# Bridges in Mathematics Grade 4 Student Book Unit 5 Module 4 Answer Key

Practicing the Bridges in Mathematics Grade 4 Student Book Answer Key Unit 5 Module 4 will help students analyze their level of preparation.

## Bridges in Mathematics Grade 4 Student Book Answer Key Unit 5 Module 4

Bridges in Mathematics Grade 4 Student Book Unit 5 Module 4 Session 1 Answer Key

Measuring the Range of Motion of Your Joints

Work with a partner to test how much you can rotate each of the joints shown below. Each of you will sketch. First sketch the ending points of the jointâ€™s rotation. Then use your pattern blocks to estimate the degree of rotation to the nearest 10 degrees. When testing your joints, only bend as far as is comfortable: donâ€™t rotate your joints until it feels difficult or painful!

Question 1.
Knee

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 240Â°. The approximate fraction of a complete turn: $$\frac{2}{3}$$.

Explanation:

The approximate degree of rotation is 240Â°as she started from 0 and stopped at 240Â°.
The approximate fraction of a complete turn: $$\frac{240}{360}$$ = $$\frac{4}{6}$$ = $$\frac{2}{3}$$

Question 2.
Shoulder: to the side

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 180Â°. The approximate fraction of a complete turn: $$\frac{1}{2}$$.

Explanation:

Question 3.
Elbow

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 180Â°. The approximate fraction of a complete turn: $$\frac{1}{2}$$.

Explanation:

Question 4.
Wrist

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 90Â°. The approximate fraction of a complete turn: $$\frac{1}{4}$$.

Explanation:

Question 5.
Shoulder: back and front

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 270Â°. The approximate fraction of a complete turn: $$\frac{3}{4}$$.

Explanation:

Question 6.

approximate degrees of rotation: ________________
approximate fraction of a complete turn: ________________
The approximate degree of rotation is 270Â°. The approximate fraction of a complete turn: $$\frac{3}{4}$$.

Explanation:

Drawing Angles of Rotation

Draw and label the angles that are equal to each fraction of a whole turn around the circle. Use your pattern blocks to make the angles exact. Remember that there are 360 degrees in a full turn around the circle.
ex: Draw and label $$\frac{1}{6}$$ turn.

Question 1.
Draw and label $$\frac{1}{2}$$ turn.

Explanation:
Given,
latex]\frac{1}{2}[/latex] turn.
latex]\frac{1}{2}[/latex] Ã— 360
180Â°.

Question 2.
Draw and label $$\frac{1}{4}$$ turn.

Explanation:
Given,
$$\frac{1}{4}$$ turn.
$$\frac{1}{4}$$ Ã— 360
90Â°

Question 3.
Draw and label $$\frac{3}{4}$$ turn.

Explanation:
Given,
$$\frac{3}{4}$$ turn.
1 turn = 360Â°
$$\frac{3}{4}$$ Ã— 360 = 270Â°

Bridges in Mathematics Grade 4 Student Book Unit 5 Module 4 Session 2 Answer Key

Geometry Measurement Problems

Mr. White asked some of his fourth graders to demonstrate making turns in their square-shaped classroom. Each of the students started their turn facing either the front or the back of the classroom.

Question 1.
Mia started facing the front wall of the classroom. She turned 60Â° to the right. Then she turned 60Â° more to the right, and then 60Â° more.
a. How many degrees did Mia turn in all? Use numbers and a labeled sketch to solve this problem.
Mia turned a total of 180Â° in all.

Explanation:
Given,
Mia started facing the front wall of the classroom
She turned 60Â° to the right.
Next, she turned 60Â° more to the right and 60Â° more.
60Â° + 60Â° + 60Â° = 180Â°

b. Which wall in the classroom was Mia facing when she stopped?
No Mia faces the back side of the classroom.

Question 2.
Marcus started facing the back of the classroom. He turned 360Â°. Then he kept on turning in the same direction, 180Â° more.
a. How many degrees did Marcus turn in all? Use numbers and a labeled sketch to solve this problem. Show all your work.
360Â° + 180Â° = 540Â°.

b. Which wall in the classroom was Marcus facing when he stopped?
Marcus faces the back side of the wall in the classroom when he stopped.

Question 3.
Sara started facing the front of the classroom. She turned 45Â° to the left, and then kept on turning to the leftâ€”80Â° more, then 45Â° more, then 120Â° more. Did she turn all the way around in a complete circle, so she was facing the front of the room again? If not, how many more degrees would she need to turn to complete the circle? Use numbers and a labeled sketch to solve this problem. Show all your work.
No, she did not turn all the way around in a complete circle. And she needed 70Â° more to turn to complete the circle.

Explanation:

Sara turned 45Â° to the left
And kept on turning to the left 80Â° more, then 45Â° more, then 120Â° more.
Total degrees she turned are 45 + 80 + 45 + 120 = 290Â°
A full turn has 360Â°
360Â° – 290Â° = 70Â°
she needed 70Â° more to turn to complete the circle.

Question 4.
Anthony started by facing the back wall of the classroom. He turned 90Â° to the right, and then 90 more degrees to the right. After that, he kept turning to the right, 45Â° more, 45Â° more, and 45Â° more. Did he turn all the way around in a complete circle? If not, how many more degrees would he need to turn to complete the circle? Use numbers and a labeled sketch to solve this problem. Show all your work.
No, she did not turn all the way around in a complete circle. And she needed 45Â° more to turn to complete the circle.

Explanation:

Given,
Anthony turned 90Â° right.
90 more degrees to the right.
the right, 45Â° more, 45Â° more, and 45Â° more.
Total degrees = 90 + 90 + 45 + 45 + 45
= 315Â°
she needed 360Â° -315Â° = 45Â° more to complete the circle.

Question 5.
Measure the two angles with your protractor. What is the difference between the measure of angle a and angle b?

The difference between the measure of angle a and angle b is _____________ degrees.
The difference between the measure of angle a and angle b is 55Â° degrees.

Explanation:

angle a = 85Â° and angle b is 30Â°
The difference between angle a and angle b is 85Â° – 30Â° = 55Â°

Question 6.
CHALLENGE If the area of a rectangle is 240 and one dimension is 40, what is the other dimension? Use numbers and a labeled sketch to solve this problem.
The other dimension is 6.

Explanation:
Given,
The area of the rectangle is 240
The other dimension is 40
Area of the rectangle is l Ã— b
240 = l Ã— b
240 = 40 Ã— b
b = 240 Ã· 40
b = 6
Hence the other dimension is 6.

Question 7.
CHALLENGE If the perimeter of a rectangle is 90 and one dimension is 20, what is the other dimension? Use numbers and a labeled sketch to solve this problem.
The other dimension is 25.

Explanation:
Given,
The perimeter of a rectangle is 90
The other dimension is 20
We know the perimeter of the rectangle is 2(l+b)
2(l+b) = 90
2(20+b) = 90
40 + 2b = 90
2b = 90 – 40
2b = 50
b = 50 Ã· 2
b = 25
Therefore the other dimension is 25.

Question 8.
CHALLENGE Write two different combinations of six turns each so that the person who is turning ends up facing the same way he started.
Note: You donâ€™t have to stick with a single turn of360Â° as long as the person who is turning ends up facing the same way he started.

Explanation:
The person started turning facing the same at 0Â°
60Â° + 90Â° + 30Â° + 45Â° + 90Â° + 45Â°Â  = 360Â°
Hence the person who is turning ended up facing the same way he started.

Turns & Fractions at the Skate Park

Question 1.
A group of kids were practicing tricks on their skateboards at the skate park. Solve the following problems about the kids and their skateboard tricks. Write and solve an equation for each problem.

a. Molly made a turn on her board that was 3 times more than Toddâ€™s. Todd turned 120Â° on his board. How many degrees did Molly turn?
My Equation: _________________
360Â°

Explanation:
Given,
Molly made a turn on her board that was 3 times more than Toddâ€™s.
Todd turned 120Â° on his board.
3 Ã— 120 = 360Â°

b. How many more degrees did Molly turn than Todd?
My Equation: _________________
240Â°

Explanation:
Molly turned 240Â° than Todd.
360Â° – 120Â° = 240Â°

c. Teri turned 160Â° on her board. Lana made a turn that was 4 that much. How many degrees did Lana turn on her board?
My Equation: _________________
40Â°

Explanation:
Given,
Teri turned 160Â° on her board.
Lana made a turn that was 4 that much.
160 Ã· 4 = 40Â°

d. How many more degrees did Teri turn than Lana?
My Equation: _________________
120Â°

Explanation:
Teri turned 120Â° than Lana.
160 – 40 = 120Â°

e. Pablo made a 360Â° turn on his board. His brother, Marco, made a turn that was $$\frac{1}{6}$$ of Pabloâ€™s. How many degrees did Marco turn on his board?
My Equation: _________________
60Â°

Explanation:
Pablo made a 360Â° turn on his board.
$$\frac{1}{6}$$ of Pabloâ€™s.
360 Ã· 60 = 60Â°

f. How many more degrees did Pablo turn than Marco?
My Equation: _________________
300Â°

Explanation:
Pablo turned 300Â° than Marco.
360Â° – 60Â° = 300Â°

Question 2.
Solve the following pairs of multiplication problems.
$$\frac{1}{2}$$ of 360 is _____________
$$\frac{1}{3}$$ of 360 is _____________
$$\frac{1}{4}$$ of 360 is _____________
$$\frac{1}{6}$$ of 360 is _____________
$$\frac{1}{2}$$ Ã— 360 = _____________
$$\frac{1}{3}$$ Ã— 360 = _____________
$$\frac{1}{4}$$ Ã— 360 = _____________
$$\frac{1}{6}$$ Ã— 360 = _____________
The pair of multiplication problems are 180, 120, 90, 60, 180, 120, 90, and 90.

Explanation:
$$\frac{1}{2}$$ Ã— 360 = 180
$$\frac{1}{3}$$ Ã— 360 = 120
$$\frac{1}{4}$$ Ã— 360 = 90
$$\frac{1}{6}$$ Ã— 360 = 60
$$\frac{1}{2}$$ Ã— 360 = 180
$$\frac{1}{3}$$ Ã— 360 = 120
$$\frac{1}{4}$$ Ã— 360 = 90
$$\frac{1}{6}$$ Ã— 360 = 90

Bridges in Mathematics Grade 4 Student Book Unit 5 Module 4 Session 3 Answer Key

Mystery Angles

Question 1.
Find the measure of each of the mystery angles below. (Hint: If you remember that a right angle measures 90Â° and a straight angle measures 180Â°, you may be able to solve some of these problems without a protractor.)
a.

mystery angle b = ______________
mystery angle b = 90Â°

Explanation:
Given,
âˆ a = 30Â° and we need to find âˆ b
We know right angle measures 90Â°
âˆ a + âˆ b = 90Â°
30Â° + âˆ b = 90Â°
âˆ b = 90Â° – 30Â°
âˆ b = 60Â°

b.

mystery angle d = ______________
mystery angle d = 45Â°

Explanation:
Given,
âˆ c = 45 and we need to find âˆ d
âˆ c + âˆ d = 90Â°
45Â° +âˆ d = 90Â°
âˆ d = 90Â° – 45Â°
âˆ d = 45Â°

c.

mystery angle f = ______________
mystery angle f = 120Â°

Explanation:
Given,
âˆ e = 60 and we need to find âˆ f
We know sum of angles in a straight line is 180Â°
âˆ f + âˆ e = 180Â°
âˆ f + 60Â° = 180Â°
âˆ f = 180Â° – 60Â°
âˆ f = 120Â°

d.

mystery angle h = ______________
mystery angle h = 30Â°

Explanation:
Given,
âˆ i = 50, âˆ g = 100 and we need to find âˆ h
sum of angles in a straight line is 180
So,
âˆ i + âˆ g + âˆ h = 180Â°
50Â° + 100Â° + âˆ h = 180Â°
150Â° + âˆ h = 180Â°
âˆ h = 180Â° – 150Â°
âˆ h = 30Â°

Question 2.
Jami knows that when the clock says itâ€™s exactly 1:00, the hands make an angle of 30Â°. What angle is formed by the hands on the clock when itâ€™s exactly 5:00? Use numbers, labeled sketches, or words to explain your answer.
The angle is formed by the hands on the clock when itâ€™s exactly 5:00 is 150Â°.

Explanation:

Bridges in Mathematics Grade 4 Student Book Unit 5 Module 4 Session 4 Answer Key

Shapes & Angles

Question 1.
Using a protractor, sketch the following shapes with the correct angles.
a. a triangle with two 50Â° angles

Explanation:
Given,
a triangle with two 50Â° angles.
We have drawn a traingle with wo 50Â° angles which is called scalene traingle.

b. a triangle with a right angle and 30Â° and 60Â° angles

Explanation:
I have drawn a picture of a triangle with a right angle and 30Â° and 60Â° angles.

Question 2.
If a quadrilateral has angles that are all the same size, what name(s) might it have?

Explanation:
A rectangle has angles that are all the same size.

Question 3.
If a quadrilateral has side lengths that are all the same size, what name(s) might it have?

Explanation:
A rhombus is a quadrilateral with four equal sides.

Review

Question 4.
Is 7 a factor of 27?
No, 7 is not a factor of 27.

Explanation:
As 7 is not divisible by 7.
Factors of 27 are 1, 3, 9, and 27.

Question 5.
Is 7 a factor of 41?
No, 7 is not a factor of 41.

Explanation:
The number 41 is a prime number. As it can only be divided by 1 or itself. Hence the factors of 41 are 1 and 41.

Question 6.
Is 7 a factor of 49?
yes, 7 is a factor of 49.

Explanation:
The factors of 49 are 1 and 7.
7 Ã— 7 = 49

Question 7.
List the factors of 100.