Place Value Puzzles
In the number 42,317, what is the value of the 3?
300
Estimate: 364 × 9 ≈ ?
About 3,600 (round 364 to 400 × 9 ≈ 3,600)
Estimate: 806 ÷ 4 ≈ ?
About 200
How many ounces are in 1 pound?
16 ounces
Write 1,000 as a product of 10s.
10 × 10 × 10
Write 2,574,068 in expanded form.
2,000,000 + 500,000 + 70,000 + 4,000 + 60 + 8
Find the exact product of 364 × 9.
3,276
Solve: 806 ÷ 4.
201 R2
Convert 2 pounds to ounces
32 ounces
Write 10 × 10 × 10 × 10 × 10 using exponential notation.
10⁵
In the number 777,890, one 7 is worth 700,000. What is the value of the other 7?
70,000
Multiply: 48 × 13
624
Divide: 962 ÷ 25
38 R12
Convert 5 pounds to ounces
80 ounces
Write 10⁶ in standard notation
1,000,000
A number has digits 3, 4, 2, 2, 7.
The 3 is worth 30,000. The 4 is worth 4,000.
One 2 is worth 20. The other is worth 200.
What is the number?
34,227
Jesse collects 120 bags with 35 cans each.
Does he reach 1,500 cans?
120 × 35 = 4,200 → Yes, he has enough
There are 378 books. Each shelf holds 50 books. How many shelves are needed?
378 ÷ 50 = 7 R28 → Need 8 shelves
A gift weighs 4 pounds. The box and shipping materials weigh 9 ounces.
What is the total weight in ounces?
4 × 16 = 64 + 9 = 73 ounces
Compare 624 × 10⁴ and 155 × 10⁵. Which is larger?
155 × 10⁵ = 15,500,000 is larger
Write 624 × 10⁴ in standard notation
6,240,000
Explain how you can use an estimate to check if your answer to a multiplication problem is reasonable.
Round the numbers to the nearest ten or hundred, multiply the rounded numbers, and compare to your exact product.
Explain what to do with the remainder when dividing 378 books by 50 to find the number of shelves.
Round the quotient up to 8 because the remainder means you need another shelf.
Explain why using grouping symbols is helpful when writing an expression for the shipping problem
Grouping symbols show which operations to do first, so you correctly add the weights after converting to ounces.
Explain how you know which number is greater: 3 × 10⁵ or 8 × 10⁴.
3 × 10⁵ = 300,000; 8 × 10⁴ = 80,000 → 3 × 10⁵ is greater because it has more tens of thousands.