Grade 3 Sample Math Tasks
(All our tasks are extensions to the NC “Unpacking sample problems.)
3.OA.1 Example: Jill bought 5 packages of cupcakes. There were 6 cupcakes in each package. How
many cupcakes did she buy? Have students represent this problem using tiles or counters to represent
the cupcakes. 5 x 6 = 30
3.OA.2 Partition Model (How many are in each group?)
Example: Joe has 12 apples. He wants to share them equally among 3 friends. How many apples does
each friend get? ? Have students represent this problem using tiles or counters to represent the
apples. 12 ÷ 3 = 4
Repeated Subtraction Model (How many groups can you make?)
Example: Laura’s dad made 12 pancakes. He gave each child 4 pancakes. How many children did he
serve? Have students represent this problem using tiles or counters to represent the pancakes.
12 ÷ 4 = 3
3.OA.3 Example: Mrs. Jones has 21 desks in her room. She puts 7 desks in each row. How many rows
are there? Have students represent this problem using tiles or counters forming arrays to represent the
desks. 21 ÷ 7 = 3
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Example of a 2-step word problem. Bill’s mom wants to divide 2 dozen brownies among 6 people. How
many brownies does each person receive? Have students represent this problem using tiles or counters
forming arrays to represent the brownies. 12 x 2 = 24 Then 24 ÷ 6 = 4
3.OA.4 Have students create fact family triangles and write the equations that relate to the triangle.
6 x 3 = 18
18
3 x 6 = 18
x/÷
6
18 ÷ 3 = 6
3
18 ÷ 6 = 3
3.OA.5
Commutative Property (order or turn-around facts)
Create arrays using tiles to demonstrate the commutative property. Turn array to see that the product
is still the same. Copy arrays onto graph paper.
Example:
5 x 3 = 15
3 x 5 = 15
Associative Property (grouping)
To show (2 x 3) x 4 = 2 x (3 x 4), use counters to show how numbers can be grouped differently in
multiplication and still get the same product. Have students create additional examples using single
digit factors.
Distributive Property (breaking numbers apart)
1st student:
2nd student:
3rd student:
7x6
7x6
7x6
7 x 5 = 35
7 x 3 = 21
5 x 6 = 30
7x1=7
7 x 3 = 21
2 x 6 = 12
35 + 7 = 42
21 + 21 = 42
30 + 12 = 42
Have students draw a 7 x 6 array on graph paper. Then color or cut rectangles within the array to
represent the distributive property.
3.OA.6 Use fact family triangles to relate division to known multiplication facts.
Example: In science class, students work in pairs. If there are 18 students in the class, how many pairs
are there?
? x 2 = 18
18
18 ÷ 2 = ?
x/÷
?
2
3.OA.7
Students should be fluent which means flexible (use distributive and other strategies to help with an
unknown fact), accurate (correct) and efficient (within 3-4 second responses). To develop this, teachers
should provide ample experiences using manipulatives, pictures, and fact family triangles. Supplement
with flashcards, computer games, Senteo quizzes, and timed tests to diagnose which facts need more
practice for each individual.
3.OA.8 Example of a 2-step problem: Jim bakes 4 cakes everyday for 5 days. He needs 25 cakes for a
big party. How many more cakes does he need to bake?
4 x 5 = 20 , 25 – 20 = 5 more cakes
Example using a variable: Sue and Kris earned $52 raking leaves. They want to buy a video game which
costs $100. Write an equation to show how much more money (m) they need to earn.
$52 + m = $100 or $100 – $52 = m
m = $48
Example using estimation Your school is collecting cans for recycling. Grade 2 collected 193 cans.
Grade 3 collected 221 cans and Grade 4 collected 78 cans. About how many total cans were collected?
Student 1
Student 2
Student 3
I first thought about 221
and 78. Their sum is about
300. Then I knew that 193
is close to 200.
I first thought about 193 which
really close to 200. I also have
2 hundreds in 221. So this
gives me a total of 4 hundreds.
When I put 21 and 78 together,
that is really close to 100. So
4 hundreds plus 1 hundred
equals 5 hundreds.
I rounded 221 to 200.
So 300 + 200 = 500
I rounded 193 to 200.
I rounded 78 to 80.
The sum of 200 + 200 + 80
is 480.
3.OA.9 Have students highlight patterns on hundred grids, addition tables and multiplication charts. For
example: Highlight even numbers on a hundred grid. Highlight multiples of 9 on a multiplication chart.
Explain the patterns that you see.
3.NBT.1