Sample Story Problems to help children move from Level 0 to Level 1
Multiplication and Division with Whole Numbers
Use story theater (©Mar Jensen)
Choose problems based on familiar children’s books, and problems based on things that happen every day in the classroom
M
____ children are playing with blocks. They
each have ___ blocks. How many blocks do
they have altogether?
3,2
2,2
4,2
M
There are _____ children at each table.
Each child has _____ crayons. How many
crayons do they have in all?
2, 3
3,3
2, 5
MD
Siti brought ____ pretty beads to school.
She gave ____ beads to each friend. How
many friends did she give the beads to?
4, 2
6, 3
8, 4
10, 5
PD
Shanna has ____ cookies. She wants to put
them into bags for her friends. She has
____ bags. How many cookies will she put
in each bag to give each person the same
amount?
10, 2
10, 5
8, 2
9, 3
Story problems should be very concrete, and might be solved using story maps, and realistic manipulatives instead of abstract counters
M
Jason drew ____ monsters. Each monster
had ____ eyes. How many eyes did Jason’s
monsters have in all?
1, 3
2, 3
Jason made _____ towers with Legos. He
used ____ Legos for each tower. How many
Legos did he use in all?
M
Kelli is putting pencils in cups. She has ___
cups. She puts ____ pencils in each cup.
How many pencils does she put in all the
cups?
2, 3
3, 2
4, 2
2, 5
3, 3
MD
Samantha brought a bag of ____cherries for
snack. She put ____ cherries on each plate.
How many plates of cherries can she make?
4, 1
6, 2
8, 4
10, 2
PD
In the garden, there were ___ spiders. They
sat on ____ flowers. The same number was
on each flower. How many were on each
flower?
6, 3
4, 2
8, 4
9, 3
Give children some experience noticing visual arrays (e.g., packs of juice boxes, chocolates in a box) and counting the number of objects in the concrete arrays.
Remember not to ask the question too soon so that children have an opportunity to represent the action in the problem
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 2 to Level 3
Multiplication and Division with Whole Numbers
Choose problems based on familiar children’s books, and problems based on things that happen every day in the classroom
M
Julian saw ___ tricycles on the playground.
How many tricycle wheels did he see?
6
7
8
9
M
Charn made ____ birthday cards for her
friends. She drew ____ balloons on each
card. How many balloons did she draw?
4, 5
6, 4
7, 3
5, 6
MD
Ralph cut out ____ balloons. He put ____
balloons on each birthday card. How many
cards did he make with all his balloons?
24, 4
28, 7
30, 15
25, 5
PD
Mr. Green has ____ new pencils. He puts
the same number of pencils in each pencil
box. He has ___ pencil boxes. How many
pencils does he put in each box?
21, 7
25, 5
28, 4
Use problems involving arrays in children’s environment (e.g., packs of juice boxes, chocolates in a box, windows on a building).
M
Miguel saw ___ packs of juice boxes on a
store shelf. There were ___ boxes in each
pack. How many juice boxes did he see in
all?
5, 3
8, 3
6, 4
7,4
M
Our class went on a neighborhood walk. We
saw a building that had ___rows of
windows. There were ___ windows in each
row. How many windows were there on the
whole side of the building?
4, 6
5, 5
3, 10
3, 8
MD
Sam has a box of ____ crayons. There are
____ crayons in each row in the box. How
many rows of crayons are in the box?
30, 10
27, 9
28, 7
25, 5
24, 8
PD
Sylvia’s mom bought ___ donuts for work.
The box had ___ rows of donuts. How many
donuts were in each row?
18, 2
30, 3
28, 4
16, 2
24, 3
MD
I counted ____ triangles in the pattern
blocks box. I put them in groups of ___.
How many groups did I make?
25, 5
30, 10
22, 2
30, 5
PD
___ children were running in the race. The
gym teacher put them in ___ groups. How
many children were in each group?
30, 6
30, 15
25, 5
20, 10
See Investigations, Grade 1, Unit 8: “Twos, Fives, and Tens”
M
There are ___ jars of paint in a box. There
are ___ boxes. How many jars of paint is
that?
3, 5
2, 10
5, 6
5, 4
10, 3
M
___ children got their hands full of finger
paint? How many fingers was that
altogether?
2
3
5
4
6
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 3 to Level 4
Multiplication and Division with Whole Numbers
Use skip counting sequences to solve problems involving groups of 2s, 5s, and 10s
o Use M, MD
o See Investigations, Grade 1, Unit 8: “Twos, Fives, and Tens”
M
How many shoes do ___ children have?
4
6
8
10
M
How many fingers do ____ children have?
2,
3
4
5
MD
Sam has ___ pennies. He wants to put them
in groups of ____. How many groups can he
make?
40, 10
40, 5
25, 5
50, 5
MD
Jillian made ____ paper flowers. She put
them in groups of ___ to make bouquets.
How many groups can she make?
15, 5
30, 5
30, 10
50, 10
Continue to build understanding of number, and to practice addition/subtraction. The child may use repeated addition to solve multiplication problems.
o Use M, MD, PD
o Use number sets that don’t necessarily include 2s, 5s, and 10s
o For bigger numbers, continue to expect some direct modeling.
M
___ boys were playing soccer. Each boy
kicked the ball __ times. How many times
did they kick the ball in all?
8, 4
7, 3
4, 6
3, 8
M
___ girls were jumping rope. Each girl had
___ beads in her hair. How many beads did
they have in all?
6, 6
3, 12
4, 15
3, 21
MD
Justin has ___ bug stickers to put in his bug
book. He puts ___ stickers on a page. How
many pages can he fill?
18, 3
24, 6
42, 6
48, 12
PD
Justin has ___ bug stickers. He wants to put
them on ___ pages. How many can he put
on each page?
27, 3
35, 7
36, 6
48, 8
Understand contexts that can be represented with arrays (e.g. rows of chairs, tiles on the floor)
M
A pan of cookies has ___ rows with __
cookies in each row. How many cookies
does the pan have in all?
3, 6
4, 5
5, 4
6, 4
M
The children in Miss Smiley’s room meet at
a corner of the room on the tile floor. There
are ___ rows of tiles. There are ___ tiles in
each row. How many tiles are there in all?
7, 4
6, 5
5, 10
10, 5
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
MD
A pan of cookies has ___ cookies arranged
in rows. There are ___ cookies in each row.
How many rows of cookies are there?
15, 5
20, 5
12, 3
30, 10
PD
There are ___ bean plants in the garden
plot. They are growing in ___ rows. How
many bean plants are in each row?
40, 8
30, 3
35, 5
50, 10
Draft: August 4, 2011
Sample Story Problems to help children move from Level 3 to Level 4
Multiplication and Division with Whole Numbers
Use story problem contexts to explore multiplying by 0, multiplying by 1, and dividing by 1, and dividing a number by itself.
M
Jenna has ___ pockets in her jacket. She
has ___ pennies in each pocket. How many
pennies does she have in all?
6, 1
4, 0
6, 0
0, 36
M
Javier went outside to look for worms. He
looked under ___ rocks. He found ___
worms under each rock. How many worms
did he find altogether?
10, 0
10, 5
15, 1
49, 0
MD
Some friends went to the park. They found
___ rocks. Then they put the rocks in equal
groups with ___ rocks in each group. How
many groups of rocks did they make?
14, 2
14, 1
10, 10
30, 1
PD
Maria helped her dad pack ___ cakes to sell
at their store. They packed ___ bags full.
They put the same number of cakes in each
bag. How many cakes did they put in each
bag?
16, 1
16, 16
24, 1
24, 24
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 4 to Level 5
Multiplication and Division with Whole Numbers
Use skip counting sequences to solve problems involving groups of 2s, 3s, 4s, 5s, and 10s. Use M, MD.
M
Barrettes come in packages of ____. For
Josie’s braids, she needed ____ packages.
How many barrettes did Josie need in all?
10, 4
4, 9
3, 8,
5, 12
M
Ciera has ___ braids. There are ___ beads
in each braid. How many beads does she
have in her hair?
5, 10
3, 5
10, 4
10, 2
MD
Andre’s mom bought ___ barrettes for her
hair salon. Barrettes come in packages of
____. How many packages did she buy?
90, 10
75, 5
36, 4
20, 2
MD
Andre’s mom bought ____ barrettes for her
hair salon. She bought ___ packages. All the
packages have the same number of
barrettes. How many barrettes were in each
package?
60, 10
50, 5
30, 3
45, 5
Use repeated addition (or subtraction) to solve M, MD, and PD story problems, particularly with groups of 6, 7, 8, and 9
M
Jose is filling ____piñatas for birthday
parties. He puts ___ candies in each one.
How many candies does he need for all the
piñatas?
7, 6
8, 9
8, 7
9, 6
M
Tammy has ___ bowls of fish. There are ___
fish in each bowl. How many fish does she
have in all?
4, 9
6, 6
7, 8
7, 7
MD
A baker has ___ doughnuts. She wants to
pack them in boxes. Each box holds ___
doughnuts. How many boxes does the baker
need for all of the doughnuts?
47, 7
36, 6
63, 7
54, 9
PD
A baker has ___ doughnuts. She packs
them in ___ boxes. She packs the same
number of doughnuts in each box. How
many doughnuts does she pack in each
box?
72, 8
36, 9
56, 8
49, 7
Understand contexts that can be represented with arrays (e.g. rows of chairs, tiles on the floor)
M
Carlton helped his dad set up chairs for a
neighborhood festival. They made ___ rows
of chairs. There were ___ chairs in each
row. How many chairs did they have
altogether?
6, 8
7, 7
7, 9
8, 10
M
Ian opened a big box of pencils. He saw ___
rows of pencils with ___ pencils in each row.
How many pencils were in the box?
10, 9
8, 7
7, 8
6, 9
8, 8
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
MD
Jackie counted ___ apples in the display at
the grocery store. She saw ___ apples in
each row. How many rows of apples did she
see?
48, 8
90, 10
63, 7
72, 9
PD
Jackie counted ____ apples in the display at
the grocery store. She saw ____ rows of
apples. Each row had the same number of
apples. How many apples were in each row?
56, 7
72, 8
81, 9
54, 9
Draft: August 4, 2011
Sample Story Problems to help children move from Level 4 to Level 5
Multiplication and Division with Whole Numbers
Use story problem contexts to explore multiplying by 0, multiplying by 1, and dividing by 1, and dividing a number by itself.
M
Each child has ___ stickers. How many
stickers to ___ children have altogether?
1, 78
0, 99
75. 1
14. 0
M
Emma is getting ____ bags of snacks ready
for a picnic. She puts ___ carrots in each
bag. How many carrots is she putting in all
the bags together?
73, 0
49, 1
100, 0
97, 1
MD
A boy had ___ candies. He gave each friend
___ candies. How many friends got
candies?
23, 1
39, 39
50, 1
98, 98
PD
A box of ____pencils was shared equally by
___ students. How many pencils did each
student get?
52,52
49, 1
84, 1
84, 84
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 5 to Level 6
Multiplication and Division with Whole Numbers
Use skip counting sequences to solve problems involving groups of 2s, 3s, 4s, 5s, and 10s
M
Jonah’s teacher asked him to ___colored
pencils on each table. There are ___ tables.
How many pencils will Jonah need?
2, 9
5, 8
3, 8
2, 7
M
Mia’s mom bought ___ packs of drinks.
There were ___ drinks in each pack. How
many drinks did she buy altogether?
5, 5
4, 10
6, 4
9, 5
MD
Chante bought crackers to school for snack.
The bag had ___crackers in it. Chante wants
to give each child ___crackers. How many
children can she give the crackers to?
60, 10
60, 5
35, 5
80, 10
PD
Daveon has ___ Spider Man cards. He is
putting them into ___ equal groups. There
will be the same number in each group. How
many cards will be in each group?
90, 10
45, 5
30, 3
36, 4
Use repeated addition (or subtraction), repeated doubling, and other additive groupings to solve M, MD, and PD story problems, particularly with groups of 6, 7, 8, and 9
M
Every day, the zoo-keeper needs ___
bananas for each monkey at the zoo. How
many bananas does she need for ___
monkeys?
6, 7
8, 9
6, 9
7, 8
M
Anna saw ___ ducks at the lake. Each duck
had ___ ducklings. How many ducklings did
Anna see?
8, 8
6, 8
7, 9
9, 9
MD
Jesse and her friends have ___ candies to
use to decorate cupcakes. They are putting
___ candies on each cupcake. How many
cupcakes can they decorate with candies?
54, 6
63, 7
72, 8
81, 9
PD
Juan’s mother gave him a bag of ___
peanuts. Juan and his three friends are
going to share the peanuts so that they each
get the same amount. How many peanuts
will each boy get?
80, 8
56, 9
72, 9
56, 7
Understand contexts that can be represented with arrays (e.g. rows of chairs, tiles on the floor)
M
Siti counted the cars in the parking lot
outside of her apartment. There were ___
rows of cars with ___ cars in each row.
How many cars were there in all?
4, 9
10, 8
7, 8
9, 6
M
Cortez noticed a box with apples at the
market. There were ___ rows of apples with
___ apples in each row. How many apples
were there altogether?
8, 9
7, 8
10, 8
6, 9
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
MD
Kaneisha made a rectangle with ___ square
tiles. Her rectangle had ___ tiles in each
row. How many rows did Kaneisha make?
54, 6
72, 9
45, 5
63, 7
PD
Cortez and his friends made ___ snow
blocks to make a wall for their snow fort.
They stacked them up in ___ rows. How
many snow blocks did they put in each row?
70, 7
48, 6
56, 8
72, 8
Draft: August 4, 2011
Sample Story Problems to help children move from Level 5 to Level 6
Multiplication and Division with Whole Numbers
Build toward an understanding of the commutative property in multiplication
o For example, use story problems with related numbers, such as 6 plates with 5 cookies on a plate, or 5 rows with 6 chairs in each row
o Use story problems with an array context
M
Darius saw ___ bird nests. He saw ___
eggs in each nest. How many eggs did he
see altogether?
6, 7
5, 10
9, 5
8, 4
M
Jamie has put ___ plates on the table. She
put ___ orange slices on each plate. How
many orange slices did she put on all the
plates together?
7, 6
10, 5
5, 9
4, 8
M
Amber helped her mother cut a pan of
brownies. When they finished cutting, there
were ____rows with ___ brownies in each
row. How many brownies were there
altogether?
8, 5
9, 7
5, 6
10, 4
M
The secretary put pictures of students on the
bulletin board. She made ___ rows with ___
pictures in each row. How many pictures did
she have?
5, 8
7, 9
6, 5
4, 10
Build toward an understanding of the inverse relationship between multiplication and division
o Use related story problems
M
Robert baked cookies after school. He put
___ rows of cookies with ___cookies in each
row on the baking sheet. How many cookies
were on each baking sheet?
8, 6
5, 7
4, 9
6, 8
MD
Robert had ___ cookies. He filled small bags
with ___cookies in a bag. How many bags
did he fill?
M
The gym teacher put all the students in
teams for field day. There were ___ teams
with ___ students on each team. How many
students were on the teams?
48, 6
35, 5
36, 9
48, 8
7, 8
6, 9
8, 10
9, 8
PD
Ms Lord’s class invited parents to see their
play. They put ___ chairs in rows. They
made ___rows. How many did they have?
56, 7
54, 6
80, 8
72, 9
Explore problems multiplying one-digit numbers times small two-digit numbers. The product should still be within 100 (e.g., 6×17; 8×12; 3×23).
M
On Tuesday, students at Leopold School
went on a field trip. Teachers packed ___
bags of apples for snack. There were ___
apples in each bag. How many apples
were there in all?
6, 15
4, 20
7, 21
5, 30
M
Houa counted ___ spiders in his backyard.
Each spider has 8 legs. How many legs did
all the spiders have?
M
Henry made ___ Valentine cards. He drew
___ hearts on each one. How many hearts
did he draw in all?
M
Felicity and her mom bought ___ dozen
eggs for their bakery business. How many
eggs was that in all?
12
14
20
26
14, 7
16, 4
22, 5
25, 4
1
4
6
9
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 5 to Level 6
Multiplication and Division with Whole Numbers
Explore division problems involving two-digit divisors or quotients, such as 96÷16, 80÷5. Expect students to solve these problems by direct modeling with tens and ones or
using repeated addition or subtraction.
MD
Mr. Flowers brought ___ flowers to sell at
the Farmer’s Market. He made bouquets
___ flowers in each bouquet. How many
bouquets did he make?
80, 5
52, 13
84, 12
75, 3
MD
David’s dad bought ___ hot dog buns for the
school picnic. The buns come in packages
of ___. How many packages did he buy?
96, 8
96, 12
88, 11
81, 3
PD
For field day, the students at Franklin
Elementary School were put into ___
groups. There were ___ students. How
many students were in each group?
12, 60
6, 72
14, 84
16, 96
PD
Cindy’s school went to a movie theater.
Altogether there were ___ students. They
sat in ___ rows. The same number of
students sat in each row. How many
students sat in each row?
90, 5
77, 11
88, 16
96, 12
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 6 to Level 7
Multiplication and Division with Whole Numbers
Understand contexts that can be represented with arrays (e.g. rows of chairs, tiles on the floor)
Continue to build toward an understanding of the commutative property in multiplication
o Use story problems with related numbers
o Use story problems with an array context
Continue to build toward an understanding of the inverse relationship between multiplication and division
o Use related story problems
Use story problems that help build toward an understanding of distributive property.
M
10 girls were shooting baskets in the gym. Each girl shot 5
baskets. Then 4 more girls came to the gym. They each shot
5 baskets. How many baskets did the girls shoot altogether?
10, 5, 4, 5
6, 12, 3, 12
M
On Monday, Shantel bought ___ bags of beads. Each bag
had ___ beads in it. On Wednesday she bought ___ more
bags of beads. The bags were the same size. How many
beads did she buy on both days together?
2, 16, 4
4, 25, 4
5, 23, 4, 23
M
Mr. Green had ___ boxes of paper clips. There were ___
paper clips in each box. Then he found ___ more boxes of
paper clips. They also had ___ paper clips in each box. How
many paper clips did he have in all?
7, 30, 2, 30
5, 25, 2, 25
3, 27, 2, 27
Solve problems multiplying one-digit × two-digit numbers. Use smaller two-digit numbers.
M
6, 16
20, 7
26, 7
M
4, 35
9, 27
8, 33
Solve division problems involving two-digit divisors or quotients.
MD
The school store has ___ erasers to sell. The erasers come
are in packages with ___ erasers in each. How many
packages of erasers are there?
96, 16
80, 5
72, 12
90, 15
PD
The school store has ____fancy pencils to sell. All the
pencils are displayed in ____ boxes. The same number of
pencils is in each box. How many pencils are in each box?
65, 5
84, 14
70, 14
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011
Sample Story Problems to help children move from Level 6 to Level 7
Multiplication and Division with Whole Numbers
Solve division story problems which involve the interpretation of remainders (Possibilities include: an extra whole unit must be included, the remainder is left off, the
remainder is the answer to the problem, or the answer includes a fractional part.)
MD
____ children are going on a field trip. They are riding in
cars. Each car can carry ___ children. How many cars are
needed all of them?
50, 4
85, 4
65, 6
69, 8
PD
The zoo-keeper has ___ bananas. She has to feed ___
monkeys. She wants to give each monkey the same
amount. How many bananas should each monkey get?
69, 12
78, 16
95, 4
MD
A farmer has ___ tomatoes. She wants to pack them in
boxes with ___ tomatoes in each box. If she packs as many
boxes as possible, how many tomatoes will be left over?
65, 4
87, 4
72, 5
Solve problems involving multiple steps/multiple operations
The grocer had ___ boxes of peaches with ___ peaches in
each box. He decided to put them into ___ new boxes
instead. Now how many peaches were in each box?
3, 28, 4
7, 35, 5
Lisa bought ___ bags of beads. There were ___ beads in
each bag. She gave away ___ beads. How many beads did
she have left?
7, 28, 43
9, 31, 55
Josh, Anna, and Grace share ___ square tiles equally. If
Josh gives ___ Grace 12 of his tiles, how many will he have
left?
72
87
94
Explore story problem contexts involving dividing by zero to help student understand why division by zero is impossible.
Give children opportunities to explain their strategies, listen to other children’s strategies, and compare strategies.
Note: These problems are intended to provide starting ideas for teachers. They are not all inclusive.
Draft: August 4, 2011