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Elementary Math Continuity of Learning Print Materials
Thank you for helping support your child’s continuity of learning. This packet
contains the print resources that support the grade level instructional lessons.
Each complete math lesson contains:
● Direct instruction through video by a Eureka Math teacher available
through myMCPS classroom or MCPS iTV
● Math guided practice using the included Problem Set during viewing
● Online discussion board question for teachers to gauge students’ initial
learning
● Live student/teacher debrief for clarifying learning and deepening
understanding
● Individual exit ticket for students to submit to teachers for assessing
continuing learning
The following is included in this packet:
● Problem set
● Template (only if referenced in the direct instruction video)
● Exit ticket
Your continued partnership is appreciated!
The Elementary Math and Science Team
Materiales Impresos de Matemáticas para la Continuidad de Aprendizaje en las
Escuelas Elementales
Gracias por ayudarnos a apoyar la continuidad de aprendizaje de su hijo. Este
paquete contiene recursos impresos que apoyan las lecciones educativas del nivel
de grado.
Cada lección completa de matemáticas contiene:
● Instrucción directa a través de video, impartida por un maestro de Eureka
Math y disponible a través de myMCPS classroom o MCPS iTV
● Práctica guiada de matemáticas durante el video, usando el Conjunto de
Problemas (Problem Set) incluido
● Tablero de discusión en línea para que los maestros calculen el aprendizaje
inicial de los estudiantes
● Revisión de la lección en vivo entre el estudiante y el maestro para clarificar
el aprendizaje y profundizar en el entendimiento
● Boleto de salida individual que los estudiantes deberán enviar a los
maestros para evaluar el aprendizaje continuo
En este paquete se incluye lo siguiente:
● Conjunto de problemas
● Formato (sólo si se hace referencia a eso en el video de instrucción directa)
● Boleto de salida
¡Se agradece su continua colaboración!
El Equipo de Matemáticas y Ciencias de las Escuelas Elementales
Lesson 3 Problem Set 4 5
Name Date
1. Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence. The first one has been done for you.
a.
34
= 14
+ 14
+ 14
34
= 3 × 14
b.
c.
d.
e.
1
1
1
1
1
Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.
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Lesson 3 Problem Set 4 5
2. Write the following fractions greater than 1 as the sum of two products. a.
b.
3. Draw a tape diagram, and record the given fraction’s decomposition into unit fractions as a multiplication sentence. a. 4
5
b. 58
c. 7
d. 74
e. 76
1
1
Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.
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©2017 Great Minds. eureka-math.org
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Lesson 3 Exit Ticket 4 5
Name Date
1. Decompose each fraction modeled by a tape diagram as a sum of unit fractions. Write the equivalent multiplication sentence. a.
b.
2. Draw a tape diagram, and record the given fraction’s decomposition into unit fractions as a multiplication sentence.
69
1
1
Lesson 3: Decompose non-unit fractions and represent them as a whole number times a unit fraction using tape diagrams.
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Lección 3:
Nombre Fecha
1. Descompón cada fracción representada por un diagrama de cinta como una suma de fracciones unitarias. Escribe el enunciado de multiplicación equivalente.a.
b.
2. Dibuja un diagrama de cinta y registra la descomposición de la fracción proporcionada en fracciones unitarias como un enunciado de multiplicación.
6
9
Descomponer fracciones no unitarias y representarlas como la multiplicación de un número entero por una fracción unitaria usando diagramas de cintas.
Lesson 4 Problem Set 4 5
Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.
Name Date
1. The total length of each tape diagram represents 1. Decompose the shaded unit fractions as the sum of smaller unit fractions in at least two different ways. The first one has been done for you.
a.
b.
c.
d.
12 = 14 + 14
12
12 = 18 + 18 + 18 + 18
12
13 1
3
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Lesson 4 Problem Set 4 5
Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.
2. The total length of each tape diagram represents 1. Decompose the shaded fractions as the sum of smaller unit fractions in at least two different ways.
a.
b.
3. Draw and label tape diagrams to prove the following statements. The first one has been done for you.
a. 25 = 4
10
b. 26 = 4
12
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Lesson 4 Problem Set 4 5
Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.
c. 34 = 6
8
d. 34 = 12
4. Show that 12 is equivalent to 48 using a tape diagram and a number sentence.
5. Show that 23 is equivalent to 6 using a tape diagram and a number sentence.
6. Show that 46 is equivalent to 812 using a tape diagram and a number sentence.
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Lesson 4 Exit Ticket 4 5
Lesson 4: Decompose fractions into sums of smaller unit fractions using tape diagrams.
Name Date
1. The total length of the tape diagram represents 1. Decompose the shaded unit fraction as the sum of smaller unit fractions in at least two different ways.
2. Draw a tape diagram to prove the following statement.
23 = 4
6
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Lección 4:
Nombre Fecha
1. La longitud total del diagrama de cintas representa 1. Descompón la fracción unitaria sombreada como la suma de fracciones unitarias menores en al menos dos maneras diferentes.
2. Dibuja un diagrama de cintas para demostrar la siguiente afirmación.
2
3
4
6 =
Descomponer fracciones en sumas de fracciones unitarias menores usando diagramas de cinta.
Lesson 5 Problem Set 4 5
Lesson 5: Decompose unit fractions using area models to show equivalence.
Name Date
1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
a. 2 rows
b. 2 rows
c. 4 rows
14
= 2
14
= 18
+ =
14
= 2 × =
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Lesson 5 Problem Set 4 5
Lesson 5: Decompose unit fractions using area models to show equivalence.
2. Draw area models to show the decompositions represented by the number sentences below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence. a. 1
2 = 3
6 b. 1
2 = 4
8
c. 12
= 510
d. 13
= 26
e. 13
= 412
f. 14
= 312
3. Explain why 112
+ 112
+ 112
is the same as 14.
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©2017 Great Minds. eureka-math.org
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Lesson 5 Exit Ticket 4 5
Lesson 5: Decompose unit fractions using area models to show equivalence.
Name Date
1. Draw horizontal lines to decompose each rectangle into the number of rows as indicated. Use the model to give the shaded area as both a sum of unit fractions and as a multiplication sentence.
a. 2 rows
b. 3 rows
2. Draw an area model to show the decomposition represented by the number sentence below. Represent the decomposition as a sum of unit fractions and as a multiplication sentence.
35
= 610
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Lección 5:
Nombre Fecha
1. Dibuja líneas horizontales para descomponer cada rectángulo en la cantidad de filas que se indica. Usa la representación para mostrar el área sombreada como la suma de fracciones unitarias y como un enunciado de multiplicación.
a. 2 filas
b. 3 filas
2. Dibuja un modelo de área para mostrar la descomposición representada en el siguiente enunciado numérico. Representa la descomposición como una suma de fracciones unitarias y como un enunciado multiplicación.
3
5
6
10 =
Descomponer fracciones unitarias usando modelos de área para mostrar equivalencia.
4 5 Lesson 6 Problem Set
Name Date
1. Each rectangle represents 1. Draw horizontal lines to decompose each rectangle into the fractional units as indicated. Use the model to give the shaded area as a sum and as a product of unit fractions. Use parentheses to show the relationship between the number sentences. The first one has been partially done for you. a. Sixths
b. Tenths
23
6
23 = 4
3 +
3 = 16 + 1
6 + 16 + 1
6 = 4
16 + 1
6 + 16 + 1
6 = �2 × � + �2 ×
� = 4
23 = 4 ×
= 4
Lesson 6: Decompose fractions using area models to show equivalence.
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4 5 Lesson 6 Problem Set
c. Twelfths
2. Draw area models to show the decompositions represented by the number sentences below. Express each as a sum and product of unit fractions. Use parentheses to show the relationship between the number sentences. a. 3
5 = 610
b. 34 = 6
8
Lesson 6: Decompose fractions using area models to show equivalence.
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4 5 Lesson 6 Problem Set
3. Step 1: Draw an area model for a fraction with units of thirds, fourths, or fifths.
Step 2: Shade in more than one fractional unit.
Step 3: Partition the area model again to find an equivalent fraction.
Step 4: Write the equivalent fractions as a number sentence. (If you’ve written a number sentence like this one already on this Problem Set, start over.)
Lesson 6: Decompose fractions using area models to show equivalence.
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4 5 Lesson 6 Exit Ticket
Name Date
1. The rectangle below represents 1. Draw horizontal lines to decompose the rectangle into eighths. Use the model to give the shaded area as a sum and as a product of unit fractions. Use parentheses to show the relationship between the number sentences.
2. Draw an area model to show the decomposition represented by the number sentence below.
45 =
810
Lesson 6: Decompose fractions using area models to show equivalence.
A STORY OF UNITSA STORY OF UNITS
6
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38 Lección 6:
Lección 6 Grupo de problemasUNA HISTORIA DE UNIDADES 4•5
c. Doceavos
2. Dibuja modelos de área para mostrar la descomposición representada por los siguientes enunciados numéricos. Expresa cada uno como la suma y el producto de fracciones unitarias. Usa paréntesis para mostrar la relación entre los enunciados numéricos.
a. 3
5
6
10 =
b. 34
68
=
Descomponer fracciones usando modelos de área para mostrar la equivalencia.
Name Date
Each rectangle represents 1.
1. The shaded unit fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you.
a. b.
c. d.
12
= 1 × 22 × 2
= 24
Lesson 7: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 7 Problem Set A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
30
©2015 Great Minds. eureka-math.org
2. Decompose the shaded fractions into smaller units using the area models. Express the equivalent fractions in a number sentence using multiplication.
a. b.
c. d.
e. What happened to the size of the fractional units when you decomposed the fraction?
f. What happened to the total number of units in the whole when you decomposed the fraction?
Lesson 7: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 7 Problem Set A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
31
©2015 Great Minds. eureka-math.org
3. Draw three different area models to represent 1 third by shading. Decompose the shaded fraction into (a) sixths, (b) ninths, and (c) twelfths. Use multiplication to show how each fraction is equivalent to 1 third.
a.
b.
c.
Lesson 7: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 7 Problem Set A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
32
©2015 Great Minds. eureka-math.org
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102
Name Date
Draw two different area models to represent 1 fourth by shading. Decompose the shaded fraction into (a) eighths and (b) twelfths. Use multiplication to show how each fraction is equivalent to 1 fourth.
a.
b.
Lesson 7: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 7 Exit Ticket A STORY OF UNITSA STORY OF UNITS
7
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Lección 7 Boleto de salidaUNA HISTORIA DE UNIDADES 4•5
49
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Lección 7:
Nombre Fecha
Dibuja dos modelos de área diferentes para representar 1 cuarto con sombreado.Descompón la fracción sombreada en (a) octavos y (b) doceavos.Usa la multiplicación para mostrar cómo cada fracción es equivalente a 1 cuarto.
a.
b.
Usar el modelo de área y la multiplicación para demostrar la equivalencia entre dos fracciones.
Name Date
Each rectangle represents 1.
1. The shaded fractions have been decomposed into smaller units. Express the equivalent fractions in a number sentence using multiplication. The first one has been done for you.
a. b.
c. d.
2. Decompose the shaded fractions into smaller units, as given below. Express the equivalent fractions in a number sentence using multiplication.
a. Decompose into tenths. b. Decompose into fifteenths.
23
= 2 × 23 × 2 =
46
Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 8 Problem Set A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
35
©2015 Great Minds. eureka-math.org
3. Draw area models to prove that the following number sentences are true.
a. 25
= 410
b. 23
= 812
c. 36
= 612
d. 46
= 812
4. Use multiplication to find an equivalent fraction for each fraction below.
a. 34
c. 76
b. 45
d. 127
5. Determine which of the following are true number sentences. Correct those that are false by changing the right-hand side of the number sentence.
a. 43
= 89
c. 45
= 1210
b. 54
= 108
d. 46
= 1218
Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 8 Problem Set A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
36
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©2017 Great Minds. eureka-math.org
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113
Name Date
1. Use multiplication to create an equivalent fraction for the fraction below.
25
2. Determine if the following is a true number sentence. If needed, correct the statement by changing the right-hand side of the number sentence.
34
= 98
Lesson 8: Use the area model and multiplication to show the equivalence of two fractions.
4 5 Lesson 8 Exit Ticket A STORY OF UNITSA STORY OF UNITS
8
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114
4 5 Lesson 9 Problem Set
Lesson 9: Use the area model and division to show the equivalence of two fractions.
Name Date
Each rectangle represents 1.
1. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division. The first one has been done for you.
a. b.
c. d.
24
= 2 ÷ 24 ÷ 2 =
12
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
39
©2015 Great Minds. eureka-math.org
4 5 Lesson 9 Problem Set
Lesson 9: Use the area model and division to show the equivalence of two fractions.
2. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division.
a. b.
c. d.
e. What happened to the size of the fractional units when you composed the fraction?
f. What happened to the total number of units in the whole when you composed the fraction?
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
40
©2015 Great Minds. eureka-math.org
4 5 Lesson 9 Problem Set
Lesson 9: Use the area model and division to show the equivalence of two fractions.
3. a. In the first area model, show 2 sixths. In the second area model, show 3 ninths. Show how both fractions can be renamed as the same unit fraction.
b. Express the equivalent fractions in a number sentence using division.
4. a. In the first area model, show 2 eighths. In the second area model, show 3 twelfths. Show how both fractions can be composed, or renamed, as the same unit fraction.
b. Express the equivalent fractions in a number sentence using division.
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
41
©2015 Great Minds. eureka-math.org
©2017 Great Minds. eureka-math.org
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4 5 Lesson 9 Exit Ticket
Lesson 9: Use the area model and division to show the equivalence of two fractions.
Name Date
a. In the first area model, show 2 sixths. In the second area model, show 4 twelfths. Show how both fractions can be composed, or renamed, as the same unit fraction.
b. Express the equivalent fractions in a number sentence using division.
A STORY OF UNITSA STORY OF UNITS
9
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©2017 Great Minds. eureka-math.org
126
4 5 Lesson 10 Problem Set
Name Date
Each rectangle represents 1.
1. Compose the shaded fraction into larger fractional units. Express the equivalent fractions in a number sentence using division. The first one has been done for you.
a. b.
c. d.
46
= 4 ÷ 26 ÷ 2 =
23
Lesson 10: Use the area model and division to show the equivalence of two fractions.
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
45
©2015 Great Minds. eureka-math.org
4 5 Lesson 10 Problem Set
2. Compose the shaded fractions into larger fractional units. Express the equivalent fractions in a number sentence using division.
a. b.
3. Draw an area model to represent each number sentence below.
a. 410
= 4 ÷ 210 ÷ 2 = 2
5 b. 6
9 = 6 ÷ 3
9 ÷ 3 = 23
Lesson 10: Use the area model and division to show the equivalence of two fractions.
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
46
©2015 Great Minds. eureka-math.org
4 5 Lesson 10 Problem Set
4. Use division to rename each fraction given below. Draw a model if that helps you. See if you can use the largest common factor.
a. 48
b. 1216
c. 1220
d. 1620
Lesson 10: Use the area model and division to show the equivalence of two fractions.
A STORY OF UNITSA STORY OF UNITS
G4-M 5-SE-1.3 .0 -06.2015
47
©2015 Great Minds. eureka-math.org
©2017 Great Minds. eureka-math.org
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4 5 Lesson 10 Exit Ticket
Name Date
Draw an area model to show why the fractions are equivalent. Show the equivalence in a number sentence using division.
410
= 25
Lesson 10: Use the area model and division to show the equivalence of two fractions.
A STORY OF UNITSA STORY OF UNITS
10
G4-M 5-ETP-1.3 .0 -06.2015©2015 Great Minds. eureka-math.org
©2017 Great Minds. eureka-math.org
140