perimeter of the garden. Subtractthe perimeter of any holes or gaps. The stu-dent with the smallest difference wins.

Unit 2 – Multiplication Lesson A

A COMMUNITY GARDEN (CONTINUED)


HOW TO PLAY: A COMMUNITY GARDEN

• The object of the game is to plant a garden consisting of eight crops on a square plot of land.The winner is the gardener who comes closest to planting a perfect square garden with no gapsbetween the crops.

• Decide on eight different crops to grow in your garden.

• Select a partner, according to your teacher’s directions.

• Shuffle the number cards and place them facedown in one pile.

• To start the game, the first player draws two cards, one representing length and one represent-ing width. That player then decides where to place this rectangle on the quarter-inch gridpaper, representing the garden.

• Color and label the crop which will be grown in the rectangle. Then record the length, width,perimeter, and area of each rectangle on the Data Recording Sheet.

• Repeat the process until each player has had eight turns.

• Draw a square fence surrounding your whole garden and find the area. Next, find the totalarea used by all the crops in the garden. Then, find the total area of the fenced-in region (thesquare). Subtract the total area of the crops from the area of the square to find the difference.

• The gardener with the smallest difference is the winner. In case of a tie, the gardener with thegreatest crop area is the winner.

Unit 2 Lesson A

A COMMUNITY GARDEN


Unit 2 Lesson A

A COMMUNITY GARDEN NAME__________________________

1

2

3

4

5

6

7

8

CropCard 1Length Width Perimeter Area

Card 2

3 4 5 6

7 8 9 10

3 4 5 6

7 8 9 10

GARDEN DATA CARD

AREA OF THE SQUARE FENCE: TOTAL AREA OF THE CROPS:


Unit 2 Lesson A

A COMMUNITY GARDEN NAME__________________________


MATERIALS

• Positive/negative game board• Game board border: Cut a strip of con-

struction paper 25" by 2". Overlap theends of the strip slightly and tape the endstogether. Tape the border to the perimeterof the positive/negative game board circleto build a wall for the circular game board.This will help prevent the dice from landingoutside the game board and slowing downthe progress of the game.

• Bingo cards• 2 dice• Pennies, tiles, or other nonrolling small

objects, about 25 per student• Copies of Two-Dice Bingo activity sheets,

pgs. 29–34• Copies of Three-Dice Bingo activity sheets,

pg. 35

VOCABULARY

product

BEFORE THE COMPUTER

• Laminate bingo cards and Two-Dice BingoCaller Card activity sheets, pgs. 29–34.Distribute 20–25 manipulatives (pennies,tiles, etc.) for students to use to cover theirbingo cards. Divide students into smallgroups of 3–6 students per group. Chooseone student from each group to be the

caller. Give each caller a Caller ProductCard. The caller may also need some addi-tional manipulatives. Give each player abingo card and have players begin by cov-ering the FREE space.

• Option: The teacher may wish to assumethe roll of caller and have all students playa few rounds of Two-Dice Bingo as a wholeclass activity. Continue until the students areready to play independently.

• The caller rolls two dice on the gameboard. If a die lies in a positive region (or more than halfway inside a positiveregion), use the face value of the die as apositive number. If a die lies in a negativeregion (or more than halfway inside a neg-ative region), use the face value of the dieas a negative number. The caller willannounce the two numbers, but not theproduct. The caller also records the twonumbers and their product on the CallerCard.

• The players multiply the values of the dice.If the product appears on any player’sbingo card, he may cover it with a pennyor a tile. The first player to get five in arow, horizontally, vertically, or diagonally,says Bingo! The player must check his orher products with the caller before beingdeclared the winner.

Unit 2 – Multiplication Lesson B

TWO-DICE BINGO


• If time runs out before anyone gets Bingo,the person with the most covered spaces isthe winner.

AT THE COMPUTER

• Reinforce student multiplication facts usingpositive and negative integers by findingthe matches in a given target range withCrater Crossing.


• Choose Crater Crossing, level 3, 4, or 7.

AFTER THE COMPUTER

• Three-Dice Bingo uses Bingo activity sheets,pgs. 33–35. The rules are the same as inTwo-Dice Bingo, but the number cards andthe bingo cards can include these addition-al numbers: (+ or –) 32, 40, 45, 48, 50,54, 60, 64, 72, 75, 80, 90, 96, 100, 104,108, 120, 125, 150, 180, 216.

Unit 2 – Multiplication Lesson B

TWO-DICE BINGO (CONTINUED)


Unit 2 Lesson B

TWO-DICE BINGO

Positive

Positive

Negative

Negative


Unit 2 Lesson B

TWO-DICE BINGO

1 2-3

-12 -10 -8

-18

-1

5 6 8

20 24 25

-4

-15

-6

-1624-30

12

30 36

Free Space

9

-24 -20 -18

-12 -9 -8

-4 -3

4 5 8

15 16 20

-16 -15

-6 -5

-2 3

9 12

24 25

Free Space

-36 -30 -24

-15 -10 -9

-5 -4

-1 2 3

9 12 16

-20 -16

-8 -6

-3 -2

4 8

24 36

Free Space 2 4-3

-12 -10 -6

-24

-1

5 9 10

16 18 20

-4

-15

-5

-16-30-36

15

24 30

Free Space

12


Unit 2 Lesson B

TWO-DICE BINGO

-36 -25 -20

-12 -9 -6

-3 -1

3 5 6

10 15 18

-16 -15

-5 -4

1 2

8 9

25 30

Free Space

-30 -24 -18

-9 -8 -6

4 5

9 10 12

18 20 24

-12 -10

-4 -3

6 8

15 16

30 36

Free Space

-36 -20 -18

-12 -10 -8

-4 -3

2 3 4

15 16 25

-16 -15

-6 -5

-2 1

9 10

30 36

Free Space

-36 -24 -20

-12 -10 -9

-3 1

6 8 9

16 24 25

-16 -15

-8 -6

2 5

10 12

30 36

Free Space


Unit 2 Lesson B

TWO-DICE BINGO

-36 -30 -20

-12 -10 -6

-3 1

5 8 9

16 18 25

-16 -15

-5 -4

3 4

10 15

30 36

Free Space

-24 -20 -18

-12 -6 -5

-2 -1

3 6 8

16 18 20

-16 -15

-4 -3

-1 2

9 15

24 36

Free Space

Free Space

TEMPLATE FOR MAKING UP YOUR OWN

TWO-DICE OR THREE-DICE BINGO CARDS


Unit 2 Lesson B

TWO-DICE BINGO

TWO-DICE BINGO CALLER CARD

-36 -30 -25

-16 -15 -12

-6 -5 -4

1 2 3

8 9 10

18 20 24 25 30 36

-24 -20 -18

-10 -9 -8

-3 -2 -1

4 5 6

12 15 16


Unit 2 Lesson B

TWO-DICE BINGO CALLER LIST

1. ________ X ________ = ________

2. ________ X ________ = ________

3. ________ X ________ = ________

4. ________ X ________ = ________

5. ________ X ________ = ________

6. ________ X ________ = ________

7. ________ X ________ = ________

8. ________ X ________ = ________

9. ________ X ________ = ________

10. ________ X ________ = ________

11. ________ X ________ = ________

12. ________ X ________ = ________

13. ________ X ________ = ________

14. ________ X ________ = ________

15. ________ X ________ = ________

16. ________ X ________ = ________

17. ________ X ________ = ________

18. ________ X ________ = ________

19. ________ X ________ = ________

20. ________ X ________ = ________

21. ________ X ________ = ________

22. ________ X ________ = ________

23. ________ X ________ = ________

24. ________ X ________ = ________

25. ________ X ________ = ________

26. ________ X ________ = ________

27. ________ X ________ = ________

28. ________ X ________ = ________

29. ________ X ________ = ________

30. ________ X ________ = ________

31. ________ X ________ = ________

32. ________ X ________ = ________

33. ________ X ________ = ________

34. ________ X ________ = ________

35. ________ X ________ = ________

36. ________ X ________ = ________


Unit 2 Lesson B

THREE-DICE BINGO CALLER CARD

-216 -180 -150

-96 -90 -80

-50 -48 -40

-18 -16 -15

-5 -4 -3

4 5 6 8 9 10

-125 -120 -108

-75 -72 -64

-36 -32 -25

-12 -10 -9

-2 -1 1

-104 -100

-54

-20

-6

3

15

36

72

120

125 150 180 216

75 80 90 96 100 104 108

64

32

12

40 45 48 50 54 60

16 18 20 24 25 30

-60

-24

-8

2


MATERIALS• Two 12-part spinners numbered 1–12, one

per player• One pencil per spinner• One paper clip per spinner• Hundreds Chart• Pennies, tiles, or small paper circles, etc.,

100 per player• Copies of Hundreds Chart and

Spinner on activity sheets, pgs. 38–39

VOCABULARY

product

BEFORE THE COMPUTER

• Laminate the Hundreds Chart and Spinneractivity sheets, pgs. 38–39. Distribute aHundreds Chart, a Spinner, and a pile ofapproximately 100 pennies to each student.Have students work in pairs.

• To determine who will go first, each playercan spin his or her spinner. The highestnumber goes first.

• The first player spins both 12-part spinnersand calculates the product of the two num-bers. The player places a penny on his orher Hundreds Chart covering the product. Ifthe product is already covered by a penny,the player can stack another penny on top.The other player should check the multipli-cation for accuracy.

• If the product is larger than 100, it is a wildnumber. The player can choose any numberfrom 1 to 100 and cover it with a penny.

• Play continues until one player gets a stackof pennies three high on any number. Thewinner is the player who has the most cov-ered numbers (or the fewest uncoverednumbers). A number that is covered withtwo or more pennies only counts as one.

• Discuss which numbers cannot be coveredby the product of the spinner numbers.Discuss strategies for playing wild num-bers—products over 100.

• Teacher Notes: The following numbers can-not occur as the product of numbers on thespinners. They can only be chosen when awild number product occurs. There areforty-seven of them.13, 17, 19, 23, 26, 29, 31, 34, 37, 38,39, 41, 43, 46, 47, 51, 52, 53, 57, 58,59, 61, 62, 65, 67, 68, 69, 71, 73, 74,75, 76, 78, 79, 82, 83, 85, 86, 87, 89,91, 92, 93, 94, 95, 97, and 98

• The following numbers can occur as prod-ucts of numbers on the spinners. There arefifty-three of them.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 14,15, 16, 18, 20, 21, 22, 24, 25, 27, 28,30, 32, 33, 35, 36, 40, 42, 44, 45, 48,49, 50, 54, 55, 56, 60, 63, 64, 66, 70,72, 77, 80, 81, 84, 88, 90, 96, 99, and100

Unit 2 – Multiplication Lesson C

WILD NUMBERS


• The following numbers are wild numbers:108, 110, 120, 121, 132, and 144.

AT THE COMPUTER

• Reinforce student multiplication facts usingpositive and negative integers by findingthe matches in a given target range withCrater Crossing.


• Choose Crater Crossing, level 3, 4, or 7.

EXTENSION ACTIVITIES

• Play Wild Numbers using a 15-part spin-ner. Discuss which numbers are possiblespinner products. Which numbers are wildnumbers? How does this change the game?Does it make it longer, shorter, harder, oreasier?

Unit 2 – Multiplication Lesson C

WILD NUMBERS (CONTINUED)


Unit 2 Lesson C

WILD NUMBERS – SPINNER

1

23

45

67

89

1011

12


Unit 2 Lesson C

WILD NUMBERS – HUNDREDS CHART

1 2 3 4 5 6 7 8 9 10

20

30

40

50

60

70

80

90

1009998979695

89

79

69

59

49

39

29

191817161514

24

34

25 26 27 28

38373635

4847464544

54 55 56 57 58

64 65 66 67 68

7877767574

84 85 86 87 88

94939291

81 82 83

71 72 73

61 62 63

51 52 53

41 42 43

31 32 33

21 22 23

11 12 13


Unit 3: Division

Division involves separating things into equal groups or fair shares. Division hasconnections to both multiplication and repeated subtraction. Although calculatorshave relieved students of the necessity of dividing with very messy divisors or dividends, it is still important to understand the concept of division and to have a successful strategy that will work if a calculator is unavailable. In this unit, students will divide with whole numbers, fractions, and decimals. They will also dogeometric division.

LESSON A – AS EASY AS APPLE PIE

Curriculum Focus: Geometric DivisionRecommended Grade Levels: Grades 3–4Lesson Duration: 45 minutes (approximate time)Objectives: Students will divide a circle into equal parts using a

protractor.

LESSON B – DIVISION OF FRACTIONS

Curriculum Focus: Division of FractionsRecommended Grade Levels: Grades 5–6Lesson Duration: 45 minutes (approximate time)Objectives: Students will strengthen their understanding of the

concept of division of fractions by creating and completinggraphical equations.

LESSON C – DIVIDE AND CONQUER: FINDING AVERAGES

Curriculum Focus: Addition, Division, AveragingRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutes (approximate time)Objectives: Students will use addition and division to find averages

of real-world data.


MATERIALS

• Copies of Round Pies activity sheet,pg. 43

• Copies of Square Cakes activity sheet,pg. 44

• Protractor• Ruler• Dice, two per pair of students

VOCABULARY

fair share degrees

BEFORE THE COMPUTER

• Have students work with a partner.Distribute Round Pies activity sheet, pg. 43, and dice to each pair of students.Explain the rules of one or both games.

• Game 1: Roll two dice to determine howmany people will share one round applepie. The sum of the numbers on the dicerepresents the number of people. Use a protractor to measure fair shares. Draw fair shares.

• Game 2: Roll a die to determine how manypies. Roll two dice to determine how manypeople will share the pies. The sum of thenumbers on the dice represents the numberof people. Use a protractor to measure fairshares. Draw fair shares.

AT THE COMPUTER

• Students can explore the use of filling inmultiplication and division puzzles to rein-force the link between the two concepts,and practice mental math skills.


• Choose Cube Quest, level 3 or 4.

AFTER THE COMPUTER

• Game 3: Roll two dice to determine howmany people will share one square choco-late cake. Distribute copies of Square Cakesactivity sheet, pg. 44. The sum of the num-bers on the dice represents the number ofpeople. Show several different ways todivide a cake into the indicated number offair shares, if possible.

Unit 3 – Division Lesson A

AS EASY AS APPLE PIE


Unit 3 Lesson A


ROUND PIES


Unit 3 Lesson A


SQUARE CAKES


MATERIALS

• Fraction pieces• Protractors• Scissors• Markers• Poster board• Copies of Division of Fractions activity


VOCABULARY

product

BEFORE THE COMPUTER

• Using Division of Fractions activity sheet,pg. 46, have students build three modelseach of 1/2, 1/3, 1/4, 1/5, 2/3, and3/4. Use a circle to represent one whole.

• Display and label one model of the frac-tions on poster board.

• Complete the first column of the Division ofFractions activity sheet, pg. 47, by dividingeach of the fraction pieces by 2. Display theresulting models and answers on the activitysheet.

• Complete the second column of the Divisionof Fractions activity sheet, pg. 47, bydividing each of the fraction pieces by 3.Display the resulting models and answerson the activity sheet.

• Complete the Division of Fractions activitysheet, pg. 48, by dividing a fraction by afraction, then create your own equations onactivity sheet, pg. 49.

AT THE COMPUTER

• Students experiment with bridge planks tounderstand how fraction pieces can be puttogether to create whole units.


• Choose Bridge Builder, Level 1, 2, or 3.

AFTER THE COMPUTER

• Have students try to make whole units withfractions such as 2/5, 3/5, 4/5, 1/6, 5/6,1/7, 1/8, 3/8, 5/8, and 7/8. Discuss dif-ferent strategies students used to makewhole units from a set of fractions.

Unit 3 – Division Lesson B

DIVISION OF FRACTIONS


12

Unit 3 Lesson B

DIVISION OF FRACTIONS NAME ____________________

Using the circle to represent one whole, draw a model of each of the following fractions:

13

14

15

23

34


=.. 2

=.. 2

=.. 2

=.. 2

=.. 2

34

15

12

13

23

Unit 3 Lesson B


23

14

=.. 3

=.. 3

=.. 3

=.. 3

=.. 3

13

12

34

Draw a model of each dividend and each quotient. Label the quotient model with the correct answer.

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:

Answer:


Unit 3 Lesson B


12

12 =..

12 =..

12 =..

12 =..

12 =..

13

34

23

1

Remember, division by 1/2 means how many times does 1/2 go into the dividend? Draw a modelof each dividend and each quotient, and label the quotient model with the correct answer.


Unit 3 Lesson B


=..

=..

=..

=..

=..

Make up five original division problems using fractions. Solve the division problems and draw mod-els of each dividend and quotient.


MATERIALS

• Divide and Conquer: Finding AveragesData Recording activity sheet, pg. 51

VOCABULARY

average mean medium

BEFORE THE COMPUTER

• Divide the class into small groups. Eachgroup of students selects five survey ques-tions that have numeric answers. Using theData Recording activity sheet, pg. 51, sur-vey the class and record the responses.Students may use some of the followingsample questions or create survey questionsof their own.

√ How many hours of television do you watch per week?

√ How tall are you?

√ What is your shoe size?

√ How many brothers and sisters do you have?

√ Surveying only students wearing shoeswith laces, ask how many lace

holes are in a shoe?

√ How many books do you own?

√ How many years have you lived in this state?

√ What time do you usually wake up on Saturday morning or go to sleep onFriday night?

• Have students find the class averageanswer to their survey questions. If neces-sary, remind them to add all their numbersand then divide by the number of studentssurveyed. Encourage students to keep anorganized list of their data and show theircalculations where appropriate.

AT THE COMPUTER

• Use The Cruncher Blaster program to makea spreadsheet. In the first column use how-ever many rows necessary to list the indi-viduals or the different questions in the sur-vey. Show students how to use the sumfunction to get a total and the average func-tion to see the mean.

• Create a picture graph or bar chart byhighlighting the data you would like to dis-play. Then, select chart from the optionsmenu.

AFTER THE COMPUTER

• Have students analyze the data and sharetheir findings either individually or in smallgroups depending on the topics chosen.

Unit 3 – Division Lesson C

DIVIDE AND CONQUER: FINDING AVERAGES


Unit 3 Lesson C

DIVIDE AND CONQUER: FINDING AVERAGES

DATA RECORDING

IntervieweeQuestion=

1Question=

2Question=

3Question=

4Question=

5Question=

6Question=

7

1.

TOTALS

AVERAGE

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.


Unit 4: Fractions

Fractions are a very important part of mathematics in the real world. In theselessons, students will use fractions in a variety of settings. They will be introduced toadding, subtracting, and comparing fractions. They will make connections betweenarea, time, and fractions.

LESSON A – FRACTIONS QUILT

Curriculum Focus: Geometric Patterns with FractionsRecommended Grade Levels: Grades 3–5Lesson Duration: 45 minutes (approximate time)Objectives: Students will divide a square into various fractional

parts. They will recognize that the sum of the fractions in this activity is always one.

LESSON B – FRACTION WAR

Curriculum Focus: Comparing FractionsRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutes (approximate time)Objectives: Students will play a fraction game similar to the card

game War. Students will compare fractions and identify equivalent fractions.

LESSON C – ELAPSED TIME

Curriculum Focus: Subtraction, Fractions of TimeRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutes (approximate time)Objectives: Students will use subtraction to find elapsed time. They

will make connections between time and fractions of an hour.


MATERIALS

• 6" x 6" squares white paper• Ruler• Pencil• Crayons, markers, or colored pencils• 7.5" x 7.5" construction paper squares• Copies of sample Fraction Quilt activity


VOCABULARY

fraction

BEFORE THE COMPUTER

• Discuss What combinations of fractions addup to one whole? Have students record allcorrect combinations like this:1/3, 1/3, 1/31/2, 1/21/2, 1/4, 1/41/2, 1/4, 1/8, 1/81/3, 1/3, 1/6, 1/61/2, 1/3, 1/61/2, 1/4, 1/8, 1/16, 1/161/4, 1/4, 1/8, 1/8, 1/4

• Distribute two 6" x 6" white paper squares,see pg. 58, to each student. Have each stu-dent decide upon a set of fractions that addup to one whole and illustrate those frac-tional parts in two different ways on thepaper squares. You may wish to use frac-tion combinations that are limited to thefractions 1/2, 1/4, and 1/8 for the firstfraction quilt squares.

• Show Fraction Quilt activity sheets, pgs. 55–58, as examples.

• First, have students divide their 6" x 6"square into the designated fractional parts.Have students exchange their designs andcheck for accuracy. Then, have studentslabel and color each fraction section.

AT THE COMPUTER




• You may want to start with Level 1 (commondenominators) to show the relationshipbetween using a set number of pieces witha given denominator and how the fractionsof that denominator need to be groupeddepending on the objective.


• Make fraction quilts using combinations thatinclude 1/3, 1/5, or 1/6.

• Challenge students to find how many different ways they can illustrate any combination of fractions that equal one.

Unit 4 – Fractions Lesson A

FRACTION QUILT


Unit 4 Lesson A

FRACTION QUILT

14

18

182

1

14

18

18

21

QUILT B

QUILT A


14

18

21

18

14

18

21

18

QUILT C

QUILT D


Unit 4 Lesson A

FRACTION QUILT

14

18

21

18

18

21

18

41

QUILT E

QUILT F


6 "

6 "


Unit 4 – Fractions Lesson B

FRACTION WAR

MATERIALS

• Copies of Fraction War activity sheet, pg.61, to make one deck for each pair of students

VOCABULARY

equivalent reduced simplest form

BEFORE THE COMPUTER

• You may wish to laminate the fraction cardsfor durability (see Fraction War activitysheet, pg. 61).

• Have each student work with a partner.Distribute a deck of 36 fraction cards toeach pair of students. Have one studentfrom each pair shuffle the cards, then dealthe entire deck. Play according to the rulesof the card game War.

• Each student holds his or her pile of cardsfacedown. Both partners simultaneouslyplace their top card on the table faceup.The student who placed the card with thelargest fraction takes both cards.

• If the two fraction cards are equivalent, thenthere is a war. Two additional pairs of cardsare placed facedown, and the fourth pair ofcards goes faceup for comparison. The stu-dent with the highest fourth card collects alleight cards. The game ends when time is upor when one partner has lost all his cards.The partner with more cards is the winner.

AT THE COMPUTER




• Levels 6 and 7 link the concept of fractionswith their equivalent percent and decimal,respectively.

• Students need to build bridges of wholeunits using a certain number of pieces fromthe combination set provided.

EXTENSION ACTIVITY

• Play Fraction Fish, using a copy of FractionFish activity sheet, pg. 62.

• Play according to the rules of Fish. Havestudents play in small groups of 3–5 stu-dents per group. Have the dealer shuffle thecards and deal five to each player. Theremaining cards go facedown in the fishingpile.

• Each player tries to collect books consistingof four equivalent fractions. Play begins atthe left of the dealer and continues in aclockwise direction. The first player may askany another player to, “Give me your... ,”followed by the name of any card in his


hand using simplest fraction form.

• For example, “Give me your one-thirds.” If the player receives one or more cards, hemay continue asking for more fractioncards. If the player being asked for cardsdoes not have any of the fraction equiva-lents, he says, ”Go Fish.“ The first playerthen takes the top card from the fishing pileand the next player takes a turn.

• If any player gets four equivalent fractioncards, it is a book and goes facedown infront of the player. Play continues until anyone player is out of cards. The winner is theplayer who has the most books.


FRACTION WAR (CONTINUED)


12

999999

3 3 4 4 4

5 5 5 5 6 6

6 6 6 7 7 7

7 7 7 8 8 8

8 8 8 9 9

1 2 1 2 3

1 2 3 4 1 2

3 4 5 1 2 3

4 5 6 1 2 3

4 5 6 78

1 2

876543

Unit 4 Lesson B

FRACTION WAR


Unit 4 Lesson B

FRACTION FISH

12

20151052015

4 6 8 3 6

9 12 3 6 9 12

4 8 12 16 4 8

12 16 5 10 15 20

5 10 15 5 10

2 3 4 1 2

3 4 2 4 6 8

1 2 3 4 3 6

9 12 1 2 3 4

2 4 6 820

3 6

161284129


MATERIALS

• Two copies of Clock Spinner activity sheet,pg. 64

• Large paper clip and small paper clip foreach spinner

• Copies of Recording Data activity sheet, pg. 65

VOCABULARY

elapsed time

BEFORE THE COMPUTER

• Students can do this activity individually or in pairs.

• Use copies of Clock Spinner activity sheet,pg. 64, one for AM and one for PM to maketwo spinners. Use a large paper clip for theminute hand and a small paper clip for thehour hand.

• Students take turns spinning each spinnerone time. Record the AM and PM times onthe Recording Data activity sheet, pg. 65.

• Use copies of Recording Data activity sheetto calculate the elapsed time from AM to PM.Also calculate the elapsed time from pm toam. Round off your answers to the nearestfive minutes. Convert your answers fromhours and minutes to hours and fractions ofhours. For example, 7 hours 20 minuteswould be 7 1/3 hours, and 8 hours 25minutes would be 8 5/12 hours.

AT THE COMPUTER




• These levels link the concept of fractionswith their equivalent percent or decimal.Some levels combine all three elementstogether.

• You may want to choose a content level thatlinks fractions with decimals and discusshow we communicate the vocabulary ofelapsed time: quarter of an hour, half anhour, etc.


• Ask students to add the elapsed times fromam to pm to the corresponding time frompm to am. Ask if they can find anddescribe a pattern.

Unit 4 – Fractions Lesson C

ELAPSED TIME


Unit 4 Lesson C

ELAPSED TIME – CLOCK SPINNER (NEED 2)

121

2

3

4

56

7

8

9

10

11


Unit 4 Lesson C

ELAPSED TIME RECORDING DATA

Hour =HourFraction of=

an HourMinutes

1

2

3

4

5

6

7

8AM

PM

AM

PM

AM

PM

AM

PM

AM

PM

AM

PM

AM

PM

AM

PM


Unit 5: Decimals and Percents

Decimals and percents are used with increasing frequency as calculators and computers have become so accessible. Decimals and percentages give us ways to describe numbers that are between two whole numbers. It is important for students to be able to make connections between fractions, decimals, and percents so they will develop a strong number sense.

LESSON A – DECIMAL AND PERCENT WAR

Curriculum Focus: Comparing Decimals and PercentsRecommended Grade Levels: Grades 3–4Lesson Duration: 45 minutes Objectives: Students will compare decimals, percents, and fractions, as

well as make connections between all three related number types.

LESSON B – HONEY, I SHRANK THE ELEPHANT

Curriculum Focus: Scale Models, Similarity, Percents, GeometryRecommended Grade Levels: Grades 4–5Lesson Duration: Two 45-minute sessions (one in class, one homework)Objectives: Students will illustrate a common percent using visual images.

LESSON C – MAKING THE GRADE

Curriculum Focus: PercentsRecommended Grade Levels: Grades 6–7Lesson Duration: 45 minutes Objectives: Students will calculate percentages using real-world data

in a realistic setting.


MATERIALS

• 16 Decimal cards – Use copies of Decimaland Percent War Cards activity sheet, pg. 69

• 20 Percent cards – Use copies of Decimaland Percent War Cards activity sheet, pg. 70

• 36 Fraction cards (optional) from Unit 4,pgs. 61–62

VOCABULARY

decimal percent

BEFORE THE COMPUTER

• Prepare the deck of cards using copies of Decimal and Percent War Cards activitysheet, pgs. 69–70. You may wish to lami-nate the cards for durability.

• Have students work in pairs or threesomes.Give one deck of Decimal War Cards andone deck of Percent War Cards to eachpair or group. Have them shuffle and dealout all the cards.

• Have each student work with a partner.Distribute a deck of 36 Decimal and PercentWar Cards to each pair of students. Haveone student from each pair shuffle thecards, then deal the entire deck. Play usingthe rules of the card game War.

• Each student holds his or her pile of cardsfacedown. Both students simultaneously

place the top card on the table faceup. Thestudent who placed the card with the largestnumber takes both cards.

• If the two cards are equivalent, then there isa war. Two more cards are placed face-down by each player, and the fourth cardgoes faceup for comparison. The studentwith the highest fourth card collects all eightcards. The game ends when time is up orwhen one partner has lost all his cards. Thepartner with more cards is the winner.

AT THE COMPUTER

• Use Bridge Builder to strengthen students‘understanding of how decimals and per-cents are linked. Students will build wholebridge units using a certain number ofbridge plank pieces—a mixture of decimalsand percents.




• Add fraction cards to the deck and playWar using fractions, decimals, and per-cents.

• Return to the computer and challenge stu-dents again with Bridge Builder. This timealso explore levels 6 and 7.

Unit 5 – Decimals and percents Lesson A

DECIMAL AND PERCENT WAR


Unit 5 Lesson A


.25 .33 .5 .66

.75 .375 .625 .1

.2 .3 .4 .5

.6 .7 .8 .9

... ...


Unit 5 Lesson A


10% 15% 20%

30% 40%

50% 60%

70% 80%

90% 100%95%85%

75%65%

55%45%

35%25%

5%


MATERIALS

• Copies of Honey, I Shrank the Elephant!activity sheets, pgs. 72–73

• Blank drawing paper• Centimeter ruler• Pencil and eraser

VOCABULARY

percentage scale lengthwidth area

BEFORE THE COMPUTER

• Give each student copies of Honey, IShrank the Elephant! activity sheets, pgs.72–73. Have each student choose a per-centage ranging from 30% to 70% in multi-ples of 10. They will be making a scaledrawing of their worksheet illustration at areduced size.

• Have students draw a grid of squares onthe original illustration worksheet. Eachsquare should measure approximately 3–4 square centimeters. Then draw a grid,at the reduced size they previously selected,on the blank drawing paper. Label thepaper with the percentage reduction theyhave chosen.

• Using the square grids as guides, studentsshould try to duplicate the original illustra-tion at a reduced size. Have studentsdescribe, orally or in writing, how they

determined their grid measurements andhow they made their reduced-size drawings.

AT THE COMPUTER

• Use Bridge Builder to strengthen students’understanding of how decimals and per-cents are linked. Students will build wholebridge units using a certain number ofbridge plank pieces—a mixture of bothdecimals and percents.


• Choose Bridge Builder, levels 5, 8 or 9.

EXTENSION ACTIVITY

• Make enlarged illustrations from 130% to 200%.

• Have students compare the lengths, widths,and areas of their illustration grids. Discuss,for example, whether the area is reduced to1/4 or 25% of the original illustration if thelength and width are reduced to 50%. If thelength and width are reduced to 40%, thearea is reduced to 16% of the original.

• Use a photocopy machine to generate several different-sized versions of one illustration. Have students try to determinethe scale and justify their conclusions.

Unit 5 – Decimals and Percents Lesson B

HONEY, I SHRANK THE ELEPHANT!


Unit 5 Lesson B



Unit 5 – Decimals and Percents Lesson C

MAKING THE GRADE

MATERIALS

• Copies of Making the Grade activity sheets,pgs. 75–76

• Calculator

VOCABULARY

average percent

BEFORE THE COMPUTER

• Facilitate a class discussion about different ways teachers can calculate grades(e.g., averages, percents, total points,observation).

• Explain to the students that they will be calculating the grades of six students byfinding percentages. 90% and up will beconsidered an A, 80% to 89% will be considered a B, 70% to 79% will be consid-ered a C, and so on.

• There are different ways to calculate thegrades. One possibility is to find a percent-age for each test, then average all five per-centages. Another possibility is to add eachstudent’s scores to get his or her total points,then divide by the total possible points andconvert to a percentage. Discuss with yourclass how you calculate grades.

• Decide how the students should calculatethe grades. Distribute copies of Making theGrade activity sheets, pgs. 75–76.

• Have students calculate a percentage foreach student and a letter grade. Also, havestudents find the average score for each testand convert that average to a percentage.

• Students can use data from their own class-work, homework, or test scores. You mayalso wish to use some sample data.

AT THE COMPUTER

• Use Bridge Builder to strengthen students’understanding of how decimals and per-cents are linked. Students will build wholebridge units using several plank pieces—amixture of both decimals and percents.


• Choose Bridge Builder, levels 5, 8 or 9.


• Calculate each student’s grade in two different ways. Are the grades the samewhen calculated in different ways? Why orwhy not?

• Use The Cruncher Blaster project, Makingthe Grade. Have students list subjects andinput test and homework assignments inwhatever point or grade system your schooluses. Have them use the average function tocalculate where they are in each subjectarea based on your school’s grade scale.


Unit 5 Lesson C

MAKING THE GRADE

1

2

3

4

5

6

Name

ASSIGNMENTS

Amy Able

Sam=Eraisord

Grades 1 2 3 4 5

Possible =Score

=

WORKSHEET 1

Ida Hofalls

Pat E. =Cake

Dot Urize

Mark =Mywerds

50 60 30 40 50

45 45 25 35 42

50 50 20 30 40

40 60 30 40 47

48 55 28 32 30

20 40 27 20 45

25 56 18 35 33

1

2

3

4

5

6

Name

ASSIGNMENTS

Hope =Forfame

Earl E. =Tubed

Grades 1 2 3 4 5

Possible =Score

=

WORKSHEET 2

L. F. Ator

Fran Tick

Tom Oro

Phil Ittup

40 20 50 40

25 38 15 45 25

20 37 16 48 35

22 34 17 43 30

23 24 18 40 32

28 29 19 35 27

29 30 13 28 31

30


Unit 5 Lesson C

MAKING THE GRADE

1

2

3

4

5

6

NAME

ASSIGNMENTS

B. Goode

I. M. Smart

Grades 1 2 3 4 5

Possible=Score

=

WORKSHEET 3

Mary Me =Pleese

Ann =Talope

Al Igator

Candy =Kane

40 50 30 30

15 35 49 25 27

18

20

18

19

17

20

40

25

35

38

33

49

30

42

44

45

30 26

30

25

10

28

18

20

25

30


Unit 6: Operations with Integers

Integers, including all whole numbers and their opposites, are used in many practi-cal applications. Temperatures, financial reports, and football yardage are just threeexamples of real-world applications of positive and negative integers. In the follow-ing lessons, students will use integers to add, subtract, multiply, and divide.

LESSON A – GOOD GUYS AND BAD GUYS

Curriculum Focus: Multiplication and Division with IntegersRecommended Grade Levels: Grades 3–4Lesson Duration: 45 minutes Objectives: Students will multiply and divide with integers.

LESSON B – SONG SURVEY

Curriculum Focus: Operations with IntegersRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutesObjectives: Students will add positive and negative integers.

LESSON C – JEOPARDY!Curriculum Focus: Addition and Subtraction of IntegersRecommended Grade Levels: Grades 6–7Lesson Duration: 45 minutesObjectives: Students will add and subtract dollar amounts and

calculate final scores.


MATERIALS• 3" x 5" cards, eight per student• Markers – dark colors, medium to wide tip,

one per student• Copies of Operations With Integers

activity sheet, pg. 81

VOCABULARY

positive negativeproduct integer

BEFORE THE COMPUTER

• Tell students the following tale and havethem follow along Good Guys or Bad Guysactivity sheet, pg. 80.

• Introduce story by telling the students:If positive means ”good“ and negativemeans ”bad,” and coming to town is positive (good), and leaving town is negative (bad), then the rules of the OldWest are consistent with the rules for multiplication of integers.

• Have pairs of students use the set of fourflash cards provided in Good Guys or BadGuys activity sheet, pg. 80. Each studentshould take a turn selecting two cards andcreating an equation that follows the rulesof the cards. The student should check hisor her partner's work.

• Have students do the Operations withIntegers–Multiplication section of the activitysheet, pg. 81. Ask them to write or describethe problem type (1–4) beside each of theiranswers. Have them compare and discusstheir answers with small groups of theirclassmates.

• Have students make flash cards of multipli-cation problems. Each student should maketwo problems of each type (1–4). Havethem write the problem on one side of the3" x 5" card and the answer on the backusing bold and/or dark markers. They mayalso wish to label their own flash cards withtheir name in small print on the answerside.

• Have students quiz themselves and eachother using their flash cards.

• Divide students into groups of 4–5 each.Have each group of students play the FlashCard Game. One student is the card holderand all the other students in the group dothe mental math.

• After the card holder reveals a flash cardproblem, the first student to say the correctanswer receives the flash card. Play contin-ues until all cards are gone from the cardholder’s hand.

• The winner is the person who has receivedthe most flash cards. That person can turn

Unit 6 – Operations with Integers Lesson A

GOOD GUYS AND BAD GUYS


in his/her pile of flash cards to the cardholder and play can continue to determinesecond and third place. Additional gamescan be played with a new card holder.

AT THE COMPUTER

• Provide reinforcement of multiplying anddividing with positive and negative integersusing the Crater Crossing activity.


• Choose Crater Crossing, levels 7, 8, or 10.


• The rules for division of integers are thesame as those for multiplication. Have students do the Operations withIntegers–Division section of the activitysheet, pg. 81. Then have students makedivision flash cards and play the Flash CardGame.

Unit 6 – Operations with Integers Lesson A

GOOD GUYS AND BAD GUYS (CONTINUED)


When the good guys come to town, it’s good. • Type 1: Positive x Positive = Positive

When the bad guys come to town, it’s bad. • Type 2: Negative x Positive = Negative

When the good guys leave town, it’s bad. • Type 3: Positive x Negative = Negative

When the bad guys leave town, it’s good. • Type 4: Negative x Negative = Positive

Unit 6 Lesson A

OPERATIONS WITH INTEGERS NAME__________________________

GOOD GUYS OR BAD GUYS

Imagine a dirt road through a small town with a postoffice on the left and a general store on the right. A coupleof horses are tied to a hitching post outside the blacksmith’scorral. Men in cowboy hats and women in long skirts moseyabout their business, when off in the distance a cloud of dustappears. Four horsemen are heading into town. The towns-people look concerned as they wonder, are they good guysor are they bad guys?

good g

uys

bad g

uys

com

ing t

oto

wn

leavin

g t

ow

n


Integer Multiplication WorksheetSolve each multiplication problem.

Type of Problem

3 x (–7) = _____ ____________

9 x 9 = _____ ____________

(–7) x (–6) = _____ ____________

–4 x 5 = _____ ____________

7 x (–5) = _____ ____________

–8 x 2 = _____ ____________

4 x 7 = _____ ____________

(–3) x (–8) = _____ ____________

–6 x 5 = _____ ____________

6 x (–9) = _____ ____________

7 x 8 = _____ ____________

(–4) x (–9) = _____ ____________

Integer Division WorksheetSolve each division problem.

Type of Problem

21 ÷ (–7) = _____ ____________

81÷ 9 = _____ ____________

(–42) ÷ (–6) = _____ ____________

–20 ÷ 5 = _____ ____________

35 ÷ (–5) = _____ ____________

–18 ÷ 2 = _____ ____________

45 ÷ 9 = _____ ____________

(–24) ÷ (–8) = _____ ____________

–30 ÷ 6 = _____ ____________

54 ÷ (–9) = _____ ____________

56 ÷ 8 = _____ ____________

(–63) ÷ (–9) = _____ ____________

Unit 6 Lesson A

OPERATIONS WITH INTEGERS NAME ____________________

• Type 1: Positive x Positive = Positive

• Type 2: Negative x Positive = Negative

• Type 3: Positive x Negative = Negative

• Type 4: Negative x Negative = Positive


MATERIALS

• Radio or cassette player • Cassette tapes• Copies of Song Survey activity sheet,

pg. 83

VOCABULARY

positive negative

BEFORE THE COMPUTER

• Prepare to play approximately ten songs forstudents to rate on a scale of –10 to +10.

Explain the rating scale as follows:–10 Strongly Dislike the Song

–5 Moderately Dislike the Song0 OK Song5 Moderately Like the Song

10 Great Song

• Numbers in between these benchmark num-bers can also be used to rate the songs.

• Distribute copies of Song Survey activitysheet, pg. 83. Play a portion of each songand have students rate the songs.

• Divide students into small groups of 4–8 stu-dents. Have them add the scores for eachsong. Compile a group rating sheet of totalrating points or average rating points. Leteach group decide and explain how theywill determine the group rating for each

song. Have a representative from eachgroup report to the class on the group’sfindings. The report should include a clearexplanation of how the songs were rated.

AT THE COMPUTER

• Use The Cruncher Blaster so each team of students can input and chart their data.Their are several different ways studentsmight determine their ratings. Have thembrainstorm as a team how to input and dis-play the data. Assist them with spreadsheetsetup once each team’s plan has beenreviewed with you. You might want them tolay it out on paper first.

• Once all data has been input, have them add a pie or bar graph to theirspreadsheet.

• Have each team print out their spreadsheetfor a classroom presentation.


• Have each team take a few minutes to pre-sent their spreadsheet findings and describehow they arrived at their ratings.

• Determine the favorite song for the entireclass using the data collected in this activity.Have the class discuss and determine howthey will choose the song.

Unit 6 – Operations with Integers Lesson B

SONG SURVEY


Unit 6 Lesson B

SONG SURVEY NAME__________________________

Thumbs=Down

Cheezy

Weak==

Moderately=Dislike

OK

10

9

8

7

6

5

4

3

2

1

-10

-9

-8

-7

-6

-5

-4

-3==

-2

-1==

Awesome

Cool

Pretty=Great

Moderately=Like

0

Song Title

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

TotalsSCORES


MATERIALS

• Jeopardy class game board (See JeopardyGame Boards activity sheets, pgs. 91–92.)

• Jeopardy category cards and questioncards (See Sample Game Questions activitysheets, pgs. 86–90.)

• Scotch tape• 3" x 5" cards (for creating your own

customized questions)• Red, yellow, and blue RIGHT and WRONG

cards• Start-up cards: 1st, 2nd, 3rd. (See

Jeopardy Game Right or Wrong activitysheet, pg. 93.)

VOCABULARY

jeopardy

BEFORE THE COMPUTER

• Create a poster-size Class Game Boardand laminate it. See Jeopardy GameBoards activity sheets, pgs. 91–92.

• You will need to run off approximately 25RIGHT and WRONG cards in all three col-ors. You can simplify and save paper bymaking the cards double-sided, with RIGHTon one side and WRONG on the oppositeside. Also, cut out three start-up cards,labeled 1st, 2nd, and 3rd. Laminate all thecards.

• You can use the prepared questions or youand your students can create customizedquestions of your own on 3" x 5" cards.

• Divide students into three teams of approxi-mately equal ability. Have students line upin the order in which they will attempt toanswer questions. Each student will attemptto answer one question, then go to the endof the line.

• Select one student to monitor the gameboard. All other students are responsible forkeeping track of the score. At the end of thegame, the student monitor will verify thescore, if necessary.

• Randomly choose five categories and tapethem at the top of the Game Board.

• Have one representative from each teamchoose a start-up card, 1st, 2nd, or 3rd, todetermine the order of play.

• Have the first player choose a category anda dollar amount, for example, FamousNames for $100.

• Read the question.

• The teacher or designated student will call on the first person to raise his hand. If the answer is correct, he adds the dollar

Unit 6 – Operations with Integers Lesson C

JEOPARDY!


Unit 6 – Operations with Integers Lesson C

JEOPARDY!

amount to the team's score. If the answer isincorrect, he subtracts the dollar amountfrom the team's score, and the remainingplayers can compete to answer the question.

• The last person to answer correctly gets toselect the next category and dollar amount.

• When the board is clear or when time isup, the team with the most money isdeclared the winner.

AT THE COMPUTER

• Provide students with the opportunity to explore using positive and negative inte-gers to fill in the third number of an equa-tion. With the higher levels of BananaSplat, students will have to add and sub-tract more than one integer to fill in themissing number.


• Choose Banana Splat, levels 5, 6, 8, or 9.These levels will give students practice withoperations using three integers, some posi-tive and some negative.


• Include additional categories on theJeopardy game board, such as MathHistory and Integers.

• Play Double Jeopardy!

• Divide the class into three teams instead of two.

• Category CardsAddition FractionsSubtraction DecimalsMultiplication PercentsDivision TimeMath History IntegersLogic Geometry


Unit 6 Lesson C

JEOPARDY! SAMPLE QUESTIONS – ADDITION

FRACTIONS

Addition• If there are 391 books at the library and 29 people return one book apiece, how many books

are there? [420]

• There were 24 people at a party when 13 more people arrived. How many total guests werethere at the party? [37]

• A football team gained 23 yards, lost 7 yards, and gained 15 yards on three consecutive plays.How many total yards did the team gain or lose after all three plays? [31]

• 148 fifth graders and 152 sixth graders attended a special assembly. How many fifth and sixthgraders attended in all? [300]

• Karen read a book with 268 pages on Tuesday and another with 214 pages on Friday. Howmany total pages did Karen read in the two days? [482]

Fractions• If you want to share 3 pies equally among 5 people, how much of a pie does each person get?

[three-fifths]

• Two-thirds of the chil dren in Mrs. Peeler’s classroom are girls. If Mrs. Peeler has 36 students,how many are girls? [24]

• 25 students out of 40 surveyed like chocolate ice cream. What fraction of students like choco-late ice cream? Give your answer in simplest form. [5/8]

• If a recipe calls for 1/2 cup of milk and you are making half the recipe, how much milk will youneed? [1/4 cup]

• Mary has 250 records in her collection. 200 of her records are rock and roll. What fraction ofher records is not rock and roll? Give your answer in simplest form. [1/5]


Unit 6 Lesson C

JEOPARDY! SAMPLE QUESTIONS – SUBTRACTION

DECIMALS

Subtraction• If there are 458 books at the library and 32 people check out one book apiece, how many

books are left? [426]

• There were 21 guests at a party when 5 people had to leave. How many people remained atthe party? [16]

• Rose planted 52 marigold seeds but only 37 plants grew. How many marigold seeds did notgrow into plants? [15]

• Randy had $20.00 to spend. He spent $18.52 on clothes. How much money did he have left?[$1.48]

• If 344 people attended a movie screening and 25 people left before the movie was over, howmany people stayed until the end of the show? [319]

Decimals• Strawberries cost $1.59 per pound. How much do 3 pounds of strawberries cost? [$4.77]

• A pair of overalls costs $28.99 before tax. If the sales tax is $2.32, what is the total cost of theoveralls. [$31.31]

• If you bought 5 pounds of apples for $.49 a pound, how much did you spend on apples?[$2.45]

• Sally had $5.00 to spend. She spent $4.19. How much money did she have left? [$.81]

• Linda earned $105.67 at her garage sale and her brother Larry earned $90.43. What aretheir combined earnings? [$196.10]


Unit 6 Lesson C

JEOPARDY! SAMPLE QUESTIONS – MULTIPLICATION

PERCENTS

Multiplication• In a movie theater there are 48 rows with 20 seats in each row. How many seats are there?

[960]

• If you and 4 friends go to the movies and admission is $7.25 apiece, how much will it cost forall of you to get in the movie theater? [$29.00]

• Jenny’s back yard is 60 feet long and 38 feet wide. How many square feet of back yard doesJenny have? [2,280 sq. ft.]

• The Smiths are building a patio that is 22 feet wide and 25 feet long. How big is the patio insquare feet? [550 sq. ft.]

• An airplane has 48 rows of seats. Each row has 12 seats. How many seats are in the airplane?[576]

Percents• A local department store is having a 25% off sale. How much will a shirt cost that was

originally priced at $22.00? [$16.50]

• If sales tax is 8%, what will the total cost of a $15.00 umbrella be including tax? [$16.20]

• A blouse is on sale for 30% off the marked price of $28.00. What is the sale price? [$19.60]

• Jane got a score of 80% on a test. If the test had 50 questions, how many did she miss? [10]

• There are 28 students in Mr. Clark’s class. 25% of them scored 100% on the last test. How manystudents scored 100%? [7]


Division• A company needs 1,000 bottle caps assembled. If 8 people are available to do the work, what

is a fair share for each? [125]

• If 5 people each have a winning lottery ticket and the jackpot is one million dollars, how muchmoney does each ticket holder get? [$200,000]

• A grocery store sold 1,848 eggs on Saturday. How many dozen eggs did it sell? [154]

• A grocery store sold 768 cans of soda over the weekend. How many six-packs of soda did it sell? [128]

• If a deck of 52 cards was dealt completely to 7 people, how many cards would each person get? [3 people would get 8 cards and 4 people would get 7 cards.]

Integers• If the temperature rises 26°, then drops 15°, what will the temperature be if it started out

at 76°? [87]

• A man earned $175.00 then lost $188.00 in the stock market. What was his net gain or loss?[loss –$13.00]

• If the temperature at night was 14° below zero, and it rose 29 degrees during the day, whatwould the high temperature be? [15°]

• If you earned $175, but you owed $82, how much money would you have earned after youpaid your debt? [$93.00]

• If a football quarterback was sacked for a 12-yard loss on first down and another 6-yard losson second down, how many yards would the team need to gain for a first down? (They must advance 10 yards from where they started for a first down.) [28 yards]

Unit 6 Lesson C

JEOPARDY! SAMPLE QUESTIONS – DIVISION

INTEGERS


Logic• Sally had $5.00 to spend on flower seeds. If pansy seeds cost 20 cents per package and

marigold seeds cost 50 cents per package, how many of each did she buy if she bought threemore marigold seed packs than pansy seed packs? [8 marigold and 5 pansy packages]

• There are three houses in a row owned by Bill, Patty, and Pete, not necessarily in that order. IfBill lives next door to Pete and Patty lives next door to Pete, who lives in the middle? [Pete]

• If an inchworm crawls up two inches then down one inch each hour, how long will it take theworm to crawl up to the top of a 12" hole? [11 hours]

• If Alan’s car is not working, Alan will take the bus. If Alan does not take the bus, what conclu-sion can you make? [Alan’s car is working.]

• 3 containers each contain two marbles—both black, both white, or one of each. If the 3 containers are labeled BW, BB, or WW, but none has the correct label, what is the smallestnumber of marbles you will need to pull from their containers in order to determine which con-tainers hold which marbles? [1... from the BW container. If it is black, then BW contains BB,WW contains BW, and BB contains WW. If it is white, then BW contains WW, WW containsBB, and BB contains BW.]

Geometry• The short sides of a right triangle measure 6 feet and 8 feet. How long is the third side?

[10 feet]

• What is the name of a geometric figure with four sides only, two of which are parallel? [trapezoid]

• What is the name for an angle which measures more than 90°? [obtuse]

• What is the name for a triangle with two congruent sides? [isosceles]

• What is the formula for finding the area of a triangle? [A = 1/2 bh]

Unit 6 Lesson C

JEOPARDY! SAMPLE QUESTIONS – LOGIC

GEOMETRY

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Unit 6

Lesson C

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Category 1 Category 2 Category 4 Category 5 Category 6Category 3

$100 $100$100 $100$100$100

$200

$300

$400

$500

$200

$300

$400

$500

$200

$300

$400

$500

$200

$300

$400

$500

$200

$300

$400

$500

$200

$300

$400

$500


Unit 6 Lesson C

JEOPARDY! GAME BOARD

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RIGHT RIGHTRIGHT

RIGHT

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RIGHT

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RIGHT

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WRONGWRONGWRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

WRONG

1st 2nd 3rd 3rd 2nd 1st


Unit 7: Logic

As students encounter real-life mathematical problems, they need to be able to think logically and make appropriate mathematical decisions. By providing students with logicgames and puzzles, we can help them acquire problem-solving skills and resources touse in their everyday lives.

LESSON A – TANGRAM PUZZLES

Curriculum Focus: Logic and Spatial ReasoningRecommended Grade Levels: Grades 3–4Lesson Duration: 45 minutes Objectives: Students will use tangrams to develop their spatial

reasoning and visualization skills.

LESSON B – THE ATTRIBUTION GAME

Curriculum Focus: ClassifyingRecommended Grade Levels: Grades 4–5Lesson Duration: 45 minutesObjectives: Students will classify and compare attributes in a game.

LESSON C – LOGIC PUZZLES

Curriculum Focus: Problem Solving and LogicRecommended Grade Levels: Grades 6–7Lesson Duration: Three 45-minute sessions Objectives: Students will solve logic puzzles using a variety of

problem-solving skills.


MATERIALS

• Tangram Worksheets, pgs. 98–102• Tangram Illustrations from the book

Grandfather Tang’s Story• Scissors• Plain paper• Resealable bags or envelopes

VOCABULARY

tangram parallelogram trapezoidright triangle right angleleg hypotenuse diagonalmidpoint perimeter areasquare

BEFORE THE COMPUTER

• Have students cut out tangram pieces fromthe Tangram Worksheet patterns. Discussthe geometric shapes using appropriatevocabulary terms and definitions.

• Challenge students to take their tangrampieces originally in the shape of a squareand reconstruct the square. Then ask themto create a rectangle from the pieces.

• Read the book Grandfather Tang’s Story byAnn Tompert. Show the illustrations to theclass. (You may wish to sketch the tangramillustrations on the board or on an over-head transparency.) Have students duplicatesome of the illustrations using their own tan-gram pieces.

• Have students write an original short storyand illustrate it with original tangram art.

• Have students create an original tangramdesign using all seven pieces. Have studentstrace the outer perimeter of their design onplain paper. Have students exchange theiroutlines with classmates and then try toplace their tangram pieces into their class-mates’ designs. There should be no gaps oroverlapping pieces.

• Make a book of the tangram shape outlinesthat students have created and place it in amath center along with a resealable bagfull of tangram pieces. If students can suc-cessfully fill a tangram design, they shoulddraw the design on their own sheet of plainpaper, showing each individual tangrampiece.

AT THE COMPUTER

• Have students explore cause and effect tounlock the rules each Blasterpal follows.


• Choose Cube Quest, math level 1 through10 (10 being the most difficult).

• You may choose to team students togetherto brainstorm as they experiment with eachpal. Can they guess the rules for what eachpal can activate and why?

Unit 7 – Logic Lesson A

TANGRAM PUZZLES



• Give each student a 6" x 6" square paper.

• Give them verbal directions for folding andcutting their seven tangram pieces.

Fold the square in half along the diagonal,creating two right triangles. Cut along thefold.

Fold one right triangle in half. Cut alongthe fold to create two right triangles. Setboth pieces aside.

Find the midpoint of the hypotenuse of theremaining large right triangle. Fold the ver-tex at the right angle so that it touches themidpoint of the hypotenuse. Cut along thefold. Set aside the small right triangle.

Take the remaining trapezoid and fold it inhalf. Cut along the fold. You will have twocongruent right trapezoids.

Fold one trapezoid to form a square and asmall right triangle.

Fold the other trapezoid to form a parallel-ogram and a small right triangle. Cut alongthe folds.

You should now have seven tangrampieces.

• Have students make original tangramdesigns using two sets of tangram pieces.

• Have students trace around the outerperimeter of their design on plain paper.Have students exchange outlines with theirclassmates and try to place their tangrampieces in the interior of their classmates’designs. There should be no gaps or over-lapping pieces.

• Have students make original tangramdesigns using from five to seven tangrampieces.

• To make the puzzles more challenging fortheir classmates to solve, do not have stu-dents state which shapes or how manypieces were used.

Unit 7 – Logic Lesson A

TANGRAM PUZZLES


Unit 7 Lesson A

TANGRAM PUZZLES


Unit 7 Lesson A

TANGRAM PUZZLES

FIGURE 1

FIGURE 2

FIGURE 3


Unit 7 Lesson A

TANGRAM PUZZLES

FIGURE 4

FIGURE 5

FIGURE 6


Unit 7 Lesson A

TANGRAM PUZZLES ANSWERS

FIGURE 1 FIGURE 2

FIGURE 3 FIGURE 4

FIGURE 5 FIGURE 6


MATERIALS

• 64 Attribute cards (See The Attribute Gameactivity sheets, pgs. 143–107.)

VOCABULARY

attribute characteristic

BEFORE THE COMPUTER

• This is a game for 2–4 players. Shuffle anddeal eight attribute cards to each player.Put the other cards facedown in a pile. Turnjust the top card faceup next to the pile.

• To play a card, a student must match atleast one attribute, shape, size, color, ornumber. Place your card faceup on top of the faceup pile.

• Play begins left of the dealer and continuesin a clockwise direction until one player isout of cards. That player is the winner.

AT THE COMPUTER

• Students can reinforce what they’ve learnedabout attributes and characteristics whilemaking monkeys in Monkey Maker.

• Students will complete attribute puzzleswhile following rules to make a certainnumber of changes from one monkey to the next.

• Students may work in pairs or individually.

• Have students sign in and select MonkeyMaker, level 1–10 (with 10 being the mostdifficult).

• The number of attributes that need to bechanged, as well as the number of monkeysin the puzzle, increases with difficulty.


• Have students play the Attribute Gameusing one of the following rules:

Students may play an attribute card if itmatches exactly one attribute.

Students may play an attribute card if itmatches two attributes.

• Have students play Attribute Solitaire, anattribute game for one person. Shuffle thedeck and place one card faceup. Try tomake the longest possible train. Go throughthe deck three cards at a time, looking onlyat every third card. You may attach a cardto the train if it matches one or more attrib-utes of the last faceup card. When a cardhas been played, you may look at the cardbelow it and play it if possible. If there is nomatch, continue going through the deckthree cards at a time. When you get to theend of the deck, begin again from the top.


THE ATTRIBUTE GAME



THE ATTRIBUTE GAME

Red

Red

Red

Red

Green

Green

Green

Green Yellow

Yellow

Yellow

Yellow Blue

Blue

Blue

Blue



THE ATTRIBUTE GAME

Red

Red

Red

Red

Green

Green

Green

Green Yellow

Yellow

Yellow

Blue

Blue

Blue

Blue

Yellow



THE ATTRIBUTE GAME

Red

Red

Red

Green

Green

Yellow

Yellow Blue

Blue

Blue

Red Green Yellow Blue

YellowGreen



THE ATTRIBUTE GAME

Red

Red

Red

Green

Green

Green Yellow

Yellow

Yellow Blue

Blue

Blue

Red Green Yellow Blue


MATERIALS

• Copies of Logic Puzzles Worksheet A activi-ty sheet, pg. 109

• Copies of Logic Puzzles Worksheet B activi-ty sheets, pgs. 110–111

BEFORE THE COMPUTER

• Choose a Problem of the Day from LogicPuzzles Worksheet A or Logic PuzzlesWorksheet B. Have small groups of studentstry to solve the problem and explain howthey arrived at their solution. Some prob-lems may take more than one day.

AT THE COMPUTER

• Have students explore cause and effect tounlock the “rules” each Blasterpal follows.

• Have students sign in and select Training.

• Choose Cube Quest, level 1 through 10 (10being the highest level of difficulty).

• You may choose to team students togetherto brainstorm as they experiment with eachpal. Can they guess the rules for what eachpal can activate and why?


• Create a logic puzzle of your own.

Unit 7 – Logic Lesson C

LOGIC PUZZLES



LOGIC PUZZLES WORKSHEET A

1. A big Indian and a little Indian are sitting inthe forest. If the little Indian is the son of thebig Indian, but the big Indian is not thefather of the little Indian, what is the rela-tionship between the two?

2. A man was put in jail and the sheriff toldhim that only close relatives were allowed tovisit. A stranger came to visit the prisonerand he told the sheriff:

“Brothers and sisters have I none.This man’s father is my father’s son.”

The sheriff thought for a moment, and thenlet the stranger visit the prisoner. Who wasthe stranger?

3. In a small town far away, there were threegroups of people. The first group alwaystold the truth, the second group always lied,and the third group sometimes told the truthand sometimes lied. One day, three men,one from each group, were talking, and astranger approached.

The stranger asked the man on the left,“What kind of man sits next to you?” “Aliar,” answered the first man.

“What kind of man are you?” the strangerasked the middle man. “I sometimes tell thetruth and sometimes I lie.”

“And what kind of man is next to you?” thestranger asked the man on the right. “Healways tells the truth,” replied the third man.

From this conversation, can you tell whichman belonged to which group?

4. A fireman stood on the middle step of aladder. As the smoke cleared, he climbed upthree steps. Then the smoke got worse, sohe had to climb down five steps. Then heclimbed up the last 6 steps and he was atthe top of the ladder. How many steps werein the ladder?

5. Some children are seated in a circle. Theyare evenly spaced and numbered in order.The 7th child is directly opposite the 17th.How many children are in the circle?

6. A total of 8 people were at a party. Eachperson shook hands exactly once with eachof the others. How many handshakes wereexchanged at the party?


1. Sally is having a party. The first time thedoorbell rings, one guest enters. The secondtime the doorbell rings, 3 guests enter. Thethird time the doorbell rings, 5 guests enter.If on each successive ring of the doorbell,the number of guests entering increases by2, how many guests will have arrived afterthe 20th ring?

2. At a local bank, the jobs of cashier, manag-er, and teller are held by Brown, Jones, andSmith, but not necessarily in that order. Theteller, who was an only child, earns theleast. Smith, who married Brown’s sister,earns more than the manager. Who haswhich job?

3. Arnold, Bill, and Carl left the theater togeth-er. Each was wearing the jacket and theshoes of someone else. Bill was wearingCarl’s jacket and Arnold’s shoes. Whosejacket and whose shoes were the other twowearing?

4. Eight men and two boys want to cross ariver using a small canoe. The canoe cancarry two boys or one man. How manytimes must the canoe cross the river to geteveryone to the other side?

5. A man buys a horse for $60, sells it for$70, buys it back for $80, and sells it for$90. How much does the man make or losein the horse trading business?

6. A farmer has a fox, a goose, and somecorn. They come to a river that they need tocross. They see a small boat that will holdjust the farmer and one other thing. The foxwill eat the goose if left alone. The goosewill eat the corn if left alone. How can thefarmer get all three things safely across theriver?

7. As I was going to St. IvesI met a man with seven wives.Every wife had seven sacks,Every sack had seven cats,Every cat had seven kittens.Kits, cats, sacks, wives,How many were going to St. Ives?

8. Alice in Wonderland wandered around inthe Forest of Forgetfulness where she wasunable to remember the day of the week. In the forest she met a lion and a unicorn.The lion lies on Monday, Tuesday, andWednesday. The unicorn lies on Thursday,Friday, and Saturday. At all other timesboth animals tell the truth.

“Yesterday was one of my lying days,” saidthe lion.

“Yesterday was one of my lying days, too,”said the unicorn.

Alice, who was very smart, was able todeduce the day. What day is it?


LOGIC PUZZLES WORKSHEET B


ANSWERS: WORKSHEET A1. Mother–son

2. The prisoner’s father

3. Left: Truth Teller,Middle: Liar, Right: Sometimes Tells Truth and

Sometimes LiesHint: Start with all six possible solutions andthen eliminate possibilities.

4. 9

5. 20

6. 28

ANSWERS: WORKSHEET B1. 400

2. Cashier: SmithManager: Brown Teller: Jones

3. Arnold—Bill’s jacket and Carl’s shoes,Carl—Arnold’s jacket and Bill’s shoes

4. The canoe will cross the river 33 times.1st trip: 2 boys cross over in the canoe.2nd trip: 1 boy stays on the bank, 1

boy returns in the canoe.3rd trip: 1 man crosses over in the

canoe alone.

4th trip: The boy on the bank returns inthe canoe leaving 1 man onthe bank. Both boys are nowtogether where they started.

Repeat the pattern 7 more times. End with33rd trip: 2 boys cross over in the canoe.

The 8 men and the 2 boys are now on the bank.

5. He makes $20.

6. 1st trip across: The farmer takes the gooseand leaves it on the other side. 1st trip back: Farmer comes back alone.

2nd trip across: The farmer takes the foxand leaves it on the other side. 2nd trip back: The farmer brings back thegoose.

3rd trip across: The farmer takes the cornand leaves the corn on the other side withthe fox.3rd trip back: The farmer comes backalone.

4th trip across: Farmer takes the goose.

7. One

8. Thursday


LOGIC PUZZLES ANSWERS

math blaster ages 9 12 - knowledge adventure

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