Adding +
You are adding the number of books on two shelves. One shelf has 248 books and the other has 157 books.
What is the total number of books?
What is 248 + 157 = 405
There are 605 students in a school. After some students go on a field trip, 289 students remain in the building.
How many students went on the field trip?
What is 605 − 289 = 316 students?
A teacher has 6 boxes of markers. Each box has 8 markers. How many markers are there in all?
What is 6 × 8 = 48 markers ?
There are 56 pencils to be shared equally among 8 students. How many pencils does each student get?
What is 56 ÷ 8 = 7 pencils?
A rectangle has a length of 9 cm and a width of 5 cm. What is its perimeter?
What is Perimeter = 2(9 + 5) = 28 cm ?
A runner jogs 2.75 km in the morning and 1.6 km in the afternoon.
How many kilometers does the runner jog in all?
What is 2.75 + 1.6 = 4.35 km
A rope is 5.0 m long. A piece of 1.75 m is cut off. How much rope is left?
What is 5.0 − 1.75 = 3.25 m?
A ribbon is 0.4 m long. A student uses 3 ribbons of the same length to decorate a poster. What is the total length of ribbon used? Show how multiplication with decimals works here.
What is 0.4 × 3 = 1.2 m ?
A 3.6‑liter jug of juice is poured equally into 4 bottles. How many liters of juice are in each bottle? Explain how you used division with decimals.
What is 3.6 ÷ 4 = 0.9 L each ?
A rectangular garden is 4.5 m long and 3 m wide. What is the area of the garden?
What is Area = 4.5 × 3 = 13.5 m² ?
You add 1/4+2/8.
Rewrite 2/8 as an equivalent fraction with denominator 4.
Then find the sum.
What is the final fraction? Explain how you know the fractions are equivalent.
What is 1/4+2/8=1/4+1/4=2/4=1/2?
You solve 7/10−1/5.
Rewrite 1/5 as an equivalent fraction with denominator 10.
Then subtract. What is the difference and how do you know your equivalent fraction is correct?
What is 7/10−1/5=7/10−2/10=5/10=1/2
You know 3/4 is equivalent to ?/8.
Use multiplication to find the missing numerator.
Then explain how you could use that equivalence to find 3×3/4 by thinking in eighths. What is the product and how did equivalent fractions help?
What is 3/4=6/8; 3 × 3/4=9/4=2 1/4
A baker has 9/10 of a cake and wants to share it equally among 3 students.
Write a division expression using fractions.
Use equivalent fractions to find how much cake each student gets. What fraction of the cake does each student receive?
What is 9/10÷3 = 9/10×1/3 = 9/30=3/10?
A right angle measures 90°.
Write a fraction of a full turn (360°) that 90° represents.
Then explain why a 45° angle is half of a right angle using equivalent fractions. What fraction of a full turn is 45°?
What is 90° = 1/4 turn; 45° = 1/8 turn ?
A store sold 389 stickers on Monday and 427 stickers on Tuesday.
Round each number to the nearest ten.
Use your rounded numbers to estimate how many stickers were sold in all.
What is your estimate and is it greater or less than the exact sum?
What is Rounded: 390 + 430 ≈ 820 stickers?
A library had 932 books. About how many books would be left if about 300 were checked out? Round to the nearest hundred to estimate. What is your estimate and why is rounding to the nearest hundred reasonable here?
What is 900 − 300 ≈ 600 books?
A crate holds 24 juice boxes. The cafeteria orders 19 crates.
Round 19 to a nearby “friendly” number.
Use your rounded number to estimate how many juice boxes they ordered. What is your estimate and is it likely more or less than the exact product?
What is 20 × 24 ≈ 480 juice boxes ?
A total of 198 stickers are divided equally into 6 packs.
Round 198 to a nearby number that is easy to divide by 6.
Use that to estimate how many stickers are in each pack. What is your estimate and is the exact answer likely a little more or a little less?
What is 198 ≈ 180; 180 ÷ 6 = 30 stickers each ?
A student measures an angle and reads 47°, but the protractor is a bit hard to see.
Round the angle to the nearest ten degrees.
Decide whether you would describe this angle as “about a right angle” or “much smaller than a right angle.” Explain your reasoning.
What is Rounded ≈ 50°, smaller than a right angle ?
Two students add numbers:
Student A: 3.4+2.75
Student B: 3.25+2.9
Without finding exact sums, decide which sum is greater and write a comparison using > , < , or =.
Explain your reasoning.
What is 3.4 + 2.75 = 6.15; 3.25 + 2.9 = 6.15?
Two subtraction problems:
A: 8.5−3.9
B: 8.5−4.02
Without fully calculating, decide which result is larger and write a comparison using > , < , or =. Explain how the size of the number being subtracted affects the result.
What is 8.5 − 3.9 = 4.6; 8.5 − 4.02 = 4.48; 4.6 > 4.48 ?
Which is greater:
6×4.5
9×3
Without computing both exactly at first, predict which is larger, then check by calculating. Write a comparison using > , < , or = and explain your reasoning.
What is 6 × 4.5 = 27; 9 × 3 = 27; = ?
Two division problems:
A: 48÷6
B: 4.8÷0.6
Decide which quotient is larger and write a comparison using > , < , or =. Explain how place value and scaling help you compare these without a calculator.
What is 48 ÷ 6 = 8; 4.8 ÷ 0.6 = 8; = ?
Compare these two situations:
Angle A is 120°.
Angle B is made by combining a 60° angle and a 45° angle.
Find the measure of Angle B.
Use > , < , or = to compare Angle A and Angle B. Explain how you know which angle is larger.
What is Angle A = 120°; Angle B = 60° + 45° = 105°; 120° > 105°