SOLUTIONS

Solutions will be posted the Monday FOLLOWING the problem of the week.

GRADE 3 SOLUTIONS:

1.) Kelly likes to exercise every day.

• • She jogs in place for 11 minutes to warm up.

  • She does jumping jacks for 17 minutes.

  • She marches in place for 9 more minutes to cool down.

What is the total amount of time, in minutes, that Kelly spends jogging, doing jumping jacks, and marching in place every day?

Kelly spends 37 minutes exercising every day. (11 + 17 + 9 =37)

2.) A farmer plants corn on 1/4 of his field. Fill in the boxes to show the part of his field where corn has been planted.

Two of the boxes should be marked to show that 2/8 or 1/4 of the field has been planted with corn:

3.) Which expression could be used to find the value of 254 + 381 ?

a.) 2 + 5 + 4 + 3 + 8 + 1

b.) 20 + 50 + 4 + 30 + 80 + 1

c.) 200 + 5 + 4 + 300 + 8 + 1

d.) 200 + 50 + 4 + 300 + 80 + 1

d.) 200 + 50 + 4 + 300 + 80 + 1

Option d shows each of the two addends written in expanded form. When added together, the expanded forms will give the sum of the two whole numbers.

4.) Which three figures have an area of 8 square inches?

a, d, and e are the three figures that have 8 square inches as the area.

6.) The figure below has a perimeter of 74 inches. What is the length of the missing side?

a.) 14 inches

b.) 8 inches

c.) 11 inches

d.) 15 inches

e.) 74 inches

The missing side is 15 inches long. To find the perimeter, you would add each side. Since one side is missing, we add the sides and subtract from the total perimeter, or 74 inches. We first had to change the 1 ft 3 in and 1 ft 2 in into 15 and 14 inches, respectively, to add and subtract the common measurements.

7.) A book cover has a length of 12 inches and a width of 8 inches. Select three ways to calculate the area of the book cover.

a.) 12 x 12

b.) 8 x 8

c.) 12 x 8

d.) 12 + 12 + 8 + 8

e.) 12 + 12 + 12 + 12 + 12 + 12 + 12 + 12

f.) 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8 + 8

8.) Select two problems that would be true if the number 7 were put in the box.

9.) Which three statements can be represented by the expression 8 x 9?

a.) Jack has 8 bags with 9 marbles in each.

b.) Sampson had 8 markers. Julie gave him 9 more.

c.) Ellie shared her 9 stickers with 8 friends.

d.) Shiloh planted 8 rows of 9 flowers.

e.) There are 8 rows of 9 cars in the parking lot.

f.) Liam had 9 toy cars, but he put 8 away.

10.) Jamie is buying bananas and pears at the grocery store. The mass of the bananas is 681 grams. The mass of the pears is 527 grams.

How much greater is the mass of the bananas than the mass of the pears?

The mass of the bananas is 154 grams greater than the mass of the pears. (681-527=154)

What was the total mass of the fruit?

The total mass of the fruit is 1,208 grams. (681 + 527 = 1,208)

11.) Suzanne drew a rectangle with a perimeter of 12 inches. One side of the rectangle was 4 inches. What were the lengths of the other three sides?

The other three sides were 4 inches, 2 inches, and 2 inches.

If one side was 4 inches, the opposite side must have been the same measurement. 4 + 4 = 8, so that means if the entire perimeter was 12 inches, 8 taken away would leave 4 inches. There are 2 sides left and based on the properties of a rectangle, they must be equal, so the remaining two sides must be 2 and 2 inches.

12.) Which three comparisons are true?

a.) 1/2 > 1/3

b.) 3/5 > 4/5

c.) 1/8 > 1/7

d.) 3/4 > 3/5

e.) 1/10 > 1/9

f.) 1/3 > 1/4

13.) Which expression could be used to find the value of 938 + 234?

a.) 9 + 3 + 8 + 2 + 3 + 4

b.) 90 + 30 + 80 + 20 + 30 + 4

c.) 900 + 200 + 3 + 3 + 8 + 4

d.) 900 + 200 + 30 + 30 + 8 + 4

14.) Alexis draws a shape. Each piece is 1/4 the area of the shape. Which shape could be the one Alexis drew?

The answer is shape b. While shapes a and d are also divided into 4 pieces, shape b is the only one where each part of the circle is an equal piece. To represent a fraction, a picture or shape must have all equal parts.

GRADE 4 SOLUTIONS:

1.) A team competes in a rowing race. There are 4 people on the team, and each person rows for the same distance. The team travels a total distance of 3,940 feet.

What is the distance that each person rows?

Each person rows 985 feet. (3,940 divided by 4 is 985)

2.) Jenny created this number line to graph the number 5/2. Show the correct point on the number line to represent 5/2.

Your point should be exactly between 2 and 3: 5/2 is the same as 2 1/2.

3.) Which two fractions are equal to 1/3?

a.) 2/5

b.) 3/6

c.) 5/15

d.) 2/6

c.) 5/15 and d.) 2/6 are both equivalent to 1/3.

4.) Ray has a collection of 20 t-shirts. The collection is made of 3 different types of shirts.

-1/2 of the shirts have words on them.

-1/5 of the shirts have pictures on them.

-3/10 of the shirts are solid colored.

Select the three number sentences that correctly compare these fractions.

a.) 1/2 > 3/10

b.) 3/10 > 1/2

c.) 3/10 > 1/5

d.) 3/10 < 1/5

e.) 1/5 < 1/2

f.) 1/2 < 1/5

5.) Mr. Smith's bicycle weighs 27 pounds. His car weighs 32 times as much as his bicycle. What is the weight, in pounds, of Mr. Smith's car?

Mr. Smith's car weighs 864 pounds. 27 x 32 is 864.

6.) Part A:

Which equation can be used to show s, the fraction of students who chose either art or phys ed?

a.) 2/10 + 3/10 = s

b.) 4/10 - 1/10 = s

c.) 2/10 + 4/10 = s

d.) 4/10 - 2/10 = s

Part B:

What fraction of all the students chose art or phys ed as their favorite special subject area?

3/5 of all students chose art or pays ed as their favorite subject area. 2/10 + 4/10 = 6/10. This can be simplified to 3/5. (Either 6/10 or 3/5 is an acceptable answer, but 3/5 is a better answer.)

7.) The length of a table is 6 feet 8 inches. How many inches is the length of the table?

The table is 80 inches long. 6 feet x 12 inches = 72 inches. 72 + 8 = 80, making the table 80 inches long in total.

8.) Crosby is building a bookcase. He puts two boards end to end to make a shelf. The first board is 3/10 meters long, the second is 37/100 meters long.

Part A

What fraction is equivalent to 3/10 and has a denominator of 100?

a.) 3/100

b.) 30/100

c.) 300/100

d.) 33/100

Part B

What is the total length, in meters, of the two boards?

The boards are 67/100 meter long. If the first was 3/10 and the second was 37/100, we needed to find a fraction equivalent to 3/10 with a denominator of 100 (as seen in Part A). 3/10 = 30/100. Add 30/100 to 37/100 and you get 67/100, which cannot be reduced.

9.) A garden contains only sunflowers and daisies. There are 6 rows of sunflowers and 8 rows of daisies. Each row of sunflowers has 9 flowers, and each row of daisies has 13 flowers.

What is the total number of flowers in the garden?

There are 158 flowers in the garden. 6 x 9 = 54, and 8 x 13 = 104. 54 + 104 = 158.

10.) The rectangle is divided into 12 equal sections.

Neil colors in 5 rectangles. Then, he colors in 4 rectangles.

Which two of these represent a fraction of the rectangle Neil colored in all? Select the two correct answers.

a.) 12/5 + 12/4

b.) 1/5 + 1/4

c.) 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12

d.) 1/9 + 12

e.) 5/12 + 4/12

11.) Select three choices that are factor pairs for the number 24.

a.) 1 and 24

b.) 2 and 12

c.) 3 and 9

d.) 4 and 7

e.) 6 and 3

f.) 7 and 6

g.) 8 and 3

12.) Which two equations represent the statement "54 is 9 times as much as 6"?

a.) 54 = 9 x 6

b.) 54 = 6 + 9

c.) 54 = 9 x 9

d.) 54 = 6 x 9

e.) 54 = 9 + 6

13.) Ben is measuring the growth of a small tree in his backyard. The first time he measures it, it is 4 meters high. After a month, it has grown 2 centimeters. After two months, it has grown an additional 4 centimeters. How many centimeters high is the tree now?

The tree is now 406 centimeters high. It started at 4 meters, which is 400 centimeters. After a month it was 400 + 2 or 402. After twi months, it grew an additional 4 centimeters, so 402 + 4 = 406.

14.) Olivia ran 5,279 feet in 10 minutes. Jose ran 6,105 feet in 10 minutes. What is the difference in the total distance each person ran?

The difference is 826 feet. 6,105 - 5,279 = 826.

GRADE 5 SOLUTIONS:

1.) Josie makes 8 hats out of colorful cloth. She uses 1/4 yard of cloth to make each hat. What is the total amount of cloth, in yards, that Josie will use to make all 8 hats?

Josie will use 2 yards of cloth to make 8 hats. (1/4 x 8 = 2)

2.) Two rectangular prisms form a large aquarium in the hospital lobby. What is the volume of the aquarium?

The volume of the aquarium is 650 cubic meters.

3.) The parts to build one phone cost $167. How much does it cost to build 289 phones?

It costs $48,263 to build 289 phones. $167 x 289 = $48,263.

4.) Mark is making meatballs. He has 6 pounds of meat. He puts 1/8 pound of meat into each meatball. What is the total number of meatballs he makes using all of the meat?

He will make 48 meatballs using all of the meat.

5.) Which three statements about rounding decimals are correct?

a.) The number 2.066 rounded to the nearest hundredth is 2.07

b.) The number 2.606 rounded to the nearest hundredth is 2.60

c.) The number 2.195 rounded to the nearest hundredth is 2.19

d.) The number 2.159 rounded to the nearest hundredth is 2.16

e.) The number 2.509 rounded to the nearest hundredth is 2.51

f.) The number 2.109 rounded to the nearest hundredth is 2.19

a, d, and e are all correct statements.

6.) The rectangular prism shown is made of cubes. Each cube is 1-cubic unit.

What is the volume, in cubic units, of the rectangular prism?

The volume of the rectangular prism is 48 cubic units. The length is 6 cubic units, the width is 4 cubic units, and the height is 2 cubic units. 6 x 4 x 2 = 48.

7.) Use the information provided to answer Part A and Part B for question 7.

Jeffrey is doing a science project where he measures the evaporation rate of three glasses of liquid. Two of the measurements from the second day of his experiment are shown.

The liquid in first cup measures 5 1/8 inches.

The liquid in the second cup measures 6 2/3 inches.

Part A:

What is the difference in depth between the first and second cup?

There is a 1 13/24 inch difference between the two cups.

Part B:

The liquid level in the third cup is ¾ inches deeper than the second cup. What is the measurement of the liquid level in the third cup, in inches?

The third cup is 7 5/12 inches deep. 6 2/3 + ¾= 6 17/12, but 17/12 is an improper fraction, or 1 5/12. 6 + 1 5/12=7 5/12

8.) Emily has a piece of paper that is 9 inches long. She is cutting it into 10 equal pieces. Which equation shows how to find the length, in inches, of each piece of paper she cuts?

a.) 9 x 10 = 90

b.) 10 ÷ 9 = 1 1/9

c.) 9 ÷ 10 = 9/10

d.) 10 - 9 = 1

e.) 9 + 10 = 19

9.) Which expression best matches the statement "the sum of 8 and 9 subtracted from 32"?

a.) 8 + 9 - 32

b.) 32 - (8 + 9)

c.) 32 - 9 + 8

d.) (8 + 9) -32

10.) Which two conversions are correct?

a.) 80 cm = 8 mm

b.) 0.8 cm = 80 mm

c.) 800 cm = 8 m

d.) 8,000 m = 8 km

e.) 800 mm = 8 cm

11.) Select three statements that correctly describe the point on the coordinate plane.

a.) The point is located at the ordered pair (5, 3)

b.) The point is located at the ordered pair (3, 5)

c.) The x coordinate is 5 and the y coordinate is 3.

d.) The x coordinate is 3 and the y coordinate is 5.

e.) The point is 3 units to the right of the origin on the x-axis and 5 units up from the origin on the y-axis.

f.) The point is 5 units to the right of the origin on the x-axis and 3 units up from the origin on the y-axis.

12.) Solve.

4 x (48 ÷ 8) + 6 x 2

The answer is 36. Using order of operations, this is the order in which you solve the problem:

4 x (48 ÷ 8) + 6 x 2

4 x (6) + 6 x 2

24 + 12

36

13.) Kyle lives 3/5 mile from school. Aidan lives 4/7 mile from school. Which student lives further from school? By how much?

Kyle lies further from school. 3/5 is greater than 4/7. To find the difference, I found a common denominator (35) and subtract. Kyle lives 1/35 mile further than Aidan.

14.) Which figure is always a rhombus?

a.) rectangle

b.) pentagon

c.) square

d.) quadrilateral

A rhombus is defined as a parallelogram with opposite equal angles and four equal sides- a square will always fit this definition as well. A rhombus is a quadrilateral (four sided shape), but a quadrilateral is not always a rhombus. That's why square is the most reasonable answer.