Place Value Detectives
In 462,815, what is the value of the digit 6?
60,000.
What operation finds the difference between two numbers?
Subtraction
“Four times as many” tells you to use which operation?
Multiplication
List the all multiples of 8 between 1 and 50.
8, 16, 24, 32, 40, and 48.
What does area measure? What does perimeter measure?
Area measures the space inside a shape and perimeter measures the distance around it.
How does the value of the 7 in 70,000 compare with the value of the 7 in 7,000?
The 7 in 70,000 is 10 times as much as the 7 in 7,000.
Before solving 6,002 − 2,785, a student estimates 6,000 − 3,000 = 3,000. How can this estimate help?
The exact answer should be near 3,000, so the estimate helps check whether it is reasonable.
Mia has 6 stickers. Explain the difference between having 3 more stickers than Mia 3 times as many stickers as Mia.
Answer: Three more is 9 stickers; three times as many is 18 stickers.
Three more is 3 + 6 which equals 9 stickers; three times as many is 3 x 6 which is 18 stickers.
Is 49 prime or composite? Prove it with a factor pair.
49 is Composite. Its factor pairs are 1 and 49, and 7 and 7.
A rectangle is 8 cm long and 3 cm wide. Write an expression for its area and an expression for its perimeter.
Area is Length x Width, so the expression is 8 × 3.
Perimeter is L + W + L + W, so the expression is 8 + 3 + 8 + 3, or (2 × 8) + (2 × 3).
Write 583 using 4 hundreds, some tens, and 3 ones.
4 hundreds + 18 tens + 3 ones
Solve: 6,002 − 2,785. Show your regrouping.
3,217.
Jay has 7 trading cards. Abby has 4 times as many. How many cards does Abby have? Write an equation and solve.
4 × 7 = 28.
Answer Statement: Abby has 28 cards.
List all factor pairs of 24.
1 and 24, 2 and 12, 3 and 8, and 4 and 6.
A rectangle has a perimeter of 30 cm and a length of 9 cm. Find its width, then its area.
9 + 9 =18
30 - 18 =12
12 divided by 2 is 6
Width = 6 cm
A = L x W, so 9 x 6 is 54. Area = 54 sq cm
A student says, “467 equals 4 hundreds + 60 tens + 7 ones.” Is the student correct? Explain and fix the representation.
No. That representation equals 1,007. Two correct representations are 3 hundreds + 16 tens + 7 ones and 4 hundreds + 6 tens + 7 ones.
A student solves 4,305 + 2,786 and gets 6,081. Find the correct sum and explain how you know the student’s answer is incorrect.
7,091.
An example explanation could be: 4,300 + 2,800 is about 7,100, so 6,081 is too low.
Aliza has 24 beads, which is 3 times as many as Zaylen has. Kamora says Zaylen has 72 beads. Explain the mistake and find Zaylen’s number.
Kamora multiplied instead of dividing. Zaylen has 8 beads because 24 ÷ 3 = 8.
A student lists the factors of 18 as 1, 2, 3, 6, and 18. What is missing? Explain how factor pairs help you check.
9 is missing. The pairs are 1 and 18, 2 and 9, and 3 and 6. Listing the factor pairs helps us see which factor is missing.
An L-shaped garden is divided into two smaller rectangles. Rectangle A measures 6 ft by 4 ft. Rectangle B measures 3 ft by 2 ft.
“A student says the total area is 24 square feet. Explain the mistake and find the correct area.”
The student only found the area of Rectangle A, not the total area of both smaller rectangles.
Area = length x width
Rectangle A: 6 x 4 =24
Rectangle B: 3 x 2 =6
Total Area: 24 + 6 =30 sq feet.
A number rounds to 35,000 when rounded to the nearest thousand. Its hundreds digit is 7. Give a possible number and explain why it works.
For example, 34,700. It rounds up to 35,000 because its hundreds digit is 7. 5 or more, up the score. 4 or less, let it rest!
The school’s reading goal is 5,000 minutes. Students read 1,875 minutes in week one and 2,468 minutes in week two. How many more minutes do they need? Write an equation and check your answer.
Answer Statement: They need 657 more minutes.
5,000 − (1,875 + 2,468) = 657.
Check: 4,343 + 657 = 5,000.
Mr. Imes class collects 8 cans. Ms. Greene’s class collects 3 times as many. Their combined goal is 40 cans. How many more cans do they need?
3 × 8 = 24
24 + 8 =32
40 - 32 = 8
Answer Statement: They need 8 more cans.I am a number between 20 and 40. I am a multiple of 6 and a factor of 72. What number could I be? Find every possibility and prove your answers.
I could be 24 and 36. Both are multiples of 6, and 24 × 3 = 72 and 36 × 2 = 72.
Two rectangles each have a perimeter of 24 units. One measures 8 feet long by 4 feet wide. The other measures 6 feet long by 6 feet wide. Do they have the same area? Use calculations to explain what this shows.
No they do not have the same area. Their areas are 32 and 36 square units.
Some shapes can have the same perimeter but different areas.