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Dear Family,
Family Letter
Content
Overview
In Unit 6 of Math Expressions, your child will apply the skills they
have learned about operations with fractions, whole numbers,
and decimals as they solve real world problems involving addition,
subtraction, multiplication, and division.
A situation equation shows the structure of the information in
a problem. A solution equation shows the operation that can
be used to solve a problem. Your child will review situation
and solution equations for addition and subtraction, and for
multiplication and division. These methods of representing
problems are particularly helpful when problems involve larger
numbers that students cannot add, subtract, multiply, or divide
mentally.
Your child will also solve multiplication and addition comparison
problems and compare those types of problems, identifying how
they are the same and how they are different.
Addition Comparison Problem
Multiplication Comparison
Problem
Terrell has 144 soccer trading
cards. Manuel has 3 more cards
than Terrell. How many cards
does Manuel have?
Elena has 74 stamps in her
collection. Hassan has 3 times
as many stamps. How many
stamps does Hassan have?
Students learn that in the addition problem, they are adding 3,
and multiplying by 3 in the multiplication problem.
© Houghton Mifflin Harcourt Publishing Company
Solving multistep problems is an important Grade 5 skill.
Your child begins by solving one-step problems, then moves to
two-step problems, and finally solves multistep problems which
involve more than two steps. Your child will represent and use
visual models and equations to find solutions for these problems.
Sincerely,
Your child’s teacher
This unit addresses the following standards from the Common Core State Standards for Mathematics with
California Additions: 5.OA.1, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.4a, 5.NF.4b, 5.NF.5, 5.NF.5a,
5.NF.5b, 5.NF.6, 5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c, and all Mathematical Practices.
UNIT 6 LESSON 1
Situation and Solution Equations for Addition and Subtraction
91
Estimada familia,
Carta a la familia
Un vistazo
general al
contenido
En la Unidad 6 de Math Expressions, su niño aplicará las destrezas
que ha aprendido acerca de operaciones con fracciones, y
números enteros y decimales, para resolver problemas de la vida
cotidiana que involucren suma, resta, multiplicación y división.
Una ecuación de situación muestra la estructura de la información
en un problema. Una ecuación de solución muestra la operación
que se puede usar para resolver el problema. Su niño repasará
ecuaciones de situación y de solución para suma y resta, y para
multiplicación y división. Estos métodos de representar problemas
son particularmente útiles cuando los problemas involucran
números grandes que los estudiantes no pueden sumar, restar,
multiplicar ni dividir mentalmente.
Su niño también resolverá problemas de comparación con
multiplicación y con suma, y comparará ese tipo de problemas,
identificando sus diferencias y semejanzas.
Problema de comparación con
suma
Problema de comparación con
multiplicación
Terrell tiene 144 tarjetas
coleccionables de fútbol.
Manuel tiene 3 tarjetas más.
¿Cuántas tarjetas tiene Manuel?
Elena tiene 74 estampillas en
su colección. Hassan tiene el
triple de estampillas. ¿Cuántas
estampillas tiene Hassan?
Los estudiantes deben notar que en el problema con suma, suman
3 y en el problema con multiplicación multiplican por 3.
Atentamente,
El maestro su niño
Esta unidad se aplican los siguientes estándares auxiliares, contenidos en los Estándares estatales comunes de
matemáticas con adiciones para California: 5.OA.1, 5.NBT.4, 5.NBT.5, 5.NBT.6, 5.NBT.7, 5.NF.1, 5.NF.2, 5.NF.3, 5.NF.4, 5.NF.4a,
5.NF.4b, 5.NF.5, 5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7, 5.NF.7a, 5.NF.7b, 5.NF.7c, y todos los de prácticas matemáticas.
92
UNIT 6 LESSON 1
Situation and Solution Equations for Addition and Subtraction
© Houghton Mifflin Harcourt Publishing Company
Resolver problemas de varios pasos es una destreza importante
del 5.° grado. Su niño comenzará resolviendo problemas de un
paso, luego de dos y finalmente resolverá problemas de varios
pasos que tengan más de dos pasos. Usará modelos visuales y
ecuaciones para representar y solucionar esos problemas.
Name
UNIT 6
Date
Review/Test
1. The model represents the length of a whale (w) and the length of a
porpoise (p). For numbers 1a–1d, select True or False for the statement.
p
w
1a. The whale is 5 times as long as the porpoise.
True
False
1b. The porpoise is 5 times as long as the whale.
1c. The whale is _1_ as long as the porpoise.
True
False
True
False
1d. The porpoise is _1_ as long as the whale.
True
False
5
5
Write a word problem for the equation.
2. _1_ ⋅ 3 = _3_
2
2
10
3. _5_ ⋅ 2 = ___
© Houghton Mifflin Harcourt Publishing Company
8
8
4. _1_ ÷ 3 = _1_
2
UNIT 6 TEST
6
93
UNIT 6
Name
Date
Review/Test
5. Write a word problem for 5 ÷ _1_ = 40.
8
6. Five students bought supplies. Two students each bought
2 pencils and an eraser. Three students each bought a pen
and 3 pencils.
Supply
Cost
pencil
$0.15
eraser
$0.59
pen
$0.49
Select the equation that can be used to find the total cost (c)
of the supplies. Mark all that apply.
A c = 2 × 0.15 + 0.59 + 0.49 + 3 × 0.15
B c = 2 × (2 × 0.15 + 0.59) + 3 × (0.49 + 3 × 0.15)
C c = 13 × 0.15 + 2 × 0.59 + 3 × 0.49
D c = 2 × (0.15 + 0.59) + 3 × (0.49 + 0.15)
E c = 4 × 0.15 + 2 × 0.59 + 3 × 0.49 + 9 × 0.15
F c = 2 × (2 × 0.15 + 0.59) + 3 × (0.49 + 0.15)
Part A
How many students are in each row? Write an equation and
use it to solve the problem.
Part B
Explain how you know your answer is reasonable.
94
UNIT 6 TEST
© Houghton Mifflin Harcourt Publishing Company
7. Students in the high school marching band are arranged in
17 equal rows. There are 85 students in the marching band.
Name
UNIT 6
Date
Review/Test
8. Penn volunteered a total of 72 hours over the last 12 weeks.
He volunteered the same number of hours each week.
Part A
How many hours did Penn volunteer in one week? Write an
equation and use it to solve the problem.
Part B
Explain how you know your answer is reasonable.
9. Henry has 2_3_ cups of flour. He uses 1_1_ cups of the flour to
4
2
bake muffins. How much flour (f) does Henry have left?
© Houghton Mifflin Harcourt Publishing Company
Part A
Complete the model to represent this problem.
Part B
Write an equation. Then solve.
Without solving the problem, choose the words that make the
sentence true.
10. Fido eats 2 cups of kibble. Fifi eats _6_ of what Fido eats.
5
more than
Fifi eats
less than
Fido.
the same as
UNIT 6 TEST
95
Name
UNIT 6
Date
Review/Test
11. Camille collects stickers. Her sticker book holds 5 stickers in each row.
When a page is full, it holds 65 stickers. How many rows (r) of stickers
are on a full page?
Part A
Complete the model to represent this problem.
r
Part B
Write an equation. Then solve.
12. Julianne and Derek made signs for their school spirit week. Julianne
made a sign that is 3_1_ feet long. Derek made a sign that is _5_ as long
2
6
as Julianne’s sign. How long is the sign Derek made? Complete the
equation.
_______ × _______ =
_______ feet
$
14. Without multiplying the numbers, classify the expression as less than
3.75 or greater than 3.75. Write the letter of the expression in the
appropriate box.
9
3 × ___
A 3__
10
4
96
UNIT 6 TEST
B 1.2 × 3.75
3
C 2 × 3__
Less than 3.75
Greater than 3.75
4
1
3 × __
D 3__
2
4
E 3.75 × 0.75
© Houghton Mifflin Harcourt Publishing Company
13. Emilio made 65 potholders. Each potholder cost him $1.65 to make.
If he sells each potholder for $2.12, how much profit will he make?
Name
UNIT 6
Date
Review/Test
15. Mr. and Mrs. Storey drove 3,200 miles during their vacation.
Mr. Storey (y) drove 3 times as many miles as Mrs. Storey (x).
Part A
Draw a model to represent the problem.
Part B
How many miles did each person drive?
16. At an electronics store, a refrigerator costs 3 times as much as a
DVD player. A dishwasher costs $125 more than a DVD player.
Part A
Use the numbers to complete the sign.
© Houghton Mifflin Harcourt Publishing Company
0
2
4
5
6
7
Item
Price
DVD player
$150
Refrigerator
$
Dishwasher
$
Part B
Mrs. Shin bought 12 refrigerators and 12 dishwashers for her
apartment building. She received a discount of $90 on the entire
purchase. Write an equation using parentheses to find the amount she
owes. Then solve.
UNIT 6 TEST
97
Name
UNIT 6
Date
Review/Test
17. For numbers 17a–17e, choose Yes or No to indicate whether
the comparison is additive.
17a. 250 times as long
Yes
No
17b. 123 more than
Yes
No
17c. $2.56 less than
17d. in _1_ the time
Yes
No
Yes
No
17e. 3.2 fewer seconds
Yes
No
2
18. Jerome scores 12 points in a basketball game. This is twice the
number of points that Jaime scores. How many points did the
rest of the team score? Solve the problem if possible. Identify
extra information or information that is needed to solve the
problem.
1
19. A car is 234 inches long. A model of the car is ___
times the
18
size of the actual car. Without solving the problem, select the
answer that is the most reasonable length of the model of
the car.
13
A ___
inches
18
13 inches
C
216 inches
D
4,212 inches
20. A python (p) is 1.5 feet longer than a boa constrictor (b).
Choose an expression from each column to create an
equation that compares the lengths of the snakes.
b + 1.5
1.5b
b
b – 1.5
98
UNIT 6 TEST
p – 1.5
=
1.5p
p + 1.5
p
© Houghton Mifflin Harcourt Publishing Company
B