math blaster - knowledge adventure

1

© Vivendi Universal Publishing, its subsidiaries and/or licensors. All Rights Reserved.

MATH BLASTER®

CROSS TERRAIN

CHALLENGETEACHER’S GUIDE

™

092801

2


© Knowledge Adventure, Inc., an indirect subsidiary of Vivendi Universal Publishing, and its licensors.All rights reserved. Math Blaster is a registered trademark of Knowledge Adventure, Inc. All other trademarksare the property of their respective owners.

Author: Barbara Wood

Producer: Lori Fitzpatrick

Associate Producer: Tommi Johnson

Design and Layout: Laurie Galvan

Proofreader: Pamela Blanford

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

is strictly prohibited.

3


Table of Contents

Credits ................................................................................................................................ 2Welcome and Overview ...................................................................................................... 3Introduction to the Teacher ............................................................................................... 5Progress Chart ................................................................................................................... 7

RECALLINGMemory Walk ..................................................................................................................... 8

VISUALIZINGMirror Image ...................................................................................................................10Cutout Competition.......................................................................................................... 13Draw ‘n Distort ................................................................................................................16

SPATIAL SENSEBlock Buildings ................................................................................................................19Cat and Rat ...................................................................................................................... 22

SEQUENCING AND PREDICTINGYou Are There! .................................................................................................................24Wipe Out ........................................................................................................................... 26Toss Up ............................................................................................................................. 28

INFERRINGCode Words ....................................................................................................................... 31Clean the Clutter ..............................................................................................................34

ANALYZING AND CLASSIFYINGOddball ............................................................................................................................. 36What’s It to Me?...............................................................................................................38

LOGICAL THINKINGOrigami Solutions ............................................................................................................ 41Toothpicks ‘n Beans......................................................................................................... 43In Balance ........................................................................................................................ 45

ANSWER KEY................................................................................................................. 47

4


PillarsHelp GC collect all the hover boards before timeruns out. Just click on the arch you want to cross.You can move only in the directions indicated, andon higher levels, you must collect the hover boardsin order.

Hamster BallUse your arrow keys to move the hamster ballaround the arena. Select the goal shape thatmatches the attributes of your shape (located at thetop of the screen). Head for the goal while avoid-ing obstacles.

ScorpionScorpions are on the loose, and you must corralthem back into their holes by activating the correctgrid pieces. To activate a grid piece, click on acolumn number and a row number. Watch out forx-shaped pieces—the scorpion goes in and you’renever sure where it will come out.

Obstacle CourseRace against time on a hover board with Max. Usethe up and down arrow keys to change lanes, theright arrow key to move forward, and the spacebarto jump. Earn extra points for performing hoverboard tricks.

PipesGC cannot escape the cave until you repair thepipe circuit. As the pipe pieces pop to your cursor,click to put them in place. Earn bonus points byconnecting all four sides of a cross piece or byincluding a preplaced piece in your circuit.

Brain SaladYou will encounter two types of puzzles. Riddles:Read the clues and enter your answer in the an-swer box. Decoding Puzzles: Use the code coordi-nates to find the picture (left chart) and the corre-sponding letter (right chart). Click the letter toenter it in the answer box.

Welcome to Math Blaster

Cross Terrain Challenge !

A brief overview of each software activity is provided here. For more detail, click the Manual button atthe Sign-in Screen. In addition, before beginning an activity, the player can click “Show Me” for ademonstration of the challenge.

®

™

5


SkillsThe activities in Math Blaster Cross Terrain Challenge help to build valuable thinking skills applicableto all academic areas. In each challenge, the student must assess the situation, review the options, anddecide on a plan of action. The student soon learns that persistence, quick thinking, and sharp logic payoff. Some of the specific critical-thinking skills addressed in the software are listed below. Levels: Thechallenge level of the software automatically adjusts as the student’s skill increases. Level information issaved under the player’s sign-in name and retrieved at the player’s next computer session.

• Memory and recall • Analyzing• Visualization • Distinguishing and classifying• Recognizing symmetry • Using coordinates• Developing spatial sense • Logical thinking• Sequencing and predicting • Inductive reasoning• Inferring and drawing conclusions • Deductive reasoning

IntroductionTo the TeacherThe challenges in Math Blaster Cross Terrain Challenge are designed to sharpen your students’ critical-thinking skills. Players work their way through five missions. Each mission includes different chal-lenges, obstacle course moves, and puzzles. As your students strive to complete a mission, they will bedeveloping a wide range of thinking skills, including visualization, sequencing, inferring, analyzing,synthesizing, and drawing conclusions.

Introducing the SoftwareBefore you introduce the software to your students, take time to read the online manual (click theManual Button on the Sign-in Screen). This online guide briefly explains the computer activities, theToolbar buttons, and the program navigation. Demonstrate the software to the class, pointing out the“Show Me” feature at the beginning of each activity (click “Show Me” for a demonstration of the activ-ity) and the Buy Time button on the Toolbar (click for extra time in the activity in exchange for points).

TipsNormally, a student must earn a set number of points to complete a mission and move to the next mis-sion. However, you may want to override this feature so that a student can skip ahead to a new activity.To do this, press Ctrl + Alt + Shift + C (Mac: Command + Alt + Shift + C) at the main mission screen.Then you can use these commands to access the activity of choice:

Activity Windows MacPillars Ctrl + P Command + PScorpion Ctrl + S Command + SPipes Ctrl + F Command + FHamster Ball Ctrl + H Command + HObstacle Course Ctrl + O Command + OBrain Salad Ctrl + E Command + E

6


Tracking ProgressYou can use the reproducible progress chart on the following page to track students’ progress through theprogram. Students can check the activities they have tried and the missions they have completed.

Classroom ActivitiesTo extend your students’ experience with the software, choose from the classroom activities on thefollowing pages. Each lesson is centered on a specific thinking skill(s), listed at the beginning of thelesson. You can help your students focus on the skill by briefly discussing its importance as you intro-duce the lesson. Like Math Blaster Cross Terrain Challenge, the lessons are targeted at students nine totwelve years of age. They contain a mix of hands-on activities, games, and reproducible activity sheets.

Knowledge Adventure Web SiteFor additional fun-filled educational activities, visit the Knowledge Adventure Web site at http://www.education.com. You will find education news, free lesson plans, and student activities suitable forboth home and school.

7


Progress ChartMath Blaster Cross Terrain Challenge

Mission Activity

1 2 3 4 5 Pillars Scorpion Pipes Hamster Obstacle Brain Ball Course Salad

Name

8


Memory Walk

Focus GroupingRecalling, memory Whole class, individual, small groups

MaterialsMemory Walk Activity Sheet (1 copy per student)2" squares of construction paper in assorted colorsplastic tub or similar container, stapler or tape, pencils

Activity1. Put the squares of colored paper into a plastic tub or a similar container. Explain that the class will

complete an activity about memory. Briefly discuss memory.• Why is it important to be able to recall information?• How does this skill help in school? At home? On the job?• Are there ways to improve memory?

2. Take the class on a walk through the school halls (or other areas such as the playground, cafeteria, oroffices). Instruct them to observe the things they see closely. Tell them that they will be asked to recallcertain details once they return to the classroom. They should not talk to their classmates about thethings they see.

3. When the class returns to the classroom, distribute the activity sheets and have each student draw asquare of colored paper from the container. Have the students tape or staple their colored square totheir activity sheet and list items they saw that contain the color.

4. When the lists are complete, group students according to color. Tell the students to compare lists andadd items if possible.

5. As a class, discuss the activity:• Were you surprised by how many or how few items you could recall?• Did most students in your group remember the same items?• Did students in your group disagree on the colors of certain items?• Discuss things that would have made the activity easier (e.g., knowing the color to look for ahead of time, taking notes or making sketches, discussing the items while on the walk).• Discuss how these memory techniques could be applied to schoolwork (e.g., read headings to identify important facts to remember in the following text, take notes or make diagrams and sketches during class and while reading, discuss what you are learning with classmates).

6. Try the activity again, taking a walk in a different location. This time assign colors ahead of time andstop periodically so students can discuss what they see and take notes or make sketches. Do memoryskills improve?

9


Memory WalkActivity Sheet

Tape or staple your colored square in the box.

On the lines below, list things you saw that contain this color.

1.

2..

3.

4.

5.

6.

7.

8.

9.

10.

11.

12..

13.

14.

15.

10


Mirror Image

Focus GroupingVisualizing, symmetry Whole class, individual

MaterialsMirror Image Activity Sheets A and B (1 copy of each per student)2'' x 3'' cardboard rectangles (1 per student)2'' x 3'' rectangles cut from clear plastic (such as transparencies) or from heavy-duty aluminum foil (donot wrinkle)Glue

Activity1. Draw an isosceles triangle on the board. Point out that one side of the triangle is a mirror image of the

other. Draw a dashed line down the middle to show the axis of symmetry. Explain that this type ofsymmetry is bilateral symmetry. The axis of symmetry can be vertical, horizontal, or even diagonal,depending upon how the triangle is turned.

2. Distribute the cardboard and the plastic (or foil) rectangles. Have students make “mirrors” by gluingthe plastic or the foil onto the cardboard.• If you are using foil, advise students to avoid wrinkling it. Glue it shiny side up.• If you are using plastic, use just a single drop of glue in each corner.

3. Distribute Activity Sheet A. Complete the top half of the page as a class. Students will be using theirmirrors to check for symmetry. Allow time for students to complete the bottom half of the page. Whatletters were they able to make?

4. Draw a sun on the board. Explain that it has radial symmetry. Ask volunteers to draw several of thepossible lines of symmetry. Draw a picket fence on the board. Ask if anyone knows what this type ofsymmetry is called (sliding symmetry).

5. Distribute Activity Sheet B and assist students as needed to use different types of symmetry to com-plete and create drawings.

ExtensionLet students use their mirrors to find symmetrical items in old magazines. Students can also use theirmirrors to distort drawings or photographs in the magazines. For example, if a mirror is placed at anangle on a portrait (instead of straight up and down along the line of symmetry), the resulting image mayhave three eyes.

sliding bilateral radialsymmetry symmetry symmetry

11


Mirror ImageActivity Sheet A

Stand your foil mirror on edge along the dashed line. Check for symmetry by standing your mirrorDoes the letter you see look the same as the real letter A? on edge along the dashed lines, one at a time.If so, the letter A is symmetrical.

Is the letter D symmetrical? ____________Is the letter A symmetrical? ______ Which is the axis of symmetry?The dashed line is the axis of symmetry. ____vertical ____horizontal ____diagonal

Try making these shapes into letters of the alphabet. There are no dashed lines, so you will need to experi-ment by putting your mirror in different spots. Some letters may be turned sideways. What letters can youmake?

V

X

XC

H MO

U

?

D○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○

○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○ ○A○

○

○

○

○

○

○

○

○

○

○

○

○

?

?

12


Mirror ImageActivity Sheet B

Finish these three designs. Which has bilateral symmetry? Radial symmetry? Sliding symmetry?

Make some symmetrical designs of your own. Try all three types of symmetry.

13


Cutout Competition

Focus GroupingVisualizing, distinguishing tessellations Individual, large groups

MaterialsCutout Competition Activity Sheets A and B (1 copy of each per student)9'' x 9'' squares of construction paper (all the same color)pencils, colored pencils, index cards, scissors, rulers

Activity1. Distribute Activity Sheet A and the construction paper squares. Tell students that they will make

cutouts to use in a game, and assist them as needed to follow the directions on the activity sheet.

2. When students are finished, divide the class into two or three teams. Give each team a plastic tub.Each team member should have a folded scrap (from Activity Sheet A), which goes into the team’stub, and a cutout, which should be exchanged with a teammate.

3. Explain the rules of the game:• Each team designates a leader.• At the starting signal, the leader holds up the scraps (still folded), one at a time. The player with the corresponding cutout should ask for the folded scrap and fit the cutout and scrap together to be sure they match. If they do not, the scrap must be returned to the tub. Note: Remind the leaders to match their own cutouts.• The winning team is the first team to match all their cutouts and scraps.

4. Play one or more games. Before each new game, the players should exchange cutouts and return theirscraps (folded) to the tub.

5. For additional practice with visualization, distribute Activity Sheet B. Explain that certain shapes(squares, for example) can fit perfectly side by side with no gaps or overlaps. We say that these shapestessellate. Ask volunteers if rectangles tessellate (yes) and if circles tessellate (no). Tessellated shapescan form interesting designs. Assist students as needed to follow the step-by-step directions for creat-ing original tessellations. The activity sheet shows a fishlike shape, but students’ shapes may or maynot look like real things.

ExtensionAfter playing Cutout Competition, let students mount their cutouts and scraps side by side on contrastingcolors of construction paper. Display the students’ work around the classroom.

14


Cutout CompetitionActivity Sheet A

3. Cut out the shape and unfold it. Keep the scrap folded as it is. How quicklywill your classmates be able to match the cutout to its folded scrap?

2. Draw any shape, beginning andending on the folded edge. Becreative. Use straight lines, curvedlines, or both.

1. Fold your construction paper square in half.

15


Cutout CompetitionActivity Sheet B

Follow these steps to make your own tessellation.

6. Trace around your pattern on a large sheetof paper. Color your tessellation as you wish.

5. Tape the shape to the bottom. You have createda pattern for a shape that will tessellate.

4. Cut a shape from the top.3. Tape the shape to the right end.

2. Cut any shape from the left endof the square.

1. Start with a square cut from an index card.(3'' by 3'' is a good size).

16


Draw ‘n DistortFocus GroupingVisualization, using coordinates Whole class, individual

MaterialsDraw ‘n Distort Activity Sheets A and B (1 copy of each per student)pencils

Activity1. Distribute Activity Sheet A. Have students follow the directions in the first paragraph and draw origi-

nal pictures on the large grid. Advise them to limit the number of lines in their drawings (the examplecontains four lines—two wheels, the top of the car, and the short line between the wheels).

2. Point out that each vertical line in the grid is labeled with a letter and each horizontal line with anumber. Explain how to identify any intersection on the grid by the letter of the vertical line and thenumber of the horizontal line. Draw a grid on the board (12 horizontal lines, 12 vertical lines) and letvolunteers use the coordinates listed in the example to copy the car from the activity sheet onto theboard.

3. Distribute Activity Sheet B. At the top of the page, have the students list the coordinates for theirdrawings. (Directions are given in Paragraph 2 on Activity Sheet A.)

4. Instruct students to use the coordinates they listed to draw their pictures on the distorted grid at thebottom of Activity Sheet B. Or have students exchange papers and draw their classmates’ pictures.Interesting distorted pictures, such as the one below, will result:

Extensions• Let students make their own distorted grids, for example, wide in the middle and narrow at the top and

bottom. How do their pictures look on these grids?• Can students explain why some continents are more accurately represented on a globe than on a map

of the world? Have students examine the lines of longitude, which are close together at the poles on aglobe, but wide apart on a flat map.

17


Draw ‘n DistortActivity Sheet A

Make a picture on the large grid by drawing straight lines from intersectionto intersection. An example is shown on the small grid at right.

On Activity Sheet B, record the coordinatesfor drawing the lines in your picture. The coordinatesfor the example at right are as follows:Line A: (E, 3), (F, 3)Line B: (B, 3), (A, 3), (A, 5), (D, 6), (E, 8), (I, 8), (J, 6), (J, 3), (I, 3)Line C: (C, 5), (D, 5), (E, 4), (E, 3), (D, 2), (C, 2), (B, 3), (B, 4), (C, 5)Line D: (G, 5), (H, 5), (I, 4), (I, 3), (H, 2), (G, 2), (F, 3), (F, 4), (G, 5)

11

10

9

8

7

6

5

4

3

2

1

A B C D E F G H I J K

18


Draw ‘n DistortActivity Sheet B

The coordinates for drawing the lines in my picture are as follows:

Line A: ________________________________________________________________

Line B: ________________________________________________________________

Line C: ________________________________________________________________

Line D: ________________________________________________________________

Line E: ________________________________________________________________

(Continue on a separate page if necessary.)

Now use the coordinates to draw your picture on the grid below!

19


Block Buildings

Focus GroupingDeveloping spatial sense, drawing and Pairsthe use of base plans

MaterialsBlock Buildings Activity Sheets A and B (1 copy of each per student pair)scissors, tape, markers

Activity1. Have students work in pairs. Give each pair a copy of Activity Sheet A. Have students construct the

blocks by cutting on the solid lines, folding on the dashed lines, and taping into a cube shape.

2. On the board, draw a base plan like the one shown here.Explain that the plan shows the outline of the base of abuilding. The numbers indicate the height of eachsection. Have the students use their blocks to constructthe building. Continue with other base plans until thestudents understand the concept.

3. Distribute Activity Sheet B. Challenge the student pairsto fill in the answers for numbers 1 and 2, without usingtheir blocks to build a model. Then have students build amodel to check their work, changing their answers asneeded. Students can use markers to color the exposedsurfaces for number 2.

4. Finally, have the student pairs use their blocks to design their own buildings. At the bottom of theactivity sheet, have each student pair draw a base plan of the building. On the back of the activitysheet, the students can draw the four views of the building: front, back, left, right.

5. Have students exchange activity sheets and use the base plans to build each other’s buildings. Do thefront, back, left, and right of the building match the four views drawn on the back of the activitysheet?

ExtensionChallenge students to draw corner views of their buildings.

BACK

FRONT

LEFTSIDE

RIGHTSIDE

2 cubeshigh

1 cubehigh

2 cubeshigh

20


Block BuildingsActivity Sheet A

21


Block BuildingsActivity Sheet B

1. The six illustrations below go with the base plan at the right.Fill in the missing words and drawings. Use your blocks toconstruct the building and check your answers.

2. Suppose you colored all the exposed surfaces blue.How many blocks would have 1 blue side? ____Two blue sides? ____ Three blue sides? ____Four blue sides? ____ Five blue sides? ____

On Your OwnUse your blocks to construct a building of your own design. Draw its base plan on the grid.Draw the front, back, left, and right views on the back of this activity sheet

A. B. C.

D. E. F.

BACK

FRONT

LEFTSIDE

RIGHTSIDE

2 cubeshigh

1 cubehigh

2 cubeshigh

Right

Front Back Left

Front LeftCorner View

Front RightCorner View

22


Cat and Rat

Focus GroupingDeveloping spatial sense, constructing mazes Whole class, individual

MaterialsCat and Rat Activity Sheet (1 copy per student)bell, colored pencils, and white paper transparent enough to use for tracing

Activity1. Discuss the history of mazes with the class, including these facts:• We do not know who made the very first mazes.• There is a well-known legend about a monster called the Minotaur, who was imprisoned in a labyrinth

(a place with mazelike passageways). The Greek hero Theseus entered the labyrinth, slew theMinotaur, and then found his way out of the maze by following a thread he had unwound as he en-tered it.

• Coins with a labyrinth design were minted on the island of Crete in about 67 B.C.• In ancient Rome maze patterns, thought to bring good luck, were often used in mosaics.

2. Take the class outside or to the gymnasium to play Cat and Rat.You will need three volunteers—a “cat,” a “rat,” and the “wind.”Have the other students form a human maze by standing in a gridformation close enough so that their fingers touch when theystretch out their arms. Explain the rules:

• The rat starts at one corner, the cat at the other.• The cat tries to catch the rat by moving through the maze.• The wind decides when to ring the bell, signaling each of the

students in the maze to turn 90 degrees. This makes it difficult (or sometimes easier) to catch the rat!

• At the end of the round, the cat, rat, and wind select replacements.• Play until each student has had a turn as the cat, rat, or wind.

3. Back in the classroom, distribute the activity sheet and paper to usefor tracing. Assist students as needed to design their own mazes.If you wish, make several copies of the completed mazes for studentsto share with classmates or family members.

Students in grid with handsoutstretched and fingers touching

Students turned 90 degrees

23


Cat and RatActivity Sheet

1. Use a colored pencil to draw a pathfrom the cat to the rat. Draw through thecenters of the squares. Make a compli-cated path with lots of turns.

2. Using a different color, draw dead-end paths leading off the first path.When you are done, there shouldbe a path through every square.

3. Put tracing paper over the grid.Trace all lines of the grid exceptfor the lines that have beencrossed by colored-pencil lines.Trace the cat and rat, too.

4. Share your maze with a friend or familymember.

24


You Are There!

Focus GroupingSequencing, writing sequential directions, Whole class, individualfollowing written directions, mapping

MaterialsYou Are There! Activity Sheet (1 copy per student)pencils

Activity1. Ask students if they have ever baked a frozen pizza. Were the directions easy to follow? Ask what the

first step was (probably preheating the oven). What were the next steps? Ask what might happen if thedirections were out of order or confusing. (The crust might be soggy, the pizza might burn, the pizzacompany’s sales would go down.)

2. Distribute the activity sheets. Explain that students will be writing directions to different locations inthe school. The directions must be clear and accurate, or the classmate who follows the directions willarrive at the wrong destination.

3. Tell students that they should each secretly select a location in the school (for example, the office, thegymnasium, or the first-grade room) and write step-by-step directions from your classroom to theselected destination. The directions should not mention the destination by name.

4. Have each student exchange his completed directions with a classmate. The classmate should read thedirections and draw a map showing the route and the final destination. (Alternatively, let the classmatewalk to the destination, following the written directions.)

5. Did the classmate arrive at the correct destination? If not, have the two students discuss the directionsand clarify them. The students may need to walk to the destination in order to determine the best wayof explaining the route.

Extensions• Have each student write directions from one state capital to another, using the scale

on the map to determine the approximate number of miles. For example: “Startat Richmond, the capital of Virginia. Go west 300 miles. Go north 200 miles.You are at ____________________, the capital of ____________________.”A classmate can follow the directions and fill in the destination.

• Let students write directions explaining how to solve various math problems (addtwo fractions, draw a parallelogram, solve a story problem). Have classmates followthe directions to be sure they work.

25


You Are There!Activity Sheet

Write directions to a destination in the school. At the end of the directions, write “You are there!” Do notinclude the name of the destination.

My Directions

Let a classmate read your directions and draw a map to show the path. Did your classmate reach thecorrect final destination?

Map

1.

2.

3.

4.

5.

6.

26


Wipe Out

Focus GroupingSequencing, predicting, testing Pairs

MaterialsWipe Out Activity Sheet (1 copy per student pair)scissors

Activity1. Ask if students have ever played a game called Nim. Nim is a very old game, which may have origi-

nated in China. The game has many variations, but the object is to avoid being the player to take thelast game token.

2. Have students work in pairs. Give each pair an activity sheet, and have the students cut apart the gametokens.

3. Explain that this version of Nim is called Wipe Out. There are twelve game tokens picturing Max onhis hover board and one token picturing Max wiping out. On each turn, a player must take either oneor two tokens. Eventually, only the wipe-out token is left. Whoever takes it, wipes out (loses).

4. Suggest that students play a few times and then try to figure out a sequence of winning moves.If students find this difficult, provide one or more of these tips:• It is easier to figure out a strategy with fewer tokens. Try playing with just two tokens (including the wipe-out token), then three, then four, etc.• Is it better to go first or second?• Will you win if you leave one token on the board? How about two? three? four?

5. Allow time for students to figure out and test a sequence of moves. Then have them change the rulesof the game to allow players to take away 1, 2, or 3 tokens. Does the sequence of moves work withthis rule? If not, try to find a sequence that does work.

ExtensionUse sixteen of the tokens (no wipe-out token) arranged on the activity sheet as shown. On your turn, takeas many tokens as you want, but all from the same row. To win, avoid taking the last token.

27


Wipe OutActivity Sheet

28


Toss Up

Focus GroupingPredicting, testing Pairs

MaterialsToss Up Activity Sheets A and B (1 copy of each per student pair)pennies (2 per student pair), pencils, colored pencilscolored paper clips or squares of colored paper to use as game tokens

Activity1. Have students work in pairs. Give each pair an activity sheet and one penny. Have each pair discuss

the problem at the top of the activity sheet and write down a prediction. Then have the pair flip a coinand use colored pencils to fill in the graph. Were their predictions correct? Tally and discuss theresults of all the student pairs:• How many times did the heads column reach 10 or more? How many times did the tails column reach 10 or more? (These two numbers are likely to be about equal since there is a 50% chance of tossing heads and a 50% chance of tossing tails.)• How many times did a column reach 14? If the answer is zero, is it possible for a column to reach 14? (It is possible, but not very likely. It is most likely that both columns will reach 10. The results may vary by 2 or 3, but probably not 4.)

2. Continue with the problem at the bottom of the activity sheet. Have the pairs discuss the problem andwrite down their predictions before flipping their coins and filling in the graph. Discuss the results:• Which column grew tallest in the various groups? (The third column—1 head/1 tail—will probably be the tallest for most groups.)• How can you explain the results? Here are the different combinations that are counted in each column. The third column grows tallest because it contains the most combinations:

First Column Second Column Third Column heads heads tails tails heads tails Coin A Coin B Coin A Coin B Coin A Coin B

3. Finally, let the student pairs use their coins to play the game on Activity Sheet B. After a few rounds,ask the students to design their own game boards and test them. Is the new game easier or moredifficult? Can all the game boards be completed?

tails headsCoin A Coin B

29


Toss UpActivity Sheet A

Flip One Coin

Flip a penny and record whether it comes upheads or tails. Flip it 20 times.

1. Predict: Which column will reach 10 or more?Heads _____ Tails _____

2. Predict: Will either column reach 14?Heads _____ Tails _____

Flip two pennies at a time and record whetheryou get two tails, two heads, or one head andone tail. Flip the coins 30 times.

1. Predict: Which column will be the tallest?Heads _____ Tails _____ Heads/Tails_____

Flip Two Coins

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Heads Tails

30

29

28

27

26

25

24

23

22

21

20

19

18

17

16

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

Two Two One Head/ Heads Tails One Tail

30


Toss UpActivity Sheet B

Rules for Toss Up1. Each player puts a token at START.2. Take turns tossing a coin. Move one space (dot)

in the direction of the arrow. Follow the H pathif you toss heads, the T path if you toss tails.

3. If you can’t move, skip your turn.4. Who can reach FINISH first?

Design Your Own

Use this space to design your own Toss Up board. Decide where to put the dots and the arrows.Mark START and FINISH. Label each path T or H. Test your game board and modify it if necessary.

T

HT

T

T

H

START

H

FINISH

31


Code Words

Focus GroupingInferring, decoding Individual

MaterialsCode Words Activity Sheets A and B (1 copy of each per student)pencils, scratch paper, scissors. Optional: calculators

Activity1. Write the word cryptography on the board. Ask if anyone knows the meaning of the word. If not, give

these hints:• crypto- comes from the Greek word for hidden• -graphy comes from the Greek word for writingCryptography is the writing of codes or secret (hidden) messages. Ask why codes are important in theworld of computers. (To keep material private when using the Internet, data is often encrypted, or sentin coded form.)

2. Distribute Activity Sheet A. Explain that the list of words is written in a secret code. Each letter in thecode corresponds to a letter of the alphabet. Students must crack the code to find out what words areon the list. Luckily, two hints are given. Read the hints at the top of the page. If necessary, help stu-dents get started:• Use the second hint to determine that fmc (Word 1) = six.• Therefore, the second word on the list must be sixty (the only 5-letter number word that begins

six-). Use these 5 letters to decode other words.• At the bottom of the page, students can record the known letters for reference.

3. Allow time for students to complete the activity sheet and check their work.

4. Distribute Activity Sheet B. Explain that students will create their own codes and make word lists forclassmates to decode. Suggest that students work on scratch paper and then copy their lists onto theactivity sheet. Instead of number words, students can use categories such as these:• States, capitals, or countries• Well-known bodies of water• Fruits or vegetables• Sports• Musical instruments• Famous explorers

5. When students have completed their activity sheets, instruct them to cut along the dashed line andexchange their lists for classmates to decode.

32


Code WordsActivity Sheet A

Can you crack the code? At the bottom of the page, keep a record of the letters as youdecode them. Use these known letters to help decode other words on the list. Hints:

• These are all number words.• The first number word tells the number of sides on a hexagon.

1. fmc

2. fmcbp

3. btmhbp

4. buqobp

5. buqrxq

6. qmatb

7. qmatbp

8. nshbp-nmxq

9. nsdhbqqo

10. nmnbqqo

11. omoqbp-omoq

12. soq

13. fmcbp-fqxqo

14. fqxqobp-bthqq

Add all the numbers together. Do they equal 530? If so, you have probably cracked the code correctly!

A =B =C =D =E =F =G =H =I =

J =K =L =M =N =O =P =Q =R =

S =T =U =V =W =X =Y =Z =

Code Letter Real Letter Code Letter Real Letter Code Letter Real Letter

33


Code WordsActivity Sheet B

My Code:


Hints:

• The topic for the words on my list is ______________________________________.

• The first word on my list tells ___________________________________________.

Words in Code:

1. __________________________ ___________________________

2. __________________________ ___________________________

3. __________________________ ___________________________

4. __________________________ ___________________________

5. __________________________ ___________________________

6. __________________________ ___________________________

7. __________________________ ___________________________

8. __________________________ ___________________________

9. __________________________ ___________________________

10. __________________________ ___________________________

A =B =C =D =E =F =G =H =I =

J =K =L =M =N =O =P =Q =R =

S =T =U =V =W =X =Y =Z =

? ! ? ! ? ! ? ! ? ! ? !? ! ? ! ? ! ? ! ? ! ? !

34


Clean the Clutter

Focus GroupingInferring, critical thinking Pairs

MaterialsClean the Clutter Activity Sheet Ascissors, pencil, pen, sticky note, envelope, pencil, marker, eraser, paper clip, sticker or stamp, rubberband: one of each per student pair

Activity1. Have students work in pairs. Distribute Activity Sheet A.

2. Ask students how they organize their desk, backpack, or locker. Do they have certain spots for books,notebooks, or other supplies? Tell students that they will organize the paper desk by following someclues. Write the clues on the board (or copy this list for each student pair):

• Stamps (or stickers) are in the left column, markers in the right, and erasers in the middle, but each is in a different row.• Pens go in the top row, paper clips in the next row, and scissors in the third row down, but each is in a different column.• The sticky notes go below the scissors.• The pencils go below the markers.• The stamps (or stickers) are far from the markers.• Envelopes go below and to the left of the erasers.

3. Distribute the items that belong in the desk (one of each per student pair)—pencils, pens, markers,paper clips, sticky notes, envelopes, erasers, rubber bands, stickers or stamps, and scissors.

4. Allow time for the student pairs to place the items in the correct spots on their paper desks. Have themreread the clues to double-check their arrangements.

35


Clean the ClutterActivity Sheet A

36


Oddball

Focus GroupingAnalyzing, classifying Whole class, individual

MaterialsOddball Activity Sheet (1 per student)pencils

Activity1. Place the following items on a table where students can see them:• red book• yellow legal pad• red pencil

2. Ask students which item is the oddball, the one that does not belong with the rest. How is it different?There are many answers, including:

• The pencil is different because it does not contain paper.• The legal pad is different because it is not red.• The book is different because the other items are writing supplies.

3. Discuss classification. Tell students that we sometimes classify things—kinds of animals, types ofnumbers, styles of art—in order to understand them better. Classification also helps us to rememberthings. For example, we know that mammals in general nurse their young, have hair, and are warm-blooded. Therefore, we do not have to memorize these facts for each different mammal.

4. Distribute the activity sheets. Explain that students should try to find an oddball in each group and tellhow it is different (Column 2). Can the students find a different oddball (Column 3)?

An activity sheet with sample answers is shown here. There are other possible answers.

ExtensionLet students create their own problem sets for a classification game. They should each think of threewords or numbers that could be grouped in two or more ways. Have each student list the three words ornumbers on an index card.

Divide the class into teams and copy one problem set at a time onto the board. Let the teams take turnsnaming and explaining the oddballs. Award one point for the first oddball, two points for the second,three points for the third, and so on.

37


OddballActivity Sheet

Items Which one Can you find ais the oddball? different oddball?Briefly say why. Why is it an oddball?

meter liter

centimeterinch

John AdamsGeorge W. Bush

Marie CurieAbraham Lincoln

sandbox airplane

upon mother

15311 3

12

bobcat whale buffalo boa constrictor

1/4 .25

2/8 1/2

38


What’s It to Me?Focus GroupingAnalyzing, classifying, analogies Whole class, individual

MaterialsWhat’s It to Me? Activity Sheet AWhat’s It to Me? Activity Sheet B (1 copy per student)scissors, pencils, plastic bucket or similar container

Activity1. Cut the cards on Activity Sheet A apart and place them in a “hat” (plastic bucket or similar container).2. Have a volunteer draw two of the cards from the bucket, for example, fish and soap. Ask the class to

brainstorm things the two items have in common:• work best in water• slippery when wet• contain fat• four-letter words• nouns

Return the cards to the bucket and repeat the activity. Alternatively, teams can compete to earn a pointfor each answer.

3. Distribute Activity Sheet B. If students are not familiar with analogies, explain that the first pair ofwords in an analogy has a fixed relationship to the second pair of words. Complete the first analogytogether as a class: pear is to tree as pumpkin is to _____. First, ask how the word pear relates to tree.(Pears grow on trees.) Then ask a volunteer for a word that relates to pumpkin in the same way (vine).

4. Allow time for students to complete their activity sheets. Discuss their answers together. An activitysheet with answers is shown here. There may be other possible answers.

?

39


What’s It to Me?Activity Sheet A

soap fish

plant cup

boat hand

40


What’s It to Me?Activity Sheet B

1. I is to me as they is to _________________________________________________

2. helium is to gas as water is to ___________________________________________

3. trout is to fish as aardvark is to ________________________________________

4. France is to Europe as United States is to ________________________________

5. heart is to blood as lung is to ___________________________________________

6. elephant is to calf as deer is to __________________________________________

7. dictionary is to word as atlas is to _______________________________________

8. boat is to water as sled is to ____________________________________________

9. square is to four as hexagon is to _______________________________________

10. run is to verb as hexagon is to __________________________________________

11. complete is to finish as locate is to ______________________________________

12. fiction is to imaginary as nonfiction is to _________________________________

13. Jupiter is to planet as collie is to ________________________________________

14. equator is to hot as pole is to ___________________________________________

15. egg is to yolk as peach is to _____________________________________________

16. arm is to elbow as leg is to _____________________________________________

17. pear is to tree as pumpkin is to _________________________________________

41


Area: 4 sq. units Proof:Fold the square diagonally.Now you can see that thesquare is made up of 2 ofthe gray shapes. Divide thetotal area (8 sq. units) by 2to find the area of 1 grayshape (4 sq. units).

Area: 2 sq. units Proof:Fold the square along bothdiagonals. Now you can seethat the square is made upof 4 of the gray shapes.Divide the total area (8 sq.units) by 4 to find the areaof 1 gray shape (2 sq. units).

Area: 4 sq. units Proof:Fold the corners inward.You can see that the grayshape is exactly half of thetotal area. Divide the totalarea (8 sq. units) by 2 tofind the area of the grayshape (4 sq. units).

Area: 1 sq. unit Proof:From the folds you madein the previous proof, youknow that the total area ofall 4 corners is 4 squareunits. Therefore, 1 cornerequals 1 square unit.

4. Continue with the shapes shown here.

Origami Solutions

Focus GroupingLogical thinking, geometric shapes, area Individual

MaterialsOrigami Solutions Activity Sheet (1 copy per student)scissors

Activity1. Ask students to recall the formula for the area of a rectangle (base x height) and, if they are familiar

with it, the formula for the area of a triangle (1/2 base x height).

2. Explain that students will find the areas of different shapes without using the usual formulas and thecalculations. Distribute the activity sheet. Have students cut out the square and follow the directionsfor folding it. When they are done, their squares should look like the one shown here.

3. Tell students that the area of the square is 8 square units. Ask volunteers to tell you the area of each ofthe shaded areas below. Can the volunteers fold their squares to explain their answers? Some proofsare given below. Students can try their own proofs for the last two shapes below.

ExtensionHave students cut their squares in half diagonally.Can they fold the resulting triangle to prove that theangles of a triangle are equal to 180 degrees?

A

B C

42


Origami SolutionsActivity Sheet

1. Cut along the heavy solid line.2. Fold diagonally along one of the light solid lines. Unfold.3. Fold diagonally along the other light solid lines. Unfold.4. Fold in one corner by folding along the dashed line. Unfold.5. Fold the other three corners in the same way. Unfold your paper and turn it over.

43


Toothpicks ‘n BeansFocus GroupingLogical thinking, working backward Individual

MaterialsBean Boxes Activity Sheet (1 copy per student)toothpicks, dried beans

Activity1. Give each student 12 toothpicks. Draw this illustration

on the board and ask students to replicate it with toothpicks:

2. Present the following challenges, one at a time. After each challenge, discuss the solution together.Point out that it often helps to work backward, visualizing the final arrangement first.

3. Give each student 5 more toothpicks in order to add 2 more boxes as shown here:Then have students try the following challenges:

Challenge: Remove 4 toothpicksto leave 1 square.Solution:

Challenge: Remove 4 toothpicksto leave 2 squares.Solution:

Challenge: Remove 2 toothpicksto leave 2 squares.Solution: (1 large, 1 small)



Challenge: Remove 2 toothpicksto leave 4 quadrilaterals.Solution: (1 large, 3 small)

4. Tell students that you have some bean box challenges that will also require logical thinking andworking backwards. Give each student twelve dried beans and an activity sheet.

5. Allow time for students to work out the problems. Then discuss their solutions as a class. (Once astudent has worked out a solution, he or she can pencil in the answer and remove the beans.) Solutionsmay vary from the ones shown in the Answer Key.

44


Toothpicks ‘n BeansActivity Sheet

6. Put beans in this box to equal exactly 100points. (Each section can hold more than onebean.)

3. Place 6 beans in this bean box so there is nomore than 1 bean in any row, column, ordiagonal.

4. Place 12 beans in this bean box so there areno more than 2 beans in any row, column, ordiagonal.

1. Place 6 beans in this bean box so that eachrow and column has an odd number of beans.

2. Place 8 beans so that there are 2 beans oneach straight line and 2 beans on each circle.

5. Place a bean in each of the 10 spots in thisarrow. Can you make the arrow point up bymoving just 3 beans?

14

12

16

13 15

45


In Balance

Focus GroupingLogical thinking, pre-algebra Whole class, individual

MaterialsIn Balance Activity Sheet (1 copy per student)pencils

Activity1. Write the following equation on the board:

2 + 1 = 1 + 1 + 12. Ask students to imagine that the numbers are represented by one-ounce and two-ounce weights on a

balance scale.• What would be on the left side of the balance? (1 two-ounce weight and 1 one-ounce weight)• What would be on the right side? (3 one-ounce weights).• If you replaced the 3 one-ounce weights with 1 three-ounce weight, would it disturb the balance? (No, because it is an equal exchange.)• Would it change the equation? (The equation would be 2 + 1 = 3.)

3. Distribute the activity sheets. Explain that students should figure out what shapes belong in the lastbalance pan and draw them in. They can solve the problems by replacing shapes with their equiva-lents. Do the first problem together as a class:

Solution:Replace the on the first balance with the equivalent from the second balance.

Now you know that = .

So the last balance should show that = .

4. Allow time for students to complete the page. Check the answers together.

ExtensionLet students create similar problems for their classmates to solve. Have them draw the problems on largeindex cards. Shuffle the cards and redistribute them.

46


In BalanceActivity Sheet

1.

2.

3.

4.

5.

47


ANSWER KEY

Math Blaster Cross Terrain Challenge

Critical Thinking

48


Block BuildingsAnswer Key to Page 21

1. The six illustrations below go with the base plan at the right.Fill in the missing words and drawings. Use your blocks toconstruct the building and check your answers.

2. Suppose you colored all the exposed surfaces blue.How many blocks would have 1 blue side? 1Two blue sides? 1 Three blue sides? 2Four blue sides? 2 Five blue sides? 2

On Your OwnUse your blocks to construct a building of your own design. Draw its base plan on the grid.Draw the front, back, left, and right views on the back of this activity sheet

A. B. C.

D. E. F.

48

BACK

FRONT

LEFTSIDE

RIGHTSIDE

2 cubeshigh

1 cubehigh

2 cubeshigh

Right

Front Back Left

Front Left, Corner View Front Right, Corner View

49


Code WordsAnswer Key to Page 32

Can you crack the code? At the bottom of the page, keep a record of the letters as youdecode them. Use these known letters to help decode other words on the list. Hints:

• These are all number words.• The first number word tells the number of sides on a hexagon.

1. fmc

2. fmcbp

3. btmhbp

4. buqobp

5. buqrxq

6. qmatb

7. qmatbp

8. nshbp-nmxq

9. nsdhbqqo

10. nmnbqqo

11. omoqbp-omoq

12. soq

13. fmcbp-fqxqo

14. fqxqobp-bthqq

Add all the numbers together. Do they equal 530? If so, you have probably cracked the code correctly!

A = gB = tC = xD = uE =F = sG =H = rI =

J =K =L =M = iN = fO = nP = yQ = eR = l

S = oT = hU = wV =W =X = vY =Z =


six

sixty

thirty

twenty

twelve

eight

eighty

forty-five

fourteen

fifteen

ninety-nine

one

sixty-seven

seventy-three

50


Clean the ClutterAnswer Key to Page 35

rubber bands

stickers orstamps

sticky notes

envelopesscissors

erasers

markers

paper clips

pens

pencils

51


OddballAnswer Key to Page 37

Items Which one Can you find ais the oddball? different oddball?

Briefly say why. Why is it an oddball?

meter liter

centimeterinch

John AdamsGeorge W. Bush

Marie CurieAbraham Lincoln

sandbox airplane

upon mother

15311 3

12

bobcat whale buffalo boa constrictor

1/4 .25

2/8 1/2

1/2Not equal to 1/4

.25Written as a

decimal

boa constrictorNot a mammal

whaleNot a land animal

11Not evenly

divisible by 3

literNot a measure

of length

George W. BushLiving in 21st

century

uponNot a noun

12Not an odd number

inchNot a metricmeasurement

Marie CurieA female

motherNot a compound

word

52


What’s It to Me?Activity Sheet B

1. I is to me as they is to _________________________________________________

2. helium is to gas as water is to ___________________________________________

3. trout is to fish as aardvark is to ________________________________________

4. France is to Europe as United States is to ________________________________

5. heart is to blood as lung is to ___________________________________________

6. elephant is to calf as deer is to __________________________________________

7. dictionary is to word as atlas is to _______________________________________

8. boat is to water as sled is to ____________________________________________

9. square is to four as hexagon is to _______________________________________

10. run is to verb as hexagon is to __________________________________________

11. complete is to finish as locate is to ______________________________________

12. fiction is to imaginary as nonfiction is to _________________________________

13. Jupiter is to planet as collie is to ________________________________________

14. equator is to hot as pole is to ___________________________________________

15. egg is to yolk as peach is to _____________________________________________

16. arm is to elbow as leg is to _____________________________________________

17. pear is to tree as pumpkin is to _________________________________________

them

water

mammal

North America

air

fawn

map

snow

six

noun

find

true

dog

cold

pit

knee

vine

53


Toothpicks ‘n BeansAnswer Key to Page 43

Activity1. Give each student 12 toothpicks. Draw this illustration

on the board and ask students to replicate it with toothpicks:

2. Present the following challenges, one at a time. After each challenge,discuss the solution(s) together. Point out that it often helps towork backward, visualizing the final arrangement(s) first.

Challenge: Remove 4 toothpicksto leave 1 square.Solution:


Challenge: Remove 2 toothpicksto leave 2 squares.Solution: (1 large, 1 small)



Challenge: Remove 2 toothpicksto leave 4 quadrilaterals.Solution: (1 large, 3 small)

3. Give each student 5 more toothpicks in order to add 2 more boxes as shown here:Then have students try the following challenges:

54


Toothpicks ‘n BeansAnswer Key to Page 44

6. Put beans in this box to equal exactly 100points. (Each section can hold more than onebean.)

3. Place 6 beans in this bean box so there is nomore than 1 bean in any row, column, ordiagonal.

4. Place 12 beans in this bean box so there areno more than 2 beans in any row, column, ordiagonal.

1. Place 6 beans in this bean box so that eachrow and column has an odd number of beans.

2. Place 8 beans so that there are 2 beans oneach straight line and 2 beans on each circle.

5. Place a bean in each of the 10 spots in thisarrow. Can you make the arrow point up bymoving just 3 beans?

14

12

16

13 15

54

55


In BalanceAnswer Key to Page 46

1.

2.

3.

4.

5.

math blaster - knowledge adventure

Documents