Dear Teachers,
During the listening tour, the Eureka Math Team enjoyed the opportunity to witness our curriculum being
implemented in St. Charles classrooms. We listened carefully to the feedback you provided about additional
resources that could support implementation and are excited to deliver a pilot version of a new resource,
Eureka Math Homework Guides, intended to help bridge the gap between the classroom and home.
Our writers have begun creating Homework Guides to provide families with insight of the understandings and
skills gained during each math lesson. The guides are designed to deliver guidance for the problems on the
homework pages (K-5)/problem sets (6-12). The problems and their worked out solutions included in each
Homework Guide were chosen intentionally and closely align with at least one problem on the
homework/problem set.
After examining your curriculum maps, we created ten Homework Guides for each grade level, K-10, and have
done our best to create these documents for immediate use. In order for these to support student learning,
please make them available for families at home. Students and their families can use the Homework Guides
to receive helpful hints when homework becomes challenging.
In order for you to help us continue to improve our curriculum and accompanying resources, we welcome any
and all feedback you and/or your students’ families can provide. After receiving feedback, our goal is to
create a Homework Guide for every lesson in the curriculum and make them available to the public.
We are excited to provide you with this pilot set of Homework Guides and even more excited to improve this
resource through your valued feedback.
Many Thanks,
The Eureka Math Team
© 2015 Great Minds. All rights reserved. greatminds.net
Lesson 19 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 19: Use tape diagrams as representations to solve
put together/take apart with total unknown and add to with
result unknown word problems.
Vocabulary
Put Together/Take Apart with Total Unknown: Put together/take apart problems do not have any action in
the story. They are simply parts (green apples and red apples or big dogs and little dogs) that are put together
or a total where the parts are separated out (9 apples, 6 are red and the rest are green).
Add to with Result Unknown: A word problem type in which one part is added to another part and the
students need to find the total. The “add to” refers to the part that is added and involves an action, for
example, frogs jumping in the pond to join other frogs.
Tape Diagram: A model used to represent the information found in a problem, in this case a word problem. It
is used as a tool for problem solving, which helps students organize the information from the problem and
leads students to the solution.
Example
Read the word problem.
Draw a tape diagram and label.
Write a number sentence and a statement that matches the story.
READ
John has 5 red racecars and 12 blue racecars. How many racecars does John have in all?
I know the first word is a name but I don’t know the name. My friend’s name is Joe and also
starts with a J so I can use Joe’s name for the story. If I’m stuck on another word I can ask for
some help from a grown up.
Lesson 19:
© 2015 Great Minds. All rights reserved. greatminds.net
Use tape diagrams as representations to solve put together/take apart
with total unknown and add to with result unknown word problems.
1
Lesson 19 Homework Guide
A Story of Units
1•4
DRAW
I can draw 5 circles for the
red racecars. I put my
circles in a rectangle to
keep them organized. I
labeled my drawing with
the number 5 and the
letter R so I know that this
rectangle represents the 5
red racecars.
R
T
I connected the two rectangles and drew a
box with a question mark labeled with the
letter T because it is the total. When I find the
total I will know the answer to the question.
?
5
12
B
I can draw 12 circles for the blue cars. I organized my circles and
put them in a rectangle labeled with the number 12 and the letter
B so I know that this rectangle represents the 12 blue racecars.
WRITE
Number Sentence
5 + 12 =
17
I drew a box around
17 because it is the
total and answers
the question.
Statement
John has 17 racecars.
Lesson 19:
© 2015 Great Minds. All rights reserved. greatminds.net
Use tape diagrams as representations to solve put together/take apart
with total unknown and add to with result unknown word problems.
2
Lesson 20 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 20: Recognize and make use of part-whole
relationships within tape diagrams when solving a variety of
problem types.
Example 1
Solve using the RDW process.
READ
Mary has 14 play practices this month. 7 practices are afterschool, the rest are in the evening. How many
practices are in the evening?
What do I know after reading
the problem?
What can I draw?
DRAW
I know the total or
the whole. I can draw
14 circles in 5-group
rows to represent the
total number of
practices.
T
14
7
A
I know there are 7 practices afterschool. I can draw a
rectangle around 7 of the circles to represent the 7
practices that are afterschool. I label the rectangle
with the letter A for afterschool.
Lesson 20:
© 2015 Great Minds. All rights reserved. greatminds.net
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
1
Lesson 20 Homework Guide
A Story of Units
1•4
T
14
7
A
7
E
I drew a rectangle around the rest of the circles. This represents the
practices that are in the evening. I count the circles and see there
are 7 practices in the evening. I label with the letter E for evening.
What does my
drawing tell me?
Number sentence
14 – 7 =
WRITE
I drew a rectangle
around the 7 because
7 is the answer to the
question.
7
Statement
Mary has 7 practices in the evening.
Lesson 20:
© 2015 Great Minds. All rights reserved. greatminds.net
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
2
Lesson 20 Homework Guide
A Story of Units
1•4
Example 2
READ
Katelyn gave some of her stickers to her friend. She had 18 stickers at first, and she still has 12 stickers left.
How many stickers did Katelyn give to her friend?
What can I draw?
What do I know after reading
the problem?
DRAW
I can draw a rectangle to
represent the stickers
Katelyn gave to her friend
and label with the letter G.
I put a ? in the rectangle
because I don’t know how
many stickers Katelyn gave
to her friend.
?
G
T
I can draw two lines
connecting the rectangles and
label the total to represent the
18 stickers.
18
12
L
I can draw a rectangle with 12 circles
labeled with the letter L to represent the 12
stickers Katelyn has left.
Lesson 20:
© 2015 Great Minds. All rights reserved. greatminds.net
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
3
Lesson 20 Homework Guide
A Story of Units
1•4
T
18
G
6
12
L
I can draw more circles and count on from 12 to 18 to
find the number of stickers Katelyn gave to her friend.
WRITE
Number sentence
6
+ 12 = 18
I drew a rectangle
around the 6 because 6
answers how many
stickers Katelyn gave to
her friend.
Statement
Katelyn gave 6 stickers to her friend.
Note
The examples above provide possible tape diagrams that students could draw to model these problems.
Students may interpret the information differently and draw the diagram in a different order. For example,
students might draw the total first to solve Example 2.
Lesson 20:
© 2015 Great Minds. All rights reserved. greatminds.net
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
4
Lesson 21 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 21: Recognize and make use of part-whole
relationships within tape diagrams when solving a variety of
problem types.
Example
Solve using the RDW process.
READ
Emi made a bracelet that was 13 centimeters long. The bracelet didn’t fit so she made the bracelet longer.
Now the bracelet is 17 centimeters long. How many centimeters did Emi add to the bracelet?
What do I know after reading the problem?
What can I draw?
DRAW
?
F
A
I can draw 13 circles to represent
the length of Emi’s bracelet at first. I
labeled with the letter F for first.
Lesson 21:
© 2015 Great Minds. All rights reserved. greatminds.net
I added a rectangle for the centimeters that
Emi added to the bracelet. I drew a ? in the
rectangle because I don’t know how many
centimeters Emi added to her bracelet. I
labeled the rectangle with an A because it
represents the amount added.
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
1
Lesson 21 Homework Guide
A Story of Units
1•4
T
17
4
13
A
F
I can draw more circles for the length Emi added to
her bracelet until the total is 17. I added 4 circles to
represent the added length. I labeled with the letter
A because it represents the length Emi added.
WRITE
Number Sentence
I drew a rectangle around
the 4 because 4 answers
the question: How many
centimeters did Emi add
to the bracelet?
13 + 4 = 17
Statement
Emi added 4 centimeters to the bracelet.
Note
This example shows one way this problem can be represented in a tape diagram. Students may interpret the
information differently and draw the diagram in a different order, yet still get the same solution.
Lesson 21:
© 2015 Great Minds. All rights reserved. greatminds.net
Recognize and make use of part-whole relationships within tape
diagrams when solving a variety of problem types.
2
Lesson 22 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 22: Write word problems of varied types.
Note
Students have been working on solving word problems on the previous lessons in this topic. This task
introduces a new level of complexity as students develop their own word problems. The example is the most
difficult problem type students will encounter in first grade because the start is unknown.
Use the tape diagrams to write a variety of word problems. Use the word bank if needed. Remember to label
your model after you write the story.
I can use the words in the box to help me think of what to
write or I can think of my own idea.
Topics (Nouns)
Actions (Verbs)
flowers
goldfish
lizards
hide
eat
stickers
rockets
cars
give
draw
get
frogs
crackers
marbles
collect
build
play
Lesson 22:
© 2015 Great Minds. All rights reserved. greatminds.net
Write word problems of varied types.
go away
1
Lesson 22 Homework Guide
A Story of Units
What does this drawing
tell me?
15
1•4
T
?
The total is 15.
11
M
A
I have some.
I add 11 more.
Beth picks some flowers for her mom in the morning. She picks 11 flowers in the afternoon. Now she
has 15 flowers for her mom. How many flowers did Beth pick in the morning?
Lesson 22:
© 2015 Great Minds. All rights reserved. greatminds.net
Write word problems of varied types.
2
Lesson 23 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 23: Interpret two-digit numbers as tens and ones,
including cases with more than 9 ones.
Note
In this topic students will determine the number of tens and ones in a two-digit number. A two-digit number
can have a variety of combinations of tens and ones (e.g., 34 = 34 ones = 3 tens 4 ones = 2 tens 14 ones = 1
ten 24 ones). Seeing numbers in this way prepares students for addition with regrouping (e.g., 12 + 8 = 1 ten
10 ones = 2 tens or 18 + 16 = 2 tens 14 ones = 3 tens 4 ones). The children will use the terms
bundle/unbundle because they are building the numbers with a partner using their fingers.
Bundling refers to making a new unit, in this case a ten.
Unbundling refers to taking a larger unit (ten) apart into smaller units (ones).
1 ten
10 ones
Example
Fill in the blanks and match the pairs that show the same amount.
I matched these pictures. They both show 32. 3 tens 2 ones is equal to 2 tens
12 ones. If I bundled 10 ones in the bottom picture it would have 3 tens 2
ones.
3 tens ____
2
____
Lesson 23:
© 2015 Great Minds. All rights reserved. greatminds.net
2 tens 12
____
____ ones
Interpret two-digit numbers as tens and ones, including cases with more
than 9 ones.
1
Lesson 23 Homework Guide
A Story of Units
1•4
Match the place value charts that show the same amount.
The place value chart shows how
many tens and ones. I can have 2
tens and 15 ones. It’s O.K. to have
more than 9 in the ones. 2 tens 15
ones is 35.
3
0
5
3
37
2
7
15
3 tens 7 ones is the same as 37 ones. I can
unbundle the 3 tens, that makes 30 ones.
Add the 7 ones, and now I have 37 ones.
Example
Emi says 29 is the same as 1 ten 19 ones, and Ben says 29 is the same as 2 tens 19 ones. Draw quick tens to
show if Emi or Ben is correct.
Emi
Ben
One straight line is a quick
ten.
Lesson 23:
© 2015 Great Minds. All rights reserved. greatminds.net
I drew 1 quick ten and 19 ones for Emi’s
drawing. I drew 2 quick tens and 19 ones for
Ben’s drawing. Emi is correct because 1 ten
19 ones is the same as 29. Ben is not correct
because 2 tens 19 ones is the same as 39.
Interpret two-digit numbers as tens and ones, including cases with more
than 9 ones.
2
Lesson 24 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 24: Add a pair of two-digit numbers when the
ones digits have a sum less than or equal to 10.
Add 10 First Strategy
Students are taught several strategies to solve an addition problem with a pair of two-digit numbers in this
topic. The first strategy introduced is Add 10 first.
Add Ten First: Break apart one of the addends with a number bond. Add the ten/tens to the other number
then add the remaining ones.
Examples
Solve using number bonds. Write the two number sentences that show that you added 10 first. Draw quick
tens and ones if that helps you.
a.
28
15 + 13 = ____
10
3
15 + 10 = 25
25 + 3 = 28
I drew 15 using quick tens and ones.
Then I broke apart 13 into 10 and 3. I
added 15 and 10, which equals 25.
Then I added the 3 ones to 25. I used x’s
to show adding the 3 ones. My answer
is 28.
Lesson 24:
© 2015 Great Minds. All rights reserved. greatminds.net
b.
39
16 + 23 = ____
10
6
33
23 + 10 = _____
33
39
_____
+ 6 = _____
I want to add 10 first, so I
broke apart 16 into 10 and
6 using a number bond. I
added 10 to 23 to get 33.
Then I added 33 and 6 to
get my answer of 39.
Add a pair of two-digit numbers when the ones digits have a sum less
than or equal to 10.
1
Lesson 24 Homework Guide
A Story of Units
1•4
Solve using number bonds.
40
17 + 23 = ____
10
7
23 + 10 = 33
40
22 + 18 = ____
10
8
33 + 7 = 40
I broke apart 17 into 10 and 7 using a
number bond. I added 10 and 23,
which equals 33. Then I added 33 and
7 to get my answer of 40.
I broke apart 18 into 10 and 8 using a number
bond. I added 22 and 10 in my head to get 32.
Then I added 32 and 8 to get the answer 40. I
didn’t write the two number sentences
because I was able to add in my head.
Note
The examples on the first page show quick ten and ones drawings, a pictorial representation of each number.
Some students may need to use these pictorial representations, while others may need concrete models,
such as linking cubes. Students who are fluent with adding ten to a two-digit number may do some of the
work mentally, as shown in the last example.
Lesson 24:
© 2015 Great Minds. All rights reserved. greatminds.net
Add a pair of two-digit numbers when the ones digits have a sum less
than or equal to 10.
2
Lesson 25 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 25: Add a pair of two-digit numbers when the ones
digits have a sum of less than or equal to 10.
Strategies
Students may use a variety of strategies and models to add a pair of two-digit numbers, the homework
examples show the following strategies:
Add Ten First: Break apart one of the addends with a number bond. Add the ten/tens to the other number
then add the remaining ones.
Add the Ones First: Break apart one of the addends and add the ones to the other number, then add the
tens. Students may look for a way to make a ten.
Examples
Solve using number bonds. This time, add the tens first. Write the 2 number sentences to show what you
did.
12 + 16 =
10
28
23 + 17 =
10
2
40
7
16 + 10 = 26
23 + 10 = 33
26 + 2 = 28
I broke apart 12 into 10 and 2 using
a number bond. I added 16 and 10
and got 26. Then I added 26 and 2.
My answer is 28.
Lesson 25:
© 2015 Great Minds. All rights reserved. greatminds.net
33 + 7 = 40
I broke apart 17 into 10 and 7. I
added 10 to 23 and got 33. Then I
added 33 and 7. My answer is 40.
Add a pair of two-digit numbers when the ones digits have a sum of less
than or equal to 10.
1
Lesson 25 Homework Guide
A Story of Units
1•4
Solve using number bonds. This time, add the ones first. Write the 2 number sentences to show what you
did.
23 + 16 =
6
39
10
10
© 2015 Great Minds. All rights reserved. greatminds.net
40
1
23 + 6 = 29
29 + 1 = 30
29 + 10 = 39
30 + 10 = 40
I broke apart 16 into 6 and 10. I added
6 to 23 and got 29. Then I added 10 to
29. My answer is 39.
Lesson 25:
11 + 29 =
I broke apart 11 into 10 and 1. I
added 1 to 29 and got 30. This is the
next 10. I added 30 and 10. My
answer is 40.
Add a pair of two-digit numbers when the ones digits have a sum of less
than or equal to 10.
2
Lesson 26 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 26: Add a pair of two-digit numbers when the
ones digits have a sum greater than 10.
Strategies
Students may use a variety of strategies and models to add a pair of two-digit numbers, the homework
examples show the following strategies:
Add Ten First: Break apart one of the addends with a number bond. Add the ten/tens to the other number
then add the remaining ones.
Make a Ten: Break apart one addend in order to make the next ten with the other addend. Then the
multiple of ten (10,20, 30…etc. ) is added to the remaining number. This strategy adds a level of complexity
because students need to know how to make the next ten, as well as how to correctly break apart the other
number.
Examples
Solve using a number bond to add ten first. Write the 2 addition sentences that helped you.
I need to use the add ten first strategy. I will break
apart one of the numbers into 10 and some ones.
39
25 + 14 = ____
10
4
10
35
25 + 10 = _____
35
4
39
____
+ ____
= _____
14 was broken apart into 10 and 4. I added
10 to 25 and got 35. Then I added 35 and 4.
My answer is 39.
Lesson 26:
© 2015 Great Minds. All rights reserved. greatminds.net
34
19 + 15 = _____
5
29
19 + 10 = _____
29
5 = _____
34
____
+ ___
15 was broken apart into 10 and 5. I
added 10 to 19 and got 29. Then I added
29 and 5. My answer is 34.
Add a pair of two-digit numbers when the ones digits have a sum greater
than 10.
1
Lesson 26 Homework Guide
A Story of Units
1•4
Solve using a number bond to make a ten first. Write the 2 number sentences that helped you.
I need to use the make a ten
strategy. I will break apart one of the
addends, to make the next ten with
the other addend. Then I will add the
ten/tens to the remaining part .
16 + 19 = ____
37
15
1
18 + 14 = ____
32
2
12
19
20
____
+ 1 = ____
18 + ____
2
20
____
= ____
20
37
____
+ 17 = ____
20 + ____
12
32
____
= ____
16 was broken apart into 15 and 1
because 19 needs 1 more to make the
next ten. I added the 1 to 19 and got 20. I
added 20 and 17. My answer is 37. It is
easy to add with tens.
Lesson 26:
© 2015 Great Minds. All rights reserved. greatminds.net
14 is broken apart into 2 and 12
because 18 needs 2 more to make the
next ten, 20. Then I added 20 and 12
to get my answer of 32.
Add a pair of two-digit numbers when the ones digits have a sum greater
than 10.
2
Lesson 27 Homework Guide
A Story of Units
1•4
G1-M4-Lesson 27: Add a pair of two-digit numbers when the
ones digits have a sum greater than 10.
Strategies for adding a pair of two-digit numbers.
Students may use a variety of strategies and models to add a pair of two-digit numbers, the homework
examples show the following strategies:
Draw Quick Tens and Ones: Quick tens are a straight line that represents 1 ten. Ones can be drawn as circles
or x’s.
Add Ten First: Break apart one of the addends with a number bond. Add the ten/tens to the other number
then add the remaining ones.
Add the Ones First: Break apart one of the addends and add the ones to the other number, then add the
tens. Students may look for a way to make a ten.
Make a Ten: Break apart one addend in order to make the next ten with the other addend. Then the multiple
of ten (10, 20,30,….etc.) is added to the remaining number.
Example: Using Quick Tens and Ones
Solve using number bonds with pairs of number sentences. You may draw quick tens and some ones to help
you.
32
15 + 17 = ____
10
I solved using quick tens and ones to
help me. First I drew 17 with quick tens
and ones. Then I broke apart 15 into 10
and 5. I added the 10 to the 17.
5
17 + 10 = 27
Then I added 5 x’s, I added 3 of the x’s to the 7, that
made a 10. Then I needed 2 more x’s to finish
drawing 5. This gave me the answer of 32.
27 + 5 = 32
Lesson 27:
© 2015 Great Minds. All rights reserved. greatminds.net
Add a pair of two-digit numbers when the ones digits have a sum greater
than 10.
1
Lesson 27 Homework Guide
A Story of Units
1•4
Example Using Add Tens First
32
18 + 14 = ____
I solved using the add ten first
strategy. I broke apart 14 into 10
and 4. I added 10 to 18, and got
28. Then I added 28 and 4. My
answer is 32.
18 + 10 = 28
28 + 4 = 32
Example Using Add the Ones First
31
19 + 12 = ____
19 + 2 = 21
21 + 10 = 31
I solved by adding the ones first,
because 2 more than 19 is 21.
Then I could quickly add the 10 to
get the answer, 31.
Example Using Make Ten
37
19 + 18 = ____
19 + 1 = 20
20 + 17 = 31
I solved using the make ten
strategy. I know that 19 needs
one more to make 20. I can easily
break apart 18 into 1 and 17. Then
I can add 20 and 17 to get 37.
Note
Students are progressing at different levels and may need materials, such as linking cubes or the pictorial
representation shown in the first example to help them. Other students will be able to solve using mental
math. Students may use a variety of strategies to solve problems. Each of the example problems can be
solved using any of the strategies the students have learned. Students may use the strategy they feel most
comfortable, based on their level of fluency with making tens and adding multiples of ten.
Lesson 27:
© 2015 Great Minds. All rights reserved. greatminds.net
Add a pair of two-digit numbers when the ones digits have a sum greater
than 10.
2
Lessons 28 and 29 Homework Guide 1•4
A Story of Units
G1-M4-Lessons 28 and 29: Add a pair of two-digit numbers with
varied sums in the ones.
Note
Lessons 28 and 29 are the last lessons in this Topic and are a time for students to consolidate their learning.
Encourage your child to use a variety of strategies when they add a pair of two digit numbers. Your child can
use any of the strategies but should be able to explain why they chose that strategy. Challenge them to solve
a problem using another strategy, if they tend to use only one of the strategies listed below.
Strategies
Draw Quick Tens and Ones: Quick tens are a straight line that represents 1 ten. Ones can be drawn as circles
or x’s.
Add Ten First: Break apart one of the addends with a number bond. Add the ten/tens to the other number
then add the remaining ones.
Add the Ones First: Break apart one of the addends and add the ones to the other number, then add the
tens. Students may look for a way to make a ten.
Make a Ten: Break apart one addend in order to make the next ten with the other addend. Then the
multiple of ten is added to the remaining number
The Arrow Way: A way to notate either adding tens first or adding ones first. The example below shows how
to solve 19 + 13 using the arrow way.
+10
+3
19  29 32
Lesson 28 &29:
© 2015 Great Minds. All rights reserved. greatminds.net
Add a pair of two-digit numbers with varied sums in the ones.
1
Lessons 28 and 29 Homework Guide 1•4
A Story of Units
Examples for Using the Arrow Way
Solve using quick tens and ones, number bonds, or the arrow way.
39
26 + 13 = ____
40
24 + 16 = ____
+10
+3
26  36  39
+10 +6
24  34  40
I solved using the arrow way because I
know 13 is 10 and 3. I can add the 10 first
to get 36 then add 3. My answer is 39.
I solved using the arrow way because I
know 16 is 10 and 6. I can add the 10 first
to get 34. I know that 34 and 6 is 40.
Examples for Using Number Bonds
Solve using quick tens and ones, number bonds, or the arrow way.
36
18 + 18 = ____
2
29
17 + 12 = ____
10
16
2
18 + 2 = 20
20 + 16 = 36
I solved using number bonds. I made
a ten. I know 18 needs 2 more to
make 20. So I broke apart the other
18 into 2 and 16. I added 20 and 16
to get my answer of 36.
Lesson 28 &29:
© 2015 Great Minds. All rights reserved. greatminds.net
I solved using number bonds. I added
17 and 2 and got 19. Then I added 19
and 10 to get my answer of 29. I
didn’t need to write the number
sentences because I can do the math
in my head.
Add a pair of two-digit numbers with varied sums in the ones.
2