Grade 3- Unit 9: Algebraic Reasoning-All Operations
Make a Sum
The class plays Make a Sum. The teacher projects a 0-9 spinner. Each student draws a game board
like the one shown on paper or on an individual dry erase board.
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The object of the game is to place digits in the boxes to produce the largest possible sum. The
teacher spins the spinner and announces the resulting digit. Each student writes the digit in one box
on his/ her game board. This process continues until the teacher spins and calls 6 digits. Once a
number is written in a box, it cannot be erased or moved. Students add the numbers to find the sum.
Points are awarded to students who arrive at the largest possible sum. After playing the game
several times, discuss the results as a class. Alternatively, students may try to find the smallest
possible sums.
Questions to ask during the game:
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If the first spin is a 9, where would you place it? Explain your reasoning.
If the first spin is a 1, where would you place it? Explain your reasoning.
If the first spin is a 5, where would you place it? Why? (Continue this line of questioning with
other digits.)
What is the general rule that you can use to produce the largest possible sum?
How would this rule change if you wanted to find the smallest possible sum?
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Multi-Step Word Problems #1
1. Jonas gave Luke 179 baseball cards. Luke received 275 cards for his birthday and bought
225 more cards at the Sports Shop. Write an equation to show how many cards Luke has
now.
2. Julius has 93 crayons and 19 markers. He has the same number of colored pencils as he has
markers. How many crayons, markers, and colored pencils does Julius have?
3. Mr. Kennard had 163 chapter books. He gave 125 books to the students in his class. A friend
gave him 45 more books. How many books did Mr. Kennard have then?
4. On Monday, Zippy Potato Chip Company had 92 pounds of potatoes to make potato chips. In
the morning they used 32 pounds of potatoes. In the afternoon they used 41 pounds. How
many pounds of potatoes did they have left at the end of the day? Mr. Kilgore had 73 yards of
wire. He used 33 yards to fix the fence. He then used 28 yards to fix the gate. How many yards
of wire did Mr. Kilgore have after finishing both jobs?
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Multi-Step Word Problems #2
1. Grayson divided his darts into equal groups by color. He has 56 darts. The darts are red,
orange, yellow, green, blue, purple, and black. Use a strip diagram to show how Grayson
divided his darts.
What division fact helps solve this problem? _________________________________________
2. Rylie collects stickers. She has 4 star stickers. Rylie has twice as many animal stickers as
star stickers. She has three times as many sports stickers as animal stickers. To find the total
number of sports stickers, Rylie writes this equation.
(4 X 2) X 3 = 24
What is another way Rylie could group the factors to find the same number of sports stickers?
_______________________________________________
3. Terri Kay is organizing the shelves at the food pantry. She has 5 cases of canned foods with
18 cans in each case. She needs to put an equal number of cans on each of the 9 shelves in
the pantry. Terri Kay uses this model to help solve the problem.
18 cans
18 cans
18 cans
18 cans
18 cans
How many cans can Terri Kay place on each shelf of the food pantry?
______________________________________________
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
4. Maurice counted the change in his pocket. He had 5 nickels and 6 dimes. How much money
did Maurice have in his pocket?
Multi-Step Word Problems Assessment
1. Henry’s goal is to read 93 pages of his book over a 3 day period. If he reads 34 pages on
Monday and 25 Tuesday, how many pages will Henry need to read on Wednesday to reach
his goal?
2. Dianne bought 48 tickets for rides at the carnival. The tickets were shared equally among 6
people. Each ride takes 2 tickets. How many rides can each person ride?
3. Jonas gave Luke 179 baseball cards. Luke received 275 cards for his birthday and bought
225 more cards at the Sports Shop. Write an equation to show how many cards Luke has
now.
4. Kayne, Emory, and Aubrey shared a package of 2 dozen pencils. How many pencils did each
child receive?
5. Mrs. Johnson needs 900 pieces of candy for her booth at the school carnival. She has one
bag that contains 288 pieces of candy and another contains 356 pieces. Write and solve an
equation that shows how many more pieces of candy Mrs. Johnson needs.
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Addition
The Houston Rockets had two home games. 14,263 people attended the first game. 15,436 attended the second
game. What is the total number of people attending the two games?
1. Pull out facts (information) and label
2. Write the question using your own words
1. Write the four math symbols
2. Circle the correct symbols to use
3. Write down all possible ways to solve
Understand (U)
Evaluate/Reasonable (Does it make Sense?) (E)
1. Take a component from each box and write a
sentence (start with the question)
Procedure/Process (P)
Solve/Check (S)
1. Pick one from Procedure/Process and solve
2. Check by using another model
3. Label your number
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Subtraction
A plane travels 5, 812 miles this week and the same plane traveled 2,495 last week. ABOUT how many more miles did
the plane travel this week than last week?
1. Pull out facts (information) and label
2. Write the question using your own words
1. Write the four math symbols
2. Circle the correct symbols to use
3. Write down all possible ways to solve
Understand (U)
Evaluate/Reasonable (Does it make Sense?) (E)
1. Take a component from each box and write a
sentence (start with the question)
Procedure/Process (P)
Solve/Check (S)
2. Pick one from Procedure/Process and solve
3. Check by using another model
4. Label your number
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Multiplication
Joe makes 8 telephone calls every day for 23 days. How many telephone calls did Joe make?
1. Pull out facts (information) and label
2. Write the question using your own words
1. Write the four math symbols
2. Circle the correct symbols to use
3. Write down all possible ways to solve
Understand (U)
Evaluate/Reasonable (Does it make Sense?) (E)
1. Take a component from each box and write a
sentence (start with the question)
Procedure/Process (P)
Solve/Check (S)
4. Pick one from Procedure/Process and solve
5. Check by using another model
6. Label your number
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Division
Jenny equally distributed a bag of 36 marbles among 4 friends. How many marbles does each friend get?
1. Pull out facts (information) and label
2. Write the question using your own words
1. Write the four math symbols
2. Circle the correct symbols to use
3. Write down all possible ways to solve
Understand (U)
Evaluate/Reasonable (Does it make Sense?) (E)
1.Take a component from each box and write a
sentence (start with the question)
Procedure/Process (P)
Solve/Check (S)
4. Pick one from Procedure/Process and solve
5. Check by using another model
6. Label your number
Name:_________________________________
Date:_____________________
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Multiplication/Division Relationship with Dominos
Picture of Domino
Algebraic Equations ( ÷ and X)
Picture Array
Ex:
3
5 x 3 = 15
3 x 5 = 15
5
15 ÷ 5 = 3
15 ÷ 3 = 5
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=15
Grade 3- Unit 9: Algebraic Reasoning-All Operations
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Addition Quiz: Please use your Place Value Chart and strategies for ALL problems.
Find the SUM for 398 and 1,249
How many toys in all if Joe has 365 and Bob has
930?
Solve for Y: y-6 = 25
Compose the following: 8,410 and 3,1694
Put your answer in written form for the following:
8,973 is one addend and the other addend is
9,219
What is the Total for the following: Part One=563
and Part Two is 95?
Use the chart below to solve for the Whole.
Estimate and find the SUM for 5,973 and 8,286
Games
1
2
3
Passing Yards
368
277
312
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Subtraction Quiz: Please use your Place Value Chart and strategies for ALL problems.
Find the Difference for 369 and 124
How many more is 500 than 230?
If the whole is 600 and the subtrahend is 399,
what is the other part?
Decompose the following: 2410 – 1694
Using REPEATED Subtraction, please solve the
following: 36-9
Using a Strip Diagram, please illustrate the
following 60-10.
A farmer planted 654 apple trees, at harvest time;
he realized that 179 trees did not produce apples.
How many apple trees were still producing
apples? (HINT) Stay focused!!
Estimate and find the Difference for 769 and 239
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Division Quiz: Please use your Place Value Chart and strategies for ALL problems.
Find the QUOTIENT for 21 ÷ 3
Using Repeated Subtraction, solve 32 / 8
Separate into equal parts the following: 64 / 8
If the Dividend is 54 and the divisor is 9, What is
the Quotient?
If the Quotient is 9 and the Dividend is 63, then
the Divisor must be?
Using a Strip Diagram, solve the following: the
Dividend is 49 and your divisor is 7.
Use the chart below to solve for the Whole.
Estimate and then find the QUOTIENT for 89
and 12
Points
Minutes
16
4
24
6
32
8
What is the relationship between the two
categories? Write the Division Equation for 12
minutes?
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Grade 3- Unit 9: Algebraic Reasoning-All Operations
Multiplication Quiz: Please use your Place Value Chart and strategies for ALL problems.
Find the Product for 8 and 7
Draw an Array and label correctly 6 x 8
Find the pattern to determine what comes next:
10 x 10 = 100
100 x 10 = 1,000
1,000 x 10 = ???
Using the following factors 96 and 8, find the
PRODUCT.
Using REPEATED Addition, please solve the
following: 6 x 5
Using a Strip Diagram, please illustrate the
following 12 x 4
A farmer planted 12 rows of carrots, in each
row, he had 8 carrots. How many carrots were
planted?
Estimate and find the PRODUCT for 28 and
499 (Hint: Once estimated, use the trailing zero
to find the product.)
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