Expressions
Write the following expression using numbers.
DO NOT SOLVE:
Divide the difference between 1,500 and 700 by 2
(1,500-700) ÷ 2
Compare the two expressions using <, >, or =. For each, explain how you can determine the answer without calculating.
10 x 2 and 2 tens
10x2 = 2tens
because 2 tens is the same as 10 x 2
Draw an area model and solve.
21 x 15
315
Is this answer reasonable? Explain why or why not.
10 x 6 = 600
No, this answer is not reasonable because there are too many 0's. The answer should not have a hundreds place.
1 yd = ____ft
1 yd = 3 ft
Write the following expression using numbers.
DO NOT SOLVE:
The sum of 3 twelves and 17 twelves
(3 x 12) + (17 x 12)
Compare the two expressions using <, >, or =. For each, explain how you can determine the answer without calculating.
20 x 3 and (20 x 2) + (20 x 2)
20 x 3 < (20 x 2) + (20 x 2)
because (20 x 2) + (20 x 2) is the same as 20 x 4
20 x 4 < 20 x 4
Draw and area model and solve.
321 × 15
4,815
Is this answer reasonable?
205.7 x 3 = 6,171
No, this answer is not reasonable because there is not decimal point/ there is no tenths place.
2.5 yds = ____ft
(solve by multiplying 2.5 x 3 because 1yd = 3 ft)
Solve:
Divide the difference between 1,500 and 700 by 2
(1,500-700) ÷ 2
=400
Compare the two expressions using <, >, or =. For each, explain how you can determine the answer without calculating.
48 × 10 and 50 tens − 3 tens
48 x 10 > 50 tens - 3 tens
because 50 tens - 3 tens is 47 tens
47 tens = 47x10
47x17 is less than 48x10
Solve using the standard algorithm:
5.25 x 15
78.75
Estimate the product first.
Then, solve by using the standard algorithm. Use your estimate to check the reasonableness of the product.
2.9 x 103
Estimated 3 x 100 = 300
Solved = 298.7
It takes 1.5 yards of fabric to make a bow. How many feet of fabric will it take to make 50 bows?
(hint: should your answer be in feet or yards?)
It will take 225 feet of fabric to make 50 bows.
1.5 yds x 50 = 75 yds
75 yds x 3 = 225 feet of fabric
Solve:
The sum of 3 twelves and 17 twelves
(3 x 12) + (17 x 12)
=240
Compare the two expressions using <, >, or =. For each, explain how you can determine the answer without calculating.
100 × 8 and 25 × (4 × 9)
100 x 2 < 25 x (4 x 4)
because I can move the parenthesis to show
(24 x 4) x 4 which is the same as 100 x 4
100 x 2 is less than 100 x 4
Solve using the standard algorithm:
2561.2 × 5.4
13,830.48
If 752 × 49 = 36,848, then 75.2 × 49
3,684.8
because the place value has changed to include 1 decimal in the factors. This should match the product.
It takes 2.2 feet of fabric to make 1 shirt. How many yards of fabric will it take to make 24 shirts?
(hint: should the answer be in feet or yards?)
It will take 17.6 yards of fabric.
2.2ft x 24 = 52.8 feet.
52.8 feet divided by 3 to convert to yards is 17.6 yards.
Write the following expression using words and then solve:
(540 + 460) × 12
12 times the sum of 540 and 460
12,000
Compare the two expressions using <, >, or =. For each, explain how you can determine the answer without calculating.
(60 + 440) x 3 and 3 times the sum of 50 and 500
(60 + 440) x 3 < 3 times the sum of 50 and 500
because 3 copies of 60 + 440 is less than 3 copies of 50 + 500.
Estimate the product first.
Then, solve by using the standard algorithm. Use your estimate to check the reasonableness of the product.
2,407 × 580
Estimated: 2,000 x 600 = 1,200,000
Solved: 1,396,060
If 3,156 × 272 = 858,432, then 315.6 × 2.72
858.432
because 3 digits were shifted behind the decimal in the factors, we need to shift the answer 3 places as well.
I can use 225 feet of fabric to make all my bows.
A manufacturer is making 1,000 times as many bows as me to sell in stores nationwide. Write an expression using exponents to show how many yards of ribbon the manufacturer will need. Do not calculate the total.
225ft x 103