· Web view11.How many LEGO bricks high will the end of the ramp be? 12 12.Build a stand this many...

Summary of LEGO WeDo 2.0 Math ChallengesWobble PullSkills Required:Measuring AnglesMultiplying and Subtracting DecimalsMaterials Needed:Modified LEGO Pull-Robot36 Dice (16 mm)ProtractorA Ramp (slope needs to be adjustable)The Challenge: Determine the weights that Pull-Robot can pull up different slopes.

Frog vs. Tadpole Skills Required:Metric LengthSimplifying FractionsMultiplying Fractions by Whole NumbersMaterials Needed:LEGO FrogLEGO TadpoleMeter StickStringCarpeted/Rug Floor SurfaceThe Challenge: Measure how far the Frog travels with a given number of hops and estimate how about how far the Tadpole will travel if taking the same number of steps.

Mantis Mania Skills Required:The Four Operations with Whole NumbersMeasuring in Centimeter Equivalent Fractions (Mantis Mania B)Multiplying Fractions by Whole Numbers (Mantis Mania B)

Materials Needed:Modified LEGO MantisMetric RulerTwo DiceThree-ring Binder with 1” RingsThe Challenge: Construct a ramp up which the Mantis will push dice.

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Steer Car Courses Skills Required:Measuring in Inches Angles and Rotation DegreesCalculating Quotients ending in .5 Materials Needed:LEGO Steer CarYard StickMasking TapeThe Challenge: Program the Steer Car to travel around a square or equilateral triangle course.

Dump ItSkills Required:Adding, Subtracting, and Multiplying DecimalsMaterials Needed:LEGO Recycling Truck7 Dice (16 mm)7 Square LEGO BricksThe Challenge: Determine the heaviest possible weight you can get the truck to dump.

EarthquakeSkills Required:Calculating Area Calculating Volume (Earthquake Data Chart Versions B and C)Multiplying Decimals (Earthquake Data Chart Version B)Multiplying Fractions (Earthquake Data Chart Version C)Materials Needed:LEGO Earthquake connected to baseplate36 DiceThe Challenge: Calculate the dimensions of various dice “buildings” and observe how long they can survive the earthquake

Bee Revolution Skills Required:Adding, Multiplying and Rounding DecimalsMaterials Needed: LEGO Flower

The Challenge: Calculate how many revolutions the bee will make, given its programmed speed and time.

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Gear Machine - Multiples of 2, 3, 4, 5, 6, 8, 9, 10, & 12 Skills required:Basic Multiplication/Division FactsMaterials Needed: LEGO Gear Machines*The Challenge:Determine the relationship between the number of blue handle turns and the number of green handle turns.

Gear Machine - Multiplying and Dividing by 10 and 100Skills required:Basic Multiplication/Division FactsMultiplying and Dividing Decimals by Powers of 10Materials Needed: LEGO Gear Machine*The Challenge: Determine the relationships between the numbers of blue handle turns, yellow handle turns, and green handle turns.

Gear Machine - Student DesignedSkills Required:Simplifying FractionsMultiplying Fractions by Whole NumbersMultiplying Fractions by Fractions (4-gear Machines)Materials Needed: LEGO Gear Machines The Challenge:Determine the relationship between the number of green handle turns and the number of blue handle turns.

Angle Maker Skills Required:Three-Digit SubtractionOne-Digit-by-Three-Digit MultiplicationDrawing Angles with a ProtractorMaterials Needed: LEGO Angle Makers*The Challenge:Determine the measure of the angle created by a given number of handle turns.

*May require some gears which are included in the WeDo 1.0 kits, but not the 2.0 kits.

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LEGO WeDo 2.0 Math Challenge

Wobble PullSkills Required:Measuring AnglesMultiplying and Subtracting Decimals

What to Build: The Pull-Robot (1a), modified as shown so that the trailer has a shorter length and higher walls.

Other Materials Needed:36 Dice (16 mm)ProtractorA Ramp (slope needs to be adjustable)

The Challenge: Determine the weights that Pull-Robot can pull up different slopes.

Procedure:

1. Create a ramp with a 10° slope. How many dice can you put in the trailer and still have the car pull them up the ramp? ______

2. How heavy is this dice load (each die weighs 4.4 g)? ______

3. Raise the ramp so that it has a 15° slope. Now how many dice can you put in the trailer and still have the car pull them up the ramp? ______

4 How heavy is this dice load? ______

5. Raise the ramp so that it has a 20° slope. Now how many dice can you pull up the ramp? ______

6. How heavy is this dice load? ______

7. How much heavier is the load that can be pulled up the 10° slope than the load that can be pulled up the 15° slope? ______ How much heavier is the load that can be pulled up the 15° slope than the load that can be pulled up the 20° slope? ______

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Wobble Pull (KEY)Skills Required:Measuring AnglesMultiplying and Subtracting Decimals

What to Build: The Pull-Robot (1a), modified as shown so that the trailer has a shorter length and higher walls.

Other Materials Needed:36 Dice (16 mm)ProtractorA Ramp (slope needs to be adjustable)

The Challenge: Determine the weights that Pull-Robot can pull up different slopes.

Procedure:

1. Create a ramp with a 10° slope. How many dice (up to 36) can you put in the trailer and still have the car pull them up the ramp? Most likely 36.

2. How heavy is this dice load (each die weighs 4.4 g)? 158.4 g, if the load is 36 dice

3. Raise the ramp so that it has a 15° slope. Now how many dice can you put in the trailer and still have the car pull them up the ramp? _____

4 How heavy is this dice load? _______

5. Raise the ramp so that it has a 20° slope. Now how many dice can you pull up the ramp? Most likely 0

6. How heavy is this dice load? Most likely 0

7. How much heavier is the load that can be pulled up the 10° slope than the load that can be pulled up the 15° slope? _______ How much heavier is the load that can be pulled up the 15° slope than the load that can be pulled up the 20° slope? _______

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Frog vs. Tadpole Skills Required:Metric LengthSimplifying FractionsMultiplying Fractions by Whole Numbers

What to Build: The Frog (4a) and the Tadpole (Guided Project 4), assembled so that the left legs of each point in the same direction as the right legs of each.

Other Materials Needed:Meter StickString

The Challenge: Measure how far the Frog travels with a given number of hops and estimate how about how far the Tadpole will travel if taking the same number of hops.

Procedure:

1. To the nearest multiple of 6, how many mm long is the Tadpole’s back Leg (including the rubber piece)? _______

2. To the nearest multiple of 6, how many mm long is the Frog’s back Leg (including the “wheel”)? ______

3. What fraction represents the relationship between the length of the Tadpole’s back legs compared the Frog’s? (Make answer #1 the numerator and answer #2 the denominator, and simplify) ______

4. Have the Frog travel 10 hops on a bare floor. Measure and record the distance traveled in cm. If the frog doesn’t travel in a straight line, use string to mark the curve of its path and then measure the length of the string once you straighten it out. Distance traveled: ______

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5. About how many cm should the Tadpole travel in 10 hops? (Multiply answer #3 by answer #4) ______

6. Have the Tadpole travel 10 hops on the same floor, then measure and record this distance in cm: ______

7. Was the distance traveled greater than, less than, or equal to the answer to #5? ______

8. Complete the chart below. First measure the frog cm traveled, then predict the distance the tadpole will travel in the same number of hops. For this prediction, you should multiply by the fraction in answer #3, and then, if necessary, adjust this answer based on what you discovered in steps #6 and #7.

Frog/Tadpole hops Frog cm Traveled Tadpole cm Traveled Calculated Prediction

Tadpole cm Traveled Actual Distance

712515

Reflection: Were your predictions close to the actual Tadpole distances traveled________Why do you think this was the case?_________________________________________________________________________________________________________________________________

Extra Challenge: About how many hops do you think it will take the frog to travel 3 meters?_____ About how many hops do you think it will take the tadpole to travel this distance? _____ Have each travel these distances and see how close your estimates were.

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Frog vs. Tadpole (KEY)Skills Required:Metric LengthSimplifying FractionsMultiplying Fractions by Whole Numbers

What to Build: The Frog (4a) and the Tadpole (Guided Project 4), assembled so that the left legs of each point in the same direction as the right legs of each.

Other Materials Needed:Meter StickString

The Challenge: Measure how far the Frog travels with a given number of hops and estimate how about how far the Tadpole will travel if taking the same number of hops.

Procedure:

1. 1. To the nearest multiple of 6, how many mm long is the Tadpole’s back Leg (including the rubber piece)? 36 mm

2. To the nearest multiple of 6, how many mm long is the Frog’s back Leg (including the “wheel”)? 54 mm

3. What fraction represents the relationship between the length of the Tadpole’s back legs compared the Frog’s? (Make answer #1 the numerator and answer #2 the denominator, and simplify) 2/3

4. Have the Frog travel 10 hops on a bare floor. Measure and record the distance traveled in cm. If the frog doesn’t travel in a straight line, use string to mark the curve of its path and then measure the length of the string once you straighten it out. Distance traveled: ______

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Frog vs. Tadpole (KEY)Skills Required:Metric LengthSimplifying FractionsMultiplying Fractions by Whole Numbers

What to Build: The Frog (4a) and the Tadpole (Guided Project 4), modified as shown so that the back legs of each point in the opposite directions.

Other Materials Needed:Meter StickStringCarpeted/Rug Floor Surface

The Challenge: Measure how far the Frog travels with a given number of steps and estimate how about how far the Tadpole will travel if taking the same number of steps.

Procedure:

1. To the nearest multiple of 6, how many mm long is the Tadpole’s back Leg (including the rubber piece)? 36 mm

2. To the nearest multiple of 6, how many mm long is the Frog’s back Leg (including the “wheel”)? 54 mm

3. What fraction represents the relationship between the length of the Tadpole’s back legs compared the Frog’s? (Make answer #1 the numerator and answer #2 the denominator, and simplify) 2/3

4. Have the Frog travel 10 steps on a carpet/rug floor, counting only left or right leg steps (do not count the steps of both legs combined). Measure and record the distance traveled in cm. If the frog doesn’t travel in a straight line, use string to mark the curve of its path and then measure the length of the string once you straighten it out. Distance traveled: _________

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Mantis Mania A Skills Required:Measuring in Centimeters The Four Operations with Whole Numbers

What to Build: The Mantis (10b), modified as shown to have its hands hanging down from the more narrow white pieces.

Other Materials Needed:Metric RulerTwo DiceThree-ring Binder with 1” Rings

The Challenge: Construct a ramp up which the Mantis will push dice.

Procedure:All measurements will be in whole cm. When necessary, round to the nearest whole.1. Begin with the mantis’ arms pulled all the way back, and its body propped up as high as

possible with its legs completely vertical. Measure and record the height from the desk/table top surface to the bottom tips of the mantis’ “hands.” ______

2. Now fully extend its arms and again measure and record the height from desk/table top surface to the bottom tips of the mantis’ “hands.” _____

3. How much higher are the fully extended hands compared to the pulled back hands? (Subtract answer #1 from answer #2.) _____

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4. How much longer are the fully extended arms compared to the pulled back arms? (One way to find this is by measuring a certain LEGO piece – observe as the arms are extending to figure out which piece this is). _______

5. The back cover of the binder will lie flat on the desk/table, and a ramp will begin going up where the spine meets the front cover. Determine the height of the beginning of the ramp by measuring and recording the width of the spine of the binder. __________

6. The front cover of the notebook will be tilted up (partially opened) to form the slope of the ramp. How long will the ramp be? (In other words, how many cm wide is the front cover?) _____

7. The Mantis will only push the dice up a portion of the ramp, that portion being the length it can extend its arms. About many times longer is the ramp than the distance the dice will be pushed? (Divide answer #6 by answer #4, do not include the reminder n your answer) ______.

8. The height gained by traveling completely up the ramp must also be this many times greater that the height the dice will gain when pushed. What will be the height gain from the beginning of the ramp to the end? (Multiply answer #7 by answer #3)______

9. Find the height of the end of the ramp. It should be the sum of the height gain and the height of the beginning of the ramp. (Add answer #5 to answer #8) ______

10. How tall is a regular LEGO brick? ______

11. How many LEGO bricks high will the end of the ramp be? ______

12. Build a stand this many bricks high to prop up the end of the ramp, and then test your ramp with the Mantis and dice to see if it works.

Reflection: Did your ramp work? _______ If not, was the slope it too steep (high) or too gradual (low)? ______ Why do you think this was the case? _________________________________________________________________________________________



Mantis Mania A (KEY)Skills Required:Measuring in Centimeters The Four Operations with Whole Numbers

What to Build: The Mantis (10b), modified as shown to have its hands hanging down from the more narrow white pieces.

Other Materials Needed:Metric RulerTwo DiceThree-ring Binder with 1” Rings


Procedure:All measurements will be in whole cm. When necessary, round to the nearest whole.1. Begin with the mantis’ arms pulled all the way back, and its body propped up as high as

possible with its legs completely vertical. Measure and record the height from the desk/table top surface to the bottom tips of the mantis’ “hands.” 5 cm?

2. Now fully extend its arms and again measure and record the height from desk/table top surface to the bottom tips of the mantis’ “hands.” 7 cm

3. How much higher are the fully extended hands compared to the pulled back hands? (Subtract answer #1 from answer #2.) 2 cm


4. How much longer are the fully extended arms compared to the pulled back arms? (One way to find this is by measuring a certain LEGO piece - the long skinny white one with “teeth”– observe as the arms are extending to figure out which piece this is). 6 cm

5. The back cover of the binder will lie flat on the desk/table, and a ramp will begin going up where the spine meets the front cover. Determine the height of the beginning of the ramp by measuring and recording the width of the spine of the binder. 4 cm

6. The front cover of the notebook will be tilted up (partially opened) to form the slope of the ramp. How long will the ramp be? (In other words, how many cm wide is the front cover?) 26 cm

7. The Mantis will only push the dice up a portion of the ramp, that portion being the length it can extend its arms. About many times longer is the ramp than the distance the dice will be pushed? (Divide answer #6 by answer #4, do not include the reminder n your answer) 4.

8. The height gained by traveling completely up the ramp must also be this many times greater that the height the dice will actually be pushed. What will be the height gain from the beginning of the ramp to the end? (Multiply answer #7 by answer #3) 8 cm

9. Find the height of the end of the ramp. It should be the sum of the height gain and the height of the beginning of the ramp. (Add answer #5 to answer #8) 12 cm

10. How tall is a regular LEGO brick? 1 cm

11. How many LEGO bricks high will the end of the ramp be? 12





Mantis Mania BSkills Required:Measuring in CentimetersEquivalent FractionsMultiplying Fractions by Whole Numbers What to Build: The Mantis (10b), modified as shown to have its hands hanging down from the more narrow white pieces.

Other Materials Needed:Metric RulerTwo diceThree-ring Binder with 1” Rings


Procedure:All measurements will be in whole cm. Ignore any remainders in division solutions.1. Begin with the mantis’ arms pulled all the way back, and its body propped up as high as

possible with its legs completely vertical. Measure and record the height from the desk/table top surface to the bottom tips of the mantis’ “hands.” ______

2. Now fully extend its arms and again measure and record the height from desk/table top surface to the bottom tips of the mantis’ “hands.” _____

3. How much higher are the fully extended hands compared to the pulled back hands? (Subtract answer #1 from answer #2.) _____


4. How much longer are the fully extended arms compared to the pulled back arms? (One way to find this is by measuring a certain LEGO piece – observe as the arms are extending to figure out which piece this is). _______

5. The back cover of the binder will lie flat on the desk/table, and a ramp will begin going up where the spine meets the front cover. Determine the height of the beginning of the ramp by measuring and recording the width is the spine of the binder. __________

6. The front cover of the notebook will be tilted up (partially opened) to form the slope of the ramp. How long will the ramp be? (In other words, how many cm wide is the front cover?) _____

7. The height to be gained by the dice is a fraction of the distance the dice is to be pushed. What is this fraction? (Make answer #3 your numerator and answer #4 your denominator and simplify) ______.

8. The height gained by traveling completely up the ramp must also be about this fraction of the length of the ramp. What will be the height gain from the beginning of the ramp to the end? (Multiply answer #7 by answer #6 include only the whole number in your answer) ______

9. Find the height that the end (highest part) of the ramp will need to be. It should be the sum of the height gain and the height of the beginning (lowest part) of the ramp. (Add answer #5 to answer #8) ______

10. How tall is a regular LEGO brick? ______

11. How many LEGO bricks high will the end of the ramp be? ______

12. Build a stand this many bricks high to prop up the end of the ramp, and then test you ramp with the Mantis and dice to see if it works.




Mantis Mania B (KEY)Skills Required:Measuring in CentimetersEquivalent FractionsMultiplying Fractions by Whole Numbers What to Build: The Mantis (10b), modified as shown to have its hands hanging down from the more narrow white pieces.

Other Materials Needed:Metric RulerTwo diceThree-ring Binder with 1” Rings


Procedure:All measurements will be in whole cm. Ignore any remainders in division solutions.1. Begin with the mantis’ arms pulled all the way back, and its body propped up as high as

possible with its legs completely vertical. Measure and record the height from the desk/table top surface to the bottom tips of the mantis’ “hands.” 5 cm

2. Now fully extend its arms and again measure and record the height from desk/table top surface to the bottom tips of the mantis’ “hands.” 7 cm

3. How much higher are the fully extended hands compared to the pulled back hands? (Subtract answer #1 from answer #2.) 2 cm


4. How much longer are the fully extended arms compared to the pulled back arms? (One way to find this is by measuring a certain LEGO piece (the long skinny white one with “teeth”– observe as the arms are extending to figure out which piece this is). 6 cm

5. The back cover of the binder will lie flat on the desk/table, and a ramp will begin going up where the spine meets the front cover. Determine the height of the beginning of the ramp by measuring and recording the width of the spine of the binder. 4 cm

6. The front cover of the notebook will be tilted up (partially opened) to form the slope of the ramp. How long will the ramp be? (In other words, how many cm wide is the front cover?) 26 cm

7. The height to be gained by the dice is a fraction of the distance the dice is to be pushed. What is this fraction? (Make answer #3 your numerator and answer #4 your denominator and simplify) 1/3.

8. The height gained by traveling completely up the ramp must also be about this fraction of the length of the ramp. What will be the height gain from the beginning of the ramp to the end? (Multiply answer #7 by answer #6, include only the whole number in your answer) 4 cm

9. Find the height of the end of the ramp. It should be the sum of the height gain and the height of the beginning of the ramp. (Add answer # 5 to answer # 8) 12 cm

10. How tall is a regular LEGO brick? 1 cm

11. How many LEGO bricks high will the end of the ramp be? 12





Steer Car Square Course Skills Required:Measuring in Inches Right Angles Calculating Quotients ending in .5

What to Build: Steer (12).

Other Materials Needed:Yard StickMasking Tape

The Challenge: Program the Steer Car to travel around a square course.

Procedure:All measurements will be inches. 1. On a bare floor use tape to form the perimeter of a one yard by one yard square.

2. You will program the steer car to travel once around the perimeter. The car will go counterclockwise, making three left hand turns. The car should finish very near to its starting point. How many long is each of the four straight sections? ____________

3. The car “loses” about 9 inches in distance each time it begins a turn and each time it ends a turn. How far will the car need to travel on the first straightaway before it starts to turn? (add 9 to answer #2)______ This number will also be the distance it needs to travel on the fourth straightaway, because this segment of the trip occurs after the final turn.

4. Both the second and third straightaways are before and after turns. How far will the car need to travel on each of these two straightaways (add the product of 9 and 2 to answer #2) _______

5. You will program the motor to turn at a speed of 8. If the car travels about 6 inches per second at this speed, how many seconds will it take the car to travel the necessary


length of first and fourth straightaways (divide answer #3 by 6; write the quotient as a decimal) _______?

6. At this speed, how many seconds will it take the car to travel the necessary length of the second and third straightaways (divide answer #4 by 6) _______?

7. What type of angle will each turn need to be (obtuse, acute, or right?) ______How many degrees is this angle? _______ To make this angle turning left, the car will also have to make a turn of this many degrees.

8. A complete circle is 360 degrees. How many of the car’s turns will make up a complete circle? (Divide 360 by answer #7) ______

9 At the speed of 8 the cars makes a complete circle in about 10 seconds. About how many seconds will it take the car to make each turn (divide 10 by answer #8 and write the quotient as a decimal) _______?

10. Now create the program for the car, using all these numbers, and test it on the course. The car is allowed to leave the course as it is making turns, but otherwise it should stay near the course and end up near where it began. If your car does not complete the course successfully, modify the program and try again.

Reflection: Did your program work the first time you tried it? _______ If not, was the problem related to the turns or distances traveled on the straightaways? ______ How did you attempt to fix this problem? _____________________________________________________________________________________________________________



Steer Car Square Course (KEY)

Skills Required:Measuring in Inches Right Angles Calculating Quotients ending in .5



The Challenge: Program the Steer Car to travel around a square course.

Procedure:All measurements will be inches. 1. On a bare floor use tape to form the perimeter of a one yard by one yard square.

2. You will program the steer car to travel once around the perimeter. The car will go counterclockwise, making three left hand turns. The car should finish very near to its starting point. How many long is each of the four straight sections? 36 in

3. The car “loses” about 9 inches in distance each time it begins a turn and each time it ends a turn. How far will the car need to travel on the first straightaway before it starts to turn? (add 9 to answer #2) 45 in This number will also be the distance it needs to travel on the fourth straightaway, because this segment of the trip occurs after the final turn.

4. Both the second and third straightaways are before and after turns. How far will the car need to travel on each of these two straightaways? (add the product of 9 and 2 to answer #2) 54 in


5. You will program the motor to turn at a speed of 8. If the car travels about 6 inches per second at this speed, how many seconds will it take the car to travel the necessary length of first and fourth straightaways? (divide answer #3 by 6; write the quotient as a decimal) 7.5

6. At this speed, how many seconds will it take the car to travel the necessary length of the second and third straightaways (divide answer #4 by 6) 9?

7. What type of angle will each turn need to be (obtuse, acute, or right?) rightHow many degrees is this angle? 90 To make this angle turning left, the car will also have to make a turn of this many degrees.

8. A complete circle is 360 degrees. How many of the car’s turns will make up a complete circle? (Divide 360 by answer #7) 4

9 At the speed of 8 the cars makes a complete circle in about 10 seconds. About how many seconds will it take the car to make each turn (divide 10 by answer #8 and write the quotient as a decimal) 2.5?


Reflection: Did your program work the first time you tried it? _______ If not, was the problem related to the turns or distances traveled on the straightaways? ______ How did you attempt to fix this problem? _____________________________________________________________________________________________________________



Steer Car Equilateral Triangle Course Skills Required:Converting Between Yards and Inches Angles and Rotation DegreesCalculating Quotients ending in .5



The Challenge: Program the Steer Car to travel around an equilateral triangle course.

Procedure:All measurement answers should be in inches. 1. On a bare floor use tape to form the perimeter of an equilateral triangle in which all sides

are a yard and a half long.

2. You will program the steer car to travel once around the perimeter. The car will go counterclockwise, making two left hand turns. The car should finish very near to its starting point. How many long is each of the three straight sections? ____________

3. The car “loses” about 9 inches in distance each time it begins a turn and each time it ends a turn. How far will the car need to travel on the first straightaway before it starts to turn? (add 9 to answer #2)______ This number will also be the distance it needs to travel on the third straightaway, because this segment of the trip occurs after the final turn.

4. The second straightaway is before and after a turn. How far will the car need to travel on each of these two straightaways? (add the product of 9 and 2 to answer #2) _______

5. You will program the motor to turn at a speed of 8. If the car travels about 6 inches per second at this speed, how many seconds will it take the car to travel the necessary


length of first and third straightaways (divide answer #3 by 6; write the quotient as a decimal)? _______

6. At this speed, how many seconds will it take the car to travel the necessary length of the second straightaway? (divide answer #4 by 6) _______

7. The sum of the measurements of triangle angles is always 180.How many degrees is each angle? (divide 180 by 3) _______

8. To make this angle turning left, the car will have to make a turn (rotation) equal the difference between 180 (which would be a complete “turn around”) and the angle created by the turn. How many degrees will the car need to rotate (turn)? (subtract answer #7 from 180) _______

9. A complete circle is 360 degrees. How many of the car’s turns will make up a complete circle? (Divide 360 by answer #8) ______

10 At the speed of 8 the cars makes a complete circle in about 10 seconds. About how many seconds will it take the car to make each turn (divide 10 by answer #9 and record a whole number quotient, ignoring any remainder) _______?


Reflection: Did your program work the first time you tried it? _______ If not, was the problem related to the turns or distances traveled on the straightaways? ______ How did you attempt to fix this problem? ____________________________________________________________________________________________________________________________________



Steer Car Equilateral Triangle Course (KEY)Skills Required:Converting Between Yards and Inches Angles and Rotation DegreesCalculating Quotients ending in .5



The Challenge: Program the Steer Car to travel around an equilateral triangle course.

Procedure:All measurement answers should be in inches. 1. On a bare floor use tape to form the perimeter of an equilateral triangle in which all sides

are a yard and a half long.

2. You will program the steer car to travel once around the perimeter. The car will go counterclockwise, making two left hand turns. The car should finish very near to its starting point. How many long is each of the three straight sections? 54 in

3. The car “loses” about 9 inches in distance each time it begins a turn and each time it ends a turn. How far will the car need to travel on the first straightaway before it starts to turn? (add 9 to answer #2) 63 in This number will also be the distance it needs to travel on the third straightaway, because this segment of the trip occurs after the final turn.

4. The second straightaway is before and after a turn. How far will the car need to travel on each of these two straightaways? (add the product of 9 and 2 to answer #2) 72 in


5. You will program the motor to turn at a speed of 8. If the car travels about 6 inches per second at this speed, how many seconds will it take the car to travel the necessary length of first and third straightaways? (divide answer #3 by 6; write the quotient as a decimal)

6. At this speed, how many seconds will it take the car to travel the necessary length of the second straightaway? (divide answer #4 by 6) 12 in?

7. The sum of the measurements of triangle angles is always 180.How many degrees is each angle? (divide 180 by 3) 60

8. To make this angle turning left, the car will have to make a turn (rotation) equal the difference between 180 (which would be a complete “turn around”) and the angle created by the turn. How many degrees will the car need to rotate (turn)? (subtract answer #7 from 180) 120

9. A complete circle is 360 degrees. How many of the car’s turns will make up a complete circle? (Divide 360 by answer #8) 3

10 At the speed of 8 the cars makes a complete circle in about 10 seconds. About how many seconds will it take the car to make each turn (divide 10 by answer #9 and record a whole number quotient, ignoring any remainder) 3?


Reflection: Did your program work the first time you tried it? _______ If not, was the problem related to the turns or distances traveled on the straightaways? ______ How did you attempt to fix this problem? ____________________________________________________________________________________________________________________________________



Dump ItSkills Required:Adding, Subtracting, and Multiplying Decimals

What to Build: The Recycling Truck (8a)

Other Materials Needed:7 Dice (16 mm)7 Square LEGO Bricks

The Challenge: Determine the heaviest possible weight you can get the truck to dump.

Procedure:

1. Examine one square brick and one die. Each die weighs 4.4 g and each brick weighs 1.16 g. Which is heavier, a die or a brick?_____ How much heavier? ____

2. You will fill the bed of the truck with loads of 8 items, in a single 2 x 4 layer (no stacking). The loads will consist of different combinations of dice and square LEGO bricks. You will test dumping each combination with the dice at the front end of the bed (closest to the cab) and the bricks at the back, and you will also test each combination with the dice at the back and the bricks at the front. Do you think you will be able to dump a heavier load with the dice at the front, with the dice at the back, or do you think the arrangement will make no difference in the weight you can dump? _______________ Why do you think this?__________________________________________________________________ ______________________________________________________________________

3. Create a program to get the truck to dump at the speed of 10. Have the truck attempt to

dump the different combinations of dice and bricks listed on the data charts on the next page. Calculate the total weight of the load and record it on the chart Next, test to see if each load will dump with all the dice at the front, and then test it with all the dice at the back. Record your results by writing “yes” or “no” in the appropriate columns.


Number of Dice

Number of Bricks

Total Weight (g)

Does it Dump with the Dice at the Front and the Bricks at the Back?

Does it Dump with the Bricks at the Front and the Dice at the Back?

1 72 63 54 45 36 27 1

4. What is the greatest amount of weight that could be dumped with the dice at the front and the bricks at the back?:_______

5. What is the greatest amount of weight that could be dumped with the bricks at the front and the dice at the back?:_______

6. Were you able to dump a heavier load with the dice at the front, at the back, or did the arrangement make no difference in the weight you could dump? ________ If there was a difference in total weight dumped between these two arrangements, what was this difference? (subtract the lesser total from the greater total in answers #4 and #5.) ___________

7. Was your hypothesis (answer #2) correct?______ Why do you think this was the case? _____________________________________________________________________ ______________________________________________________________________

Extra Challenge: Use the chart to help you determine the weight of 8 dice ______ and 8 bricks ______ (In other word, find these values without multiplying 8 by the weight of one unit).



Dump It (KEY)Skills Required:Adding, Subtracting, and Multiplying Decimals

What to Build: The Recycling Truck (8a)

Other Materials Needed:7 Dice (16 mm)7 Square LEGO Bricks

The Challenge: Determine the heaviest possible weight you can get the truck to dump.

Procedure:

1. Examine one square brick and one die. Each die weighs 4.4 g and each brick weighs 1.16 g. Which is heavier, a die or a brick? A die How much heavier? 3.24 g

2. You will fill the bed of the truck with loads of 8 items, in a single 2 x 4 layer (no stacking). The loads will consist of different combinations of dice and square LEGO bricks. You will test dumping each combination with the dice at the front end of the bed (closest to the cab) and the bricks at the back, and you will also test each combination with the dice at the back and the bricks at the front. Do you think you will be able to dump a heavier load with the dice at the front, with the dice at the back, or do you think the arrangement will make no difference in the weight you can dump? _______________ Why do you think this?__________________________________________________________________ ______________________________________________________________________

3. Create a program to get the truck to dump at the speed of 10. Have the truck attempt to

dump the different combinations of dice and bricks listed on the data charts on the next page. Calculate the total weight of the load and record it on the chart Next, test to see if each load will dump with all the dice at the front, and then test it with all the dice at the back. Record your results by writing “yes” or “no” in the appropriate columns.

Number Number Total Does it Dump with the Does it Dump with the


of Dice of Bricks Weight (g) Dice at the Front and the Bricks at the Back?

Bricks at the Front and the Dice at the Back?

1 7 12.522 6 15.763 5 194 4 22.245 3 25.486 2 28.727 1 31.96

4. What is the greatest amount of weight that could be dumped with the dice at the front and the bricks at the back?:_______

5. Were you able to dump a heavier load with the dice at the front, at the back, or did the arrangement make no difference in the weight you could dump? Dice at the back If there was a difference in total weight dumped between these two arrangements, what was this difference? (subtract the lesser total from the greater total in answers #4 and #5.) ___________

7. Was your hypothesis (answer #2) correct?______ Why do you think this was the case? _____________________________________________________________________ _____________________________________________________________________

Extra Challenge: Use the chart to help you determine the weight of 8 bricks 9.28 g and of 8 dice 35.2 g (In other words, find these values without multiplying 8 by the weight of one unit).

Explanation: 12.52 – 3.24 = 9.28 g and 31.96 + 3.24 = 35.2. 3.24 is the difference between the weight of one brick and one die, and this is also the amount by which the values on the chart are increasing.



EarthquakeSkills Required:Calculating Area

Optional Skills Required:Calculating Volume (Earthquake Data Chart Versions B and C)Multiplying Decimals (Earthquake Data Chart Version B)Multiplying Fractions (Earthquake Data Chart Version C)

What to Build: Earthquake (3a); modified as shown so that a base plate is the “ground” for the quake.

Other Materials Needed:36 Dice

The Challenge: Calculate the dimensions of various dice “buildings” and observe how long they can survive the earthquake

Procedure:

1. What kind of dice “building” do you think will survive longer in an earthquake – one that is lower and longer, or one that is higher and shorter in length? ______

2. You will build 3 different rectangular prism buildings out of 36 dice, each having a base width of 3 dice. The first building will be 2 dice high, the second will be 3 dice high, and the third will be 4 dice high. As the buildings get higher, the length will shorten.

3. As you build each building, use your math skills to calculate the dimensions and record them on the “Earthquake Data Chart.”


4. Test how long each building survives an earthquake by dong the following: Run a program in which the motor rotates at a speed of 2. Hold the motor still during the “quake,” but do not touch the baseplate. First run the program for 1 second. If the building survives, run a 2-second program, then continue adding one second at a time to the program (leaving the speed at 2) until at least one die falls over. Once that happens, record the programmed time minus one under the “Seconds Survived” column. If the building survives a 10-second quake, then stop testing this building and write “10+” under “Seconds Survived.”

Earthquake Data Chart Version A

Height Base Width

Base Length

Base Area

Volume Seconds Survived

2 Dice 3 Dice 36 Dice



5. After you have finished testing all three buildings and completed your “Earthquake Data Chart,” reflect back on your hypothesis (answer #1). Were you correct?__________Why or why not? __________________________________________________________________________________________________________________________



Earthquake Data Chart Version BA side of a die is 1.6 cm long

Heightin Dice

Heightin cm

Base Widthin Dice

Base Widthin cm

Base Lengthin Dice

Base Lengthin cm

Base Areain Dice

Base Areaincm2

Volumein Dice

Volumein cm3

Seconds Survived

2 3 36

3 3 36

4 3 36




Earthquake Data Chart Version CA side of a die is 5/8 inches long

Heightin Dice

Heightin cm

Base Widthin Dice

Base Widthin cm

Base Lengthin Dice

Base Lengthin cm

Base Areain Dice

Base Areaincm2

Volumein Dice

Volumein cm3

Seconds Survived

2 3 36

3 3 36

4 3 36



Earthquake Data Charts (KEY)Version A

Height Base Width

Base Length

Base Area

Volume Seconds Survived

2 Dice 3 Dice 6 Dice 18 Dice 36 Dice



Version B; a side of a die is 1.6 cm long.Heightin Dice

Heightin cm

Base Widthin Dice

Base Widthin cm

Base Lengthin Dice

Base Lengthin cm

Base Areain Dice

Base Areaincm2

Volumein Dice

Volumein cm3

Seconds Survived

2 3.2 3 4.8 6 9.6 18 46.08 36 147.456

3 4.8 3 4.8 4 6.4 12 30.72 36 147.456

4 6.4 3 4.8 3 4.8 9 23.04 36 147.456

Version C; a side of a die is 5/8 inches long.Heightin Dice

Heightin cm

Base Widthin Dice

Base Widthin cm

Base Lengthin Dice

Base Lengthin cm

Base Areain Dice

Base Areaincm2

Volumein Dice

Volumein cm3

Seconds Survived

2 1¼ 3 1 7/8 6 3 3/4 18 7 1/32 36 8 101/128

3 1 7/8 3 1 7/8 4 2½ 12 4 11/16 36 8 101/128

4 2½ 3 1 7/8 3 1 7/8 9 3 33/64 36 8 101/128



Bee Revolution Skills Required:Adding, Multiplying and Rounding Decimals

What to Build: The Flower (5a; Actually, you only build the bee. The flower is not necessary)


Procedure:

1. At a speed of 1, the bee makes about 0.6 revolutions during the first second of the program and 0.45 revolutions for every second thereafter. About how many revolutions should the bee make during 7 seconds at a speed of 1?______

2. Run a program in which the bee revolves for 8 seconds at a speed of 1, and count the revolutions. Was your estimation (answer #1) close?______

3. At a speed of 3, the bee makes about .8 revolutions during the first second of the program and 0.65 revolutions for every second thereafter. About how many revolutions should the bee make during 8 seconds at a speed of 3? ______

4. Run a program in which the bee revolves for 8 seconds at a speed of 3, and count the revolutions. Was your estimation (answer #3) close? ______

5. At a speed of 5, the bee makes about 1.1 revolutions during the first second of the program and 0.75 revolutions for every second thereafter. About how many revolutions should the bee make during 10 seconds at a speed of 5?______


Extra Challenge: About how many revolutions should the bee make with a program in which the bee revolves for 6 seconds at a speed of 1, then 6 seconds at a speed of 3, and then 6 seconds at a speed of 5?______ Test your calculations by writing this program and running it.



Bee Revolution (KEY)Skills Required:Adding, Multiplying and Rounding Decimals

What to Build: The Flower (5a; Actually, you only build the bee. The flower is not necessary)


Procedure:

1. At a speed of 1, the bee makes about 0.6 revolutions during the first second of the program and 0.45 revolutions for every second thereafter. About how many revolutions should the bee make during 7 seconds at a speed of 1? 3


3. At a speed of 3, the bee makes about .8 revolutions during the first second of the program and 0.65 revolutions for every second thereafter. About how many revolutions should the bee make during 8 seconds at a speed of 3? 5


5. At a speed of 5, the bee makes about 1.1 revolutions during the first second of the program and 0.75 revolutions for every second thereafter. About how many revolutions should the bee make during 10 seconds at a speed of 5? 8


Extra Challenge: About how many revolutions should the bee make with a program in which the bee revolves for 6 seconds at a speed of 1, then 6 seconds at a speed of 3, and then 6 seconds at a speed of 5? 11 Test your calculations by writing this program and running it.



Gear Machine 16:8 Skills Required:Basic Multiplication/Division Facts

Gears Needed:

What to Build:

The same gear machine is pictured twice, from two different sides.

The Challenge: Determine the relationship between the number of blue handle turns and the number of green handle turns.

Procedure:1. How many teeth are on the gear turned directly by the blue handle?____

2. How many teeth are on the gear turned directly by the green handle?____

3. How many times bigger is the gear turned directly by blue handle compared to the one turned directly by the green handle? (divide answer #1 by answer #2) _____

4. Turn the blue handle completely around once. Does the green handle turns this many (answer to #3) times?______ If not, check your work for steps 1-3.


5. Now complete the chart below. To find “Green Handle Turns,” multiply “Blue Handle Turns” by answer #3. You can then check your answers by turning the blue handle and counting the turns of the green handle.

Blue Handle Turns

Green Handle Turns

123456789101112

6. Use the chart to fill in the blanks below.

a. 3 x 2 =___b. __ x 2 = 10c. 7 x 2 = __d. 2 x 5 =___e. __ x 2 = 20f. 6 x 2 =__

g. __ x 2 = 8h. 8 x 2 =__i. 2 x __ = 4j. __ x 2 = 22k. __ x 2 = 2 l. 2 x __ = 18



Gear Machine 16:8 (Multiples of 2; KEY)Skills Required:Basic Multiplication/Division Facts

Gears Needed:

What to Build:



Procedure:1. How many teeth are on the gear turned directly by the blue handle? 16

2. How many teeth are on the gear turned directly by the green handle? 8

3. How many times bigger is the gear turned directly by blue handle compared to the one turned directly by the green handle? (divide answer #1 by answer #2) 2





Gears Needed:

What to Build:


The Challenge:Determine the relationship between the number of green handle turns to number of blue handle turns.







Blue Handle Turns

Green Handle Turns

123456789101112


a. 3 x 3 =___b. __ x 3 = 27c. 7 x 3 = __d. 3 x 5 =___e. __ x 3 = 33f. 3 x 10 =__

g. __ x 3 = 3h. 8 x 3 =__i. 3 x __ = 36j. __ x 3 = 18k. __ x 3 = 6 l. 3 x __ = 12



Gear Machine 24:8 (Multiples of 3; KEY)Skills Required:Basic Multiplication/Division Facts

Gears Needed:

What to Build:


The Challenge:Determine the relationship between the number of green handle turns to number of blue handle turns.

Procedure:. How many teeth are on the gear turned directly by the blue handle? 24







Gears Needed:

What to Build:

The same gear machine is pictured twice, from two different sides..

The Challenge:Determine the relationship between the number of blue handle turns and the number of green handle turns.







Blue Handle Turns

Green Handle Turns

123456789101112


a. 5 x 2 =___b. __ x 5 = 20c. 7 x 5 = __d. 12 x 5 =___e. __ x 5 = 40f. 6 x 5 =__

g. __ x 5 = 5h. 9 x 5 =__i. 5 x __ = 15j. __ x 5 = 55k. __ x 5 = 25 l. 5 x __ = 50



Gear Machine 40:8 (Multiples of 5; KEY)

Skills Required:Basic Multiplication/Division Facts

Gears Needed:

What to Build:

The same gear machine is pictured twice, from two different sides..


Procedure:1. How many teeth are on the gear turned directly by the blue handle? 40






Gear Machine 16:8 & 16:8


Gears Needed:

What to Build:




Procedure:1. How many teeth are on the gear turned directly by the blue handle? _____ 2. How many teeth are on the gear connected to the gear turned directly by the blue

handle? _____

3. How many times bigger is the gear turned directly by blue handle compared to its connecting gear? (divide answer #1 by answer #2) _____

4. How many teeth are on the gear on the other end of the axle from the gear in answer #2? _____

5. How many teeth are on the gear turned directly by the green handle? _____

6. How many times bigger is the gear in answer #4 compared to the gear turned directly by the green handle (divide answer #4 by answer #5) _____

7. To find the number of times green handle turns for each blue handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #3 times answer #6) _____.

8. Turn the blue handle completely around once. Does the green handle turns completely around this many (answer to #7) times?______ If not, check your work for steps 1-7.



Blue Handle Turns

Green Handle Turns

123456789101112


a. 10 x 4 =___b. __ x 4 = 28c. 12 x 4 = 48d. 4 x 9 =___e. __ x 4 = 24f. 2 x 4 =___

g. __ x 4 = 4h. __ x 4 = 20i. 4 x __ = 44j. __ x 4 = 16k. 3 x 4 =___l. 4 x ___ = 32


Gear Machine 16:8 & 16:8 (Multiples of 4; KEY)Procedure:1. How many teeth are on the gear turned directly by the blue handle? 16 2. How many teeth are on the gear connected to the gear turned directly by the blue

handle? 8

3. How many times bigger is the gear turned directly by blue handle compared to its connecting gear? (divide answer #1 by answer #2) 2

4. How many teeth are on the gear on the other end of the axle from the gear in answer #2? 16


6. How many times bigger is the gear in answer #4 compared to the gear turned directly by the green handle (divide answer #4 by answer #5) 2

7. To find the number of times green handle turns for each blue handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #3 times answer #6) 4.






Gears Needed:

What to Build:





2. How many teeth are on the gear connected to the gear turned directly by the blue handle?____


4. How many teeth are on the gear on the other end of the axle from the gear in answer #2?______







Blue Handle Turns

Green Handle Turns

123456789101112


a. 3 x 6 =___b. __ x 6 = 48c. 12 x 6 =___d. 6 x 9 =___e. __ x 6 = 42f. 2 x 6 =___

g. 4 x 6 =___h. 6 x ___ = 66i. __ x 6 = 36j. 10 x 6 =___k. 6 x ___ = 6l. ___ x 6 = 30



Gear Machine 16:8 & 24:8 (Multiples of 6; KEY)Procedure:1. How many teeth are on the gear turned directly by the blue handle? 16

2. How many teeth are on the gear connected to the gear turned directly by the blue handle? 8





7. To find the number of times green handle turns for each blue handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #3 times answer #6) 6





Gears Needed:

What to Build:







4. How many teeth are on the gear on the other end of the axle from the gear in answer #2?______







Blue Handle Turns

Green Handle Turns

123456789101112


a. 9 x 9 =___b. __ x 9 = 9c. 7 x 9 = __d. 9 x 5 =___e. __ x 9 = 99f. 6 x 9 =__

g. __ x 9 = 18h. __ x 9 = 36i. 9 x __ = 72j. __ x 9 = 27k. 10 x 9 =__l. 9 x __ = 108














Gears Needed:

What to Build:







4. How many teeth are on the gear on the other end of the axle from the gear connected to the gear turned directly by the blue handle?______


6. How many times bigger is the gear in answer #4 compared to the gear turned directly by the green handle (multiply answer #4 times answer #5) _____





Blue Handle Turns

Green Handle Turns

123456789101112


a. 10 x 10 =___b. __ x 10 = 30c. 12 x 10 = __d. 4 x 10 =___e. __ x 10 = 10f. 10 x 8 =__

g. __ x 10 = 90h. __ x 10 = 60i. 5 x __ = 50j. __ x 10 = 70k. 2 x 10 =__l. 10 x __ = 110













Gear Machine 16:8, 16:8 & 16:8


Gears Needed:

What to Build:




A B C

D E F

Procedure:1. Record the number of teeth found on each gear:

A____ B____ C____ D____ E____ F____

2. Gear A drives Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) ____

3. Gear C drives Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) ____

4. Gear E drives Gear F. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) ____

5. To find the number of times green handle turns for each blue handle turn, find the product of the three relationships between the pairs of connecting gears. (multiply answer #2 times answer #3 times answer #4) _____.




Blue Handle Turns

Green Handle Turns

123456789101112


a. 12 x 8 =___b. __ x 8 = 48c. 2 x 8 = __d. 8 x 4 =___e. __ x 8 = 80f. 11 x 8 =__

g. __ x 8 = 24h. __ x 8 = 56i. 8 x __ = 40j. __ x 8 = 72k. 8 x 8 =__l. 8 x __ = 8


Gear Machine 16:8, 16:8 & 16:8 (Multiples of 8; KEY)Procedure:1. Record the number of teeth found on each gear:

A 16 B 8 C 16 D 8 E 16 F 8

2. Gear A drives Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) 2

3. Gear C drives Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) 2

4. Gear E drives Gear F. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) 2

5. To find the number of times green handle turns for each blue handle turn, find the product of the three relationships between the pairs of connecting gears. (multiply answer #2 times answer #3 times answer #4) 8




Gear Machine 16:8, 16:8 & 24:8


Gears Needed:

What to Build:




A B C

D E F

Procedure:

1. Record the number of teeth found on each gear:

A___ B____ C____ D____ E____ F____

2. Gear A drives Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) ____

3. Gear C drives Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) ____

4. Gear E drives Gear F. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) ____

5. To find the number of times green handle turns for each blue handle turn, find the product of the three relationships between the pairs of connecting gears. (multiply answer #2 times answer #3 times answer #4) _____.




Blue Handle Turns

Green Handle Turns

123456789101112


a. 12 x 3 =___b. __ x 12 = 60c. 12 x 10 = __d. 4 x 12 =___e. __ x 12 = 84f. 12 x 8 =__

g. __ x 12 = 144h. __ x 12 = 12i. 12 x __ = 132j. __ x 12 = 72k. 2 x 12 =__l. 12 x __ = 108


Gear Machine 16:8, 16:8 & 24:8 (Multiples of 12; KEY)1. Record the number of teeth found on each gear:

A 16 B 8 C 16 D 8 E 24 F 8

2. Gear A drives Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) 2

3. Gear C drives Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) 2


5. To find the number of times green handle turns for each blue handle turn, find the product of the three relationships between the pairs of connecting gears. (multiply answer #2 times answer #3 times answer #4) 8




Gear Machine 16:8, 40:8, 40:8, & 16:8

Skills Required:Basic Multiplication/Division FactsMultiplying and Dividing Decimals by Powers of 10

Gears Needed/What to Build

:

The same gear machine is pictured three times, from three different angles. It is important to note, in case you are looking at a black and white image, that the yellow handle is in the middle.

The Challenge: Determine the relationships between the numbers of blue handle turns, yellow handle turns, and green handle turns.


A B C D

E F G H

Procedure:

1. Record the number of teeth found on each gear:A ____ B ____ C ____ D ____ E ____ F ____ G ____ H ____

2. Gear A in driven by Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) ____

3. Gear C is driven by Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) ____

4. To find the number of times the yellow handle turns for each blue handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #2 times answer #3) ____

5. Turn the yellow handle and count how many complete turns it needs to make until the blue handle makes one complete turn (do not attempt to turn the blue handle). Did the number of yellow handle turns match answer #4?______ If not, check your work for steps 1-4.

6. Gear E drives Gear F. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) ___

7. Gear G drives Gear H. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) ___

8. To find the number of times the green handle turns for each yellow handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #6 times answer #7) ____

9. Turn the yellow handle completely around once. Does the green handle turns completely around this many (answer to #7) times?______ If not, check your work for steps 5-8.

10 How many times will you need to turn the green handle around until blue handle turns completely around once (multiply answer #4 times answer number 8) ____

11. Write this number (answer 9) as a power of ten.______


12. Reference the answers above and your gear machine to complete the chart. In the second column, on each row, you will write either “Times” or “Divided by.” In the third column, on each row, you will circle either “10” or “102.”

The Number of this Handle’s Turns

Times or Divided by

10 or 102 Equals the Number of this Handle’s Turns

Blue YellowYellow (Y) Blue (B)Yellow (Y) Green (G)Green (G) Yellow (Y)Blue (B) Green (G)Green (G) Blue (B)

13. Using the chart above to help you solve the equations below, and then use your gear machine to check the reasonableness of your answers.

A. 2.1 Y = _____ G

B. 35 G = _____ Y

C. 15 Y = _____ B

D. 0.26 B = _____ y

E. 47 G = _____ B

F. 0.23 B = _____ G

G. 32 G = _____ Y = _____ B

H. 0.03 B = _____ Y = _____ G


Gear Machine 16:8, 40:8, 40:8, & 16:8(Multiplying and Dividing by 10 and 100; KEY)Procedure:

1. Record the number of teeth found on each gear:A 16 B 8 C 40 D 8 E 40 F 8 G 16 H 8

2. Gear A in driven by Gear B. How many times more teeth does Gear A have compared to Gear B? (divide the number of teeth on Gear A by the number on Gear B) 2

3. Gear C is driven by Gear D. How many times more teeth does Gear C have compared to Gear D? (divide the number of teeth on Gear C by the number on Gear D) 5

4. To find the number of times the yellow handle turns for each blue handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #2 times answer #3) 10

5. Turn the yellow handle and count how many complete turns it needs to make until the blue handle makes one complete turn (do not attempt to turn the blue handle). Did the number of yellow handle turns match answer #4?______ If not, check your work for steps 1-4.


7. Gear G drives Gear H. How many times more teeth does Gear E have compared to Gear F? (divide the number of teeth on Gear E by the number on Gear F) 2

8. To find the number of times the green handle turns for each yellow handle turn, find the product of the two relationships between the pairs of connecting gears. (multiply answer #6 times answer #7) 10

9. Turn the yellow handle completely around once. Does the green handle turns completely around this many (answer to #7) times?______ If not, check your work for steps 5-8.

10. How many times will you need to turn the green handle around until blue handle turns completely around once (multiply answer #4 times answer # 8) 100

11. Write this number (answer 9) as a power of ten.102


12 Reference the answers above and your gear machine to complete the chart. In the second column, on each row, you will write either “Times” or “Divided by.” In the third column, on each row, you will circle either “10” or “102.”

The Number of this Handle’s Turns

Times or Divided by

10 or 102 Equals the Number of this Handle’s Turns

Blue Times 10 YellowYellow (Y) Divided by 10 Blue (B)Yellow (Y) Times 10 Green (G)Green (G) Divided by 10 Yellow (Y)Blue (B) Times 102 Green (G)Green (G) Divided by 102 Blue (B)

13. Using the chart above to help you solve the equations below, and then use your gear machine to check the reasonableness of your answers.

A. 2.1 Y = 21 G

B. 35 G = 3.5 Y

C. 15 Y = 1.5 B

D. 0.26 B = 2.6 y

E. 47 G = .47 B

F. 0.23 B = 23 G

G. 32 G = 3.2 Y = .32 B

H. 0.03 B = 0.3 Y = 3 G



Gear Machine – Student Designed, 2 Gears

Skills Required:Simplifying FractionsMultiplying Fractions by Whole Numbers

What to Build:

The same gear machine is pictured twice, from two different sides. Use this machine as a model, but you do not have to use the exact same gears, Just make sure that the gear turned directly by blue handle is larger than the gear turned directly by green handle.

The Challenge:Determine the relationship between the number of green handle turns and the number of blue handle turns.

Procedure:1. How many teeth are on the gear turned directly by the green handle?____


3. To find the fraction of a turn the blue handle makes for each green handle turn, create a fraction that represents the relationship between the numbers of teeth on these gears. (Make answer #1 your numerator, and answer #2 your denominator) _____

4. Simplify the fraction from answer #3. ______


5. Now multiply by the number found in #4 to complete the Input (green handle turns) Output (blue handle turns) Chart below. You should check your answers by turning the blue handle and counting the turns of the green handle.

Green handle Turns

Blue handle Turns

123456789101112


a. __ x 7 =___b. __ x 3 = ___c. 12 x __ = ___d. __ x 8 =___e. __ x 1 = ___f. 9 x __ =___

g. __ x 11 = ___h. 6 x __ = ___i. 2 x __ = ___j. __ x 4 = ___k. 5 x __ =___l. 10 x __ = ___



Gear Machine – Student Designed, 4 Gears

Skills Required:Simplifying FractionsMultiplying Fractions by Fractions and Whole Numbers

What to Build:

The same gear machine is pictured twice, from two different sides. Use this machine as a model, but you do not have to use the exact same gears. Just make sure that the gear turned directly by blue handle is larger than its connecting gear, and that the gear turned directly by green handle is smaller than its connecting gear

The Challenge:Determine the relationship between the number of green handle turns and the number of blue handle turns.

Procedure:1. How many teeth are on the gear turned directly by the green handle?____

2. How many teeth are on the gear connected to the gear turned directly by the green handle?____

3. Create a fraction that represents the relationship between the numbers of teeth on these gears. (Make answer #1 your numerator, and answer #2 your denominator) _____



6. How many teeth are on the gear turned directly by the blue handle?____


7. Create a fraction that represents the relationship between the numbers of teeth on these gears. (Make answer #5 your numerator, and answer #6 your denominator) _____


9. To find the fraction of a turn the blue handle makes for each green handle turn, find the product of the fractions representing the pairs of connecting gears. (multiply answer #4 times answer #8) _____.

10. Turn the green handle completely around once. Does the blue handle complete this fraction (answer to #9) of a turn?______ If not, check your work for steps 1-9.


11. Now multiply by the number found in #10 to complete the Input (green handle turns) Output (blue handle turns) Chart below. You should check your answers by turning the blue handle and counting the turns of the green handle.

Green handle Turns

Blue handle Turns

123456789101112


a. __ x 7 =___b. __ x 3 = ___c. 12 x __ = ___d. __ x 8 =___e. __ x 1 = ___f. 9 x __ =___

g. __ x 11 = ___h. 6 x __ = ___i. 2 x __ = ___j. __ x 4 = ___k. 5 x __ =___l. 10 x __ = ___



Angle Maker - Part 1 Skills Required:Three-Digit SubtractionOne-Digit by Three Digit MultiplicationDrawing Angles with a Protractor

Gears Needed:

40-teeth and 8-teeth

What to Build:

The same angle maker is pictured twice, from two different sides. .

The Challenge:Determine the measure of the angle created by a given number of handle turns.

Procedure:1. Align the gray angle “rays” and turn the handle until the one of the rays

completes a full rotation, and the rays are aligned again. How many times did you need to turn the handle completely around in order for this to happen_____

2. How many degrees does a ray rotate each time the handle makes a full turn (divide 360 by answer #1)? ____


3. This (answer #2) is also the measure of the angle made by turning the handle around once. Use a protractor to draw an angle of this degree on paper, then create this angle with one handle rotation. Put the gear machine angle on top of the angle you drew. Do the angles match? _____

4. Create an angle by turning the handle twice. How many degrees should this angle measure? (multiply answer #2 by 2) ________

5. Draw this angle and put the gear machine angle on top of it. Do the angles match? _____

6. Now create an angle by turning the handle three times. How many degrees should this angle measure? (multiply answer #2 by 3 and subtract this number from 360) ________


8. Now create an angle by turning the handle four times. How many degrees should this angle measure? (multiply answer #2 by 4 and subtract this number from 360) ________


Extra Challenge: Determine the angles created by the following number of handle turns, and check your answers by seeing if the angle machine matches angles that are drawn:

6 Turns ____ 8 Turns ____ 11 Turns ____ 15 Turns ____ 13 Turns ____



Angle Maker - Part 1 (KEY)Skills Required:Three-Digit SubtractionOne-Digit by Three Digit MultiplicationDrawing Angles with a Protractor

Gears Needed:


What to Build:

The same angle maker is pictured twice, from two different sides.

The Problem:Determine the measure of the angle created by a given number of handle turns.


completes a full rotation, and the rays are aligned again. How many times did you need to turn the handle completely around in order for this to happen? 5

2. How many degrees does a ray rotate each time the handle makes a full turn (divide 360 by answer #1)? 72


3. This (answer #2) is also the measure of the angle made by turning the handle around once. Use a protractor to draw an angle of this degree on paper, then create this angle with one handle rotation. Put the gear machine angle on top of the angle you drew. Do the angles match? _____

4. Create an angle by turning the handle twice. How many degrees should this angle measure? (multiply answer #2 by 2) 144


6. Now create an angle by turning the handle three times. How many degrees should this angle measure? (multiply answer #2 by 3 and subtract this number from 360) 144


8. Now create an angle by turning the handle four times. How many degrees should this angle measure? (multiply answer #2 by 4 and subtract this number from 360) 72



6 Turns 72 8 Turns 144 11 Turns 72 15 Turns 0 14 Turns 72 13 Turns 144



Angle Maker - Part 2 Skills Required:Three-Digit SubtractionOne-Digit by Three Digit MultiplicationDrawing Angles with a Protractor

Gears Needed:


What to Build:


The Challenge:Determine the measure of the angle created by a given number of handle turns.


completes 3 full rotations, and the rays are aligned again. How many times did you need to turn the handle completely around in order for this to happen?_____

2. How many degrees total did the ray rotate? (multiply 3 times 360) _____

3. How many degrees does a ray rotate each time the handle makes a full turn (divide answer #2 by answer #1)? ____


4. This (answer #3) is also the measure of the angle made by turning the handle around once. Draw a degree of this angle on paper, then create an angle with one handle rotation. Put the gear machine angle on top of the angle you drew. Do the angles match? _____

4. Create an angle by turning the handle twice. How many degrees should this angle measure? (multiply answer #3 by 2 and subtract this product from 180) ________

5. Complete the “Handle Turns/Angle Created” chart below. Multiply the left hand number by the answer to #3. Then, subtract 360 from all products between 360 and 720, and subtract 720 from all products between 720 and 1080. After doing the preceding step(s), subtract from 360 any numbers that are greater than 180.

Handle Turns Angle Degrees123456789


11 Turns ____ 12 Turns ____ 17 Turns ____ 15 Turns ____ 21 Turns ____



Angle Maker - Part 2 (KEY)Skills Required:Three-Digit SubtractionOne-Digit by Three Digit MultiplicationDrawing Angles with a Protractor

Gears Needed:


What to Build:


The Challenge: Determine the measure of the angle created by a given number of handle turns.


completes 3 full rotations, and the rays are aligned again. How many times did you need to turn the handle completely around in order for this to happen? 10

2. How many degrees total did the ray rotate? (multiply 3 times 360) 1080


3. How many degrees does a ray rotate each time the handle makes a full turn (divide answer #2 by answer #1)? 108

4. This (answer #3) is also the measure of the angle made by turning the handle around once. Draw a degree of this angle on paper, then create an angle with one handle rotation. Put the gear machine angle on top of the angle you drew. Do the angles match? _____

4. Create an angle by turning the handle twice. How many degrees should this angle measure? (multiply answer #3 by 2 and subtract this product from 180) 144

5. Complete the “Handle Turns/Angle Created” chart below. Multiply the left hand number by the answer to #3. Then, subtract 360 from all products between 360 and 720, and subtract 720 from all products between 720 and 1080. After doing the preceding step(s), subtract from 360 any numbers that are greater than 180.

Handle Turns Angle Degrees1 1082 1443 364 725 1806 727 368 1449 108


11 Turns 108 12 Turns 144 17 Turns 36 15 Turns 180 20 Turns 0 26 Turns 72


Date post:	27-May-2018
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