Operations & Algebraic Thinking
A school ordered 18 boxes of pencils. Each box contained 24 pencils.
a. How many pencils were ordered in all?
b. If the pencils are shared equally among 9 classrooms, how many pencils will each classroom receive?
What is:
a. 432 pencils
b. 48 pencils per classroom
The school library has 52,489.7 books.
a. Round the number to the nearest thousand.
b. Write the number in 5th grade expanded form.
What is:
a. 52,000
b. (5x10,000)+(2x1,000)+(4x100)+(8x10)+(9x1)+(7x1/10)
Sophia ran 3/4 mile on Monday and 1/8 mile on Tuesday.
a. How far did she run altogether?
b. Show or explain how you added the fractions.
What is:
a. 7/8 mile
b. Convert 3/4 to 6/8, then add 6/8 + 1/8.
A rectangular garden is 12 feet long and 9 feet wide.
a. What is the area of the garden?
b. What is the perimeter?
What is:
a. 108 square feet
b. 42 feet
A coordinate grid shows a point at (6, 4).
a. How many units right is the point from the origin?
b. How many units up?
What is:
a. 6 units
b. 4 units
Mrs. Lopez bought 7 packs of markers. Each pack cost $5.85.
a. Write an expression to represent the total cost.
b. Solve the problem.
What is:
a. 7 × 5.85
b. $40.95
A runner completed a race in 14.36 seconds. Another runner finished in 13.92 seconds.
a. Which runner was faster?
b. How much faster were they?
What is:
a. The runner with 13.92 seconds
b. 0.44 seconds
A recipe uses 2/3 cup of milk for one batch of muffins.
a. How much milk is needed for 3 batches?
b. Explain your multiplication.
What is:
a. 2 cups
b. 2/3 × 3 = 6/3 = 2
A fish tank measures 10 inches long, 6 inches wide, and 8 inches high.
a. What is the volume of the tank?
b. Explain how you found the volume.
What is:
a. 480 cubic inches
b. Multiply length × width × height.
Explain how a rectangle and a square are alike and different.
What is:
Both have 4 sides and 4 right angles. A square has all equal sides, while a rectangle does not always.
A student solved the problem 48 ÷ 6 + 12 by first dividing and then adding.
a. Explain why the student’s strategy is correct.
b. What is the answer?
What is:
a. Division comes before addition in order of operations.
b. 20
A science class measured rainfall amounts of 2.5 cm, 1.75 cm, and 0.9 cm.
a. What was the total rainfall?
b. Explain how you lined up the decimals.
What is:
a. 5.15 cm
b. The decimal points are lined up vertically.
A tank was filled with water to 7/10 of its capacity. Later, 2/10 of the water was used.
a. What fraction of the tank remains full?
b. Simplify if possible.
What is:
a. 5/10
b. 1/2
A student measured pencils with lengths of 4 1/2 inches, 5 inches, 4 3/4 inches, and 5 1/4 inches.
a. Which pencil was the longest?
b. What is the difference between the longest and shortest pencil?
What is:
a. 5 1/4 inches
b. 3/4 inch
A triangle has angle measures of 35°, 65°, and 80°.
a. Is the triangle acute, right, or obtuse?
b. Explain your answer.
What is:
a. Acute
b. All angles are less than 90°.
There are 325 students going on a field trip. Each bus can hold 42 students.
a. How many buses are needed?
b. Explain how you found your answer.
What is:
a. 8 buses
b. Since 325 ÷ 42 = 7 remainder 31, another bus is needed.
A factory produced 3,450 bottles each day for 12 days.
a. How many bottles were produced altogether?
b. Estimate the answer using rounding.
What is:
a. 41,400 bottles
b. About 42,000 bottles
A class shared 5 pizzas equally among 8 students.
a. How much pizza did each student receive?
b. Explain your reasoning.
What is:
a. 5/8 pizza
b. Divide 5 pizzas into 8 equal shares.
A recipe calls for 2 liters of juice. If you only have measuring cups marked in milliliters, how many milliliters are needed?
What is 2,000 milliliters?
Draw or describe a quadrilateral with exactly one pair of parallel sides.
What is a trapezoid?
A grocery store sold 145 apples on Monday and twice as many on Tuesday.
a. How many apples were sold on Tuesday?
b. How many apples were sold altogether?
What is:
a. 290 apples
b. 435 apples
Divide 48.6 ÷ 6.
a. Solve.
b. Explain how the decimal is placed in the quotient.
What is:
a. 8.1
b. The decimal in the quotient is placed directly above the decimal in the dividend.
Compare 5/6 and 7/8.
a. Which fraction is greater?
b. Use a model, benchmark, or common denominator to explain.
What is:
a. 7/8
b. Possible explanation: 5/6 = 20/24 and 7/8 = 21/24, so 7/8 is greater.
The table below shows the number of books read by students:
Emma – 12 Noah – 15 Ava – 9 Liam – 14
a. Who read the most books?
b. How many books were read altogether?
What is:
a. Noah
b. 50 books
A shape has 8 equal sides and 8 equal angles.
a. Name the shape.
b. Explain how you know.
What is:
a. Octagon
b. An octagon has 8 sides and 8 angles.