Operations and
Algebraic Thinking
Algebraic Thinking
Write each of the following as an equation:
3 groups of 5 items is 15.
The product of 4 and 7 is 28.
36 is 4 times as many as 9.
What is:
3 x 5 = 15
4 x 7 = 28
36 = 4 x 9
What is the value of the 5 in the following numbers?
53,247 and 8,569
Compare the value of 5 in these two numbers.
50,000 and 500
The five in 53,247 is 100 times the value of the 5 in 8,569.
Find the difference.
75,037 - 56,353
829,334 - 354,456
75,037 - 56,353 = 18,684
829,334 - 354,456 = 474,878
Fill in the missing number to make each set of fractions equivalent.
1/5 = __ /10
3/6 = 1 / __
6/8 = __ / 4
1/5 = 2/10
3/6 = 1/2
6/8 = 3/4
Write each fraction as a decimal, or each decimal as a fraction.
7/10 = __
__ = 0.68
35/100 = __
7/10 = 0.7
68/100 = 0.68
35/100 = 0.35
Carlos read 4 books in the month of May. In June, he plans to read 3 times as many books as he read in May. How many books does he plan to read in June?
Write the equation and answer.
Equation: 4 x 3 = 12
Answer: 12 books.
Write the following numeral in word form and expanded form.
214,530
Word form: two hundred fourteen thousand, five hundred thirty
Expanded form: 200,000+10,000+4,000+500+30
Find the product.
53 x 7
726 x 8
5,038 x 6
53 x 7 = 371
726 x 8 = 5,808
5,038 x 6 = 30,228
Use <, >, or = to compare each set of fractions.
2/3 __ 4/6
3/5 __ 2/3
2/5 __ 1/4
2/3 = 4/6
3/5 < 2/3
2/5 > 1/4
Use < , >, or = to compare each set of decimals.
0.7 __ 0.07
0.48 __ 0.5
0.2 __ 0.20
0.7 > 0.07
0.48 < 0.5
0.2 = 0.20
DAILY DOUBLE
Milo and Meg together earned $5 an hour for helping their neighbor with yardwork. If they worked for 8 hours, how much money would each of them get?
$20 each.
Use <, >, or = to compare each set of numbers.
3,729 __ 3,279
547,389 __ 547,839
8,891 __ 8,918
3,729 > 3,279
547,389 < 547,839
8,891 < 8,918
Find the product.
66 x 34
92 x 25
66 x 34 = 2,244
92 x 25 = 2,300
Find the sum or difference. Simplify.
5/8 + 1/8
4/5 - 3/5
2/5 + 3/5
5/6 - 3/6
5/8 + 1/8 = 6/8 = 3/4
4/5 - 3/5 = 1/5
2/5 + 3/5 = 5/5 = 1
5/6 - 3/6 = 2/6 = 1/3
Find the product.
4 x 3/8
3 x 3/4
4 x 5/2
Kristy is making cupcakes for her 6 friends. If 2/3 of her friends want chocolate, how many chocolate cupcakes will she make?
4 x 3/8 = 12/8 = 1 1/2
3 x 3/4 = 9/4 = 2 1/4
4 x 5/2 = 20/2 = 10
List the first 8 multiples of each number and all of the factors of each number.
8
12
25
Multiples of 8: 8, 16, 24, 32, 40, 48, 56, 64
Factors of 8: 1, 2, 4, 8
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96
Factors of 12: 1, 2, 3, 4, 6, 12
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200
Factors of 25: 1, 5, 25
Round 4,851 to the nearest hundred.
Round 18,327 to the nearest thousand.
Round 127,138 to the nearest ten thousand.
4,851 rounded to the nearest hundred is 4,900.
18,327 rounded to the nearest thousand is 18,000.
127,138 rounded to the nearest ten thousand is 130,000.
Find the quotient.
536 / 7
9,265 / 9
536 / 7 = 76 r4
9,265 / 9 = 1,029 r4
DAILY DOUBLE
Write an equation and solve.
Jackson brought cookies to school to share with his friends. By morning recess, 3/5 of the cookies were left. After recess, another 1/5 of the cookies were eaten. What fraction of cookies did they have left to enjoy after lunch?
3/5 - 1/5 = 2/5
2/5 of the cookies were left to enjoy after lunch.
Find an equivalent fraction. Then find a sum. Simplify.
6/10 + 30/100
9/100 + 4/10
40/100 + 2/10
6/10 + 30/100 = 60/100 + 30/100 = 90/100 = 9/10
9/100 + 4/10 = 9/100 + 40/100 = 49/100
40/100 + 2/10 = 4/10 + 2/10 = 6/10
or 40/100 + 20/100 = 60/100
Use the rule to create a pattern with at least 8 terms. Then explain what you notice about the pattern.
Start with 5, add 7.
5, 12, 19, 26, 33, 40, 47, 54
The numbers alternate between odds and evens.
There are two prime numbers.
Etc.
Find the sum.
65,229 + 36,374
273,534 + 249,372
65,229 + 36,374 = 101,603
273,534 + 249,372 = 522,906
DAILY DOUBLE
Write an equation and solve.
On Monday, Lisa read for 45 minutes. On Tuesday, she read for 70 minutes. On Wednesday, Lisa read twice as long as she did on Monday. How much time has Lisa spent reading so far in the week?
45 + 70 + (45 x 2) = 205
Lisa has read for 205 minutes so far this week.
Find the sum or difference. Simplify.
4 3/5 + 2 2/5
4 1/3 - 1 1/3
2 1/6 + 2 2/6
4 2/6 - 3 3/6
4 3/5 + 2 2/5 = 6 5/5 = 7
4 1/3 - 1 1/3 = 3
2 1/6 + 2 2/6 = 4 3/6 = 4 1/2
4 2/6 - 3 3/6 = 5/6
Write an equation and solve.
Kristy is making cupcakes for her 6 friends. If 2/3 of her friends want chocolate, how many chocolate cupcakes will she need to make?
6 x 2/3 = 12/3 = 4
Kristy will need to make 4 chocolate cupcakes.