The Number Line Shuffle
What is -5 + 8?
Answer: 3
Student Explanation: Imagine a thermometer or a vertical number line. Start at -5 (5 degrees below zero). Moving +8 means going UP 8 spaces. Crossing 0 takes 5 spaces, and going 3 more spaces lands on +3
What is 3.5 + 2.25?
Answer: 5.75
Student Explanation: Line up the decimal points like dollar amounts: $3.50 + $2.25 = $5.75.
Solve: 5/6 - 1/3.
Answer: 3/6 (or 1/2)
Student Explanation: Change 1/3 into an equivalent fraction with 6 on the bottom: 1/3 X 2/2 = 26. Subtract the numerators: 56 - 26 = 36, which simplifies to 12.
A rectangular garden has a length of 12.5 feet and a width of 8 feet. How many square feet of soil are needed to cover the entire area of the garden?
Answer: 100 square feet
The area of a rectangle is found by multiplying length by width (Area = b × h).
Multiply the dimensions: 12.5 × 8 = 100 sq ft.
How many inches are in 1 foot?
12 inches
Which number is smaller: -8 or -2?
Answer: -8
Student Explanation: Think about money or temperature. Owing someone $8 leaves you with less money than owing someone $2. On a horizontal number line, numbers further to the left are always smaller.
What is 0.4 X 5?
Answer: 2.0 (or 2)
Student Explanation: Multiply 45=20. Since 0.4 has one digit after the decimal point, place the decimal point one place from the right in your answer (2.0).
What is 3 / 4 written as a decimal?
Answer: 0.75
Student Explanation: Think of money: 3 quarters out of 4 quarters equals 75 cents ($0.75). Or divide 3 / 4=0.75
A triangle has a base of 14 inches and an area of 42 square inches. What is the height of the triangle?
Answer: 6 inches
The formula for the area of a triangle is Area = ½ × b × h (or base × height ÷ 2).
Plug in what you know: 42 = (14 × height) ÷ 2.
Undo the division by multiplying 42 × 2 = 84.
Find the missing number: 84 ÷ 14 = 6 inches.
A box is packed with unit cubes. If it holds 3 layers of 10 cubes, what is the total volume of the box?
30 cubicunits (3 X 10)
Solve: -10 - (- 4) = ?
Answer: -6
Student Explanation: Subtracting a negative is the same as adding a positive (taking away a debt makes you richer!). Rewrite the problem as -10+4. Starting at -10 and moving 4 steps right on the number line gives -6.
Which decimal is larger: 0.45 or 0.05?
Answer: 0.45
Student Explanation: Compare place values from left to right. Look at the tenths place: 0.45 has 4 tenths (like 40 cents), while 0.05 has 0 tenths (like 5 cents). Since 40cents>5cents, 0.45 is larger.
Which fraction is bigger: 2 / 3 or 3 / 5?
Answer: 23
Student Explanation: Convert both to decimals or find a common denominator (15):
2 /3 = 10/15 =0.67 and 3/5= 9/15=0.60
Since 10 out of 15 is larger than 9 out of 15, 23 is larger.
A park shaped like a parallelogram has a base of 20 meters, a height of 15 meters, and a slanted side length of 18 meters.
If you want to put grass seed over the entire inside area, how many square meters do you need to cover?
Answer: 300 square meters Don't fall for the trap! For area, always use the straight vertical height, not the slanted side.
Formula for parallelogram area: Area = base × height.
Multiply base (20) times height (15): 20 × 15 = 300 sq meters.
(Note: The 18 m slanted side would only be used if you were finding perimeter!)
What is the volume of a rectangular prism with length=4cm, width=2cm, and height=3cm?
24cm3
Arrange these integers from LEAST to GREATEST: 4, -7, 0, -2, 1.
Answer: -7, -2, 0, 1, 4
Student Explanation: Place them on a number line from left to right. The furthest left (most negative) is -7, followed by -2, then 0, then 1, and finally 4.
Order these decimals from LEAST to GREATEST: 0.5, 0.05, 0.405, 0.45.
Answer: 0.05, 0.405, 0.45, 0.5
Student Explanation: Add zeros at the end so every number has 3 decimal places: 0.050,0.405,0.450,0.500 Now compare them like whole numbers 50<405<450<500
Find an equivalent fraction for 2 / 5 with a denominator of 10
Answer: 4 / 10
Student Explanation: To change the bottom number from 5 to 10, multiply by 2 (5 X 2=10). Do the exact same to the top number: 2 X 2=4. So, 2 / 5 = 4 /10.
An L-shaped community playground can be split into two smaller rectangles:
Rectangle A: 10 yards long and 6 yards wide.
Rectangle B: 8 yards long and 4 yards wide.
What is the total area of the entire playground?
Answer: 92 square yards
Find the area of Rectangle A: 10 × 6 = 60 sq yards.
Find the area of Rectangle B: 8 × 4 = 32 sq yards.
Add the two areas together: 60 + 32 = 92 sq yards.
How many feet are in 3 yards? (1yard=3feet)
9 feet
A football team lost 8 yards on their first play. On their second play, they gained 12 yards. What was the team's total net change in yards after both plays?
Answer: +4 yards (or a gain of 4 yards) Student Explanation: A loss of 8 yards is represented by -8. A gain of 12 yards is represented by +12. Combine them using addition: -8+12=4. On a number line, start at -8 and move 12 spaces to the right to land on +4.
A gas station charges $3.25 per gallon of gasoline. If Sofia fills up her car with 12 gallons, how much does she pay for the gas?
Answer: $39.00 Student Explanation: Multiply the price per gallon by the number of gallons: 3.25 X 12. Multiply 325 X 12=3900. Because 3.25 has two decimal places, place the decimal two spots from the right to get 39.00. She pays $39.00.
A bakery had 7 /8 of a sheet cake left at the end of the day. A customer came in and bought 1 / 2 of the remaining cake. What fraction of the whole sheet cake did the customer buy?
Answer: 7 / 16 of the cake
Student Explanation: Finding a fraction of a fraction means multiplying: 7/8 X 1/2. Multiply the numerators together (7 X 1=7 ) and the denominators together (8 X 2=16). The customer bought 7 / 16 of the whole
A dog park owner has 48 meters of fencing to build a square dog park.
First, find the length of one side of the park. Then, calculate the total square area inside the park for dogs to play.
Answer:
Side length = 12 meters; Total Area = 144 square meters Step 1 (Perimeter): A square has 4 equal sides. Divide the total fencing (48 m) by 4: 48 ÷ 4 = 12 meters per side. Step 2 (Area): Multiply side times side (side × side) to find the space inside:
12 × 12 = 144 square meters
A fish tank has a base area of 20 square inches and a height of 5 inches. What is its total volume?
100 inches3