GRADE 4 SUPPLEMENT
Set A10 Number & Operations: Multiplying Whole Numbers by
Fractions
Includes
HH Activity 1: Multiplying Fractions on the Geoboard
HH Activity 2: Quick Sketches & Fraction Arrays
HH Activity 3: Fraction Word Problems & Arrays
HH Independent Worksheet 1: Pizza Party Planning
HH Independent Worksheet 2: Brownie Dessert
HH Independent Worksheet 3: Multiplying Fractions with Arrays
HH Independent Worksheet 4: Company’s Coming!
A10.1
A10.9
A10.13
A10.17
A10.19
A10.21
A10.23
Skills & Concepts
HH Add fractions with like denominators
HH Write an equation showing a fraction a ⁄b as the sum of a number of the unit fraction 1 ⁄b
HH Write an equation to show a fraction as the sum of other fractions with the same denominator
HH Demonstrate an understanding that a fraction a ⁄b is a multiple of the unit fraction 1 ⁄b
HH Write an equation showing that a fraction a ⁄b is the product of a × 1 ⁄b
HH Multiply a fraction by a whole number
HH Solve word problems in which fractions are multiplied by a whole number
HH Use a visual area model to multiply a whole number by a fraction
P201309
Bridges in Mathematics Grade 4 Supplement
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
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P201309
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Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Set A10 H Activity 1
ACTIVITY
Multiplying Fractions on the Geoboard
Overview
You’ll need
Students re-examine problems from Bridges Unit 6: Session 3, and consider how the relationship between areas
on a geoboard might be represented using multiplication.
Students then consider additional models on the geoboard
in which fractions are multiplied by a whole number.
HH Fractions on a Geoboard: Multiplying Fractions, pages
A10.5–A10.7 (run a class set.)
Skills & Concepts
HH Paper/pen for use on the display
HH Geoboards and geobands or Geoboard App (online
or iPad) for display
HH Geoboards and geobands for students, optional
HH Write an equation showing a fraction ⁄b as the sum of
a number of the unit fraction 1 ⁄b (CCSS 4.NF.3)
HH Colored pencils, optional
HH Express a fraction as the sum of other fractions with the
same denominator in more than one way (CCSS 4.NF.3b)
Note When you represent the symbolic form for a fraction,
please use a horizontal bar.
a
HH Demonstrate an understanding that a fraction a ⁄b is a
multiple of the unit fraction 1 ⁄b (CCSS 4.NF.4a)
HH Write an equation showing that a fraction a ⁄b is the
product of a × 1 ⁄b (CCSS 4.NF.4a)
HH Use an area model to multiply a fraction by a whole
number (CCSS 4.NF.4b)
HH Explore fraction relationships and operations using a
visual model
HH Find equivalent fractions
Instructions for Multiplying Fractions on the Geoboard
1. Distribute copies of Fractions on a Geoboard: Multiplying Fractions and display the top portion. Give students time to build all the regions on their geoboards.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
DATE
Fractions on a Geoboard Multiplying Fractions
In the illustration below, the whole geoboard has an area of 1.
A
B
C
D E
1
Look at the visual models below and think about what you notice about the
relationships between the regions on the geoboard. How could you express your
observations using multiplication? Explain your thinking in words and record
your observations in a multiplication equation.
2. Write C + C = B on the whiteboard. Have student pairs discuss if the equation is true. Ask for a
volunteer to share. Then ask student
pairs to consider
using multiplication
to show the relationship beVisual Model
Explanation
Multiplication Equation
a
tween regions B and C.
2 x 81 = 41
There are 2 C’s in Part B
B
C
C
b
© The Math Learning Center D
D
D
D
D
D
D
D
Bridges in Mathematics Grade 4 Supplement • A10.1
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 1 Multiplying Fractions on the Geoboard cont.
3. After students have had a chance to share observations with a partner, ask for volunteers to share
with the class.
Teacher Jesse, where do you see multiplication in the relationship between C and B?
Jesse Well, if two Cs equal B, that’s like saying that 2 × C = B.
Lauren And since C is 1⁄8, you could write 2 × 1⁄8 = 1⁄4.
Max I see it as 1⁄4 = 2 × 1⁄8
4. Complete information in the first row as students write on their own sheets.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
DATE
Fractions on a Geoboard Multiplying Fractions
In the illustration below, the whole geoboard has an area of 1.
A
B
C
D E
1
Look at the visual models below and think about what you notice about the
relationships between the regions on the geoboard. How could you express your
observations using multiplication? Explain your thinking in words and record
your observations in a multiplication equation.
Visual Model
Explanation
Multiplication Equation
a
There are 2 C’s in Part B
1
8
2x
=
1
4
B
C
C
b
D
D
D
D
D
D
D
D
5. Look at the next visual model. With student input, review ways that the relationship between D and
A could be represented with addition. Compile a list of equivalent equations on the board.
A
c
C
C
C
C
A
1
16
+ 161 + 161 + 161 + 161 + 161 + 161 + 161 = 21
(continued on next page)
4
16
2
16
+
+ 162 + 162 +
4
16
=
1
2
2
16
=
8
16
Teacher Does anyone know another way we could write 8 ⁄16?
Mia One half. You can see it on the geoboard. 8 is half of 16.
A10.2 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 1 Multiplying Fractions on the Geoboard cont.
6. Ask students to help you write an explanation such as “There are 8 D’s in section A.” By writing the
explanation, students will begin to more explicitly see fraction equations as a sum of the number of a
unit fraction.
7. Then ask each student to record one way that relationship between D and A could be expressed using
multiplication. Share with partners. Then ask for volunteers to share the multiplication equation.
Marin If 1⁄16 + 1⁄16 + 1⁄16 + 1⁄16 + 1⁄16 + 1⁄16 + 1⁄16 + 1⁄16 = 8⁄16, it’d be a lot easier to write 8 × 1⁄16 = 8⁄16.
Josh Mine was like Marin’s. But I said that 8 × 1⁄16 = 1⁄2. 8 is half of 16, like Mia said.
Marin
8
⁄16 and 1⁄2 are the same thing.
Cybil How can 8 × 1⁄16 be 1⁄2?
Teacher Josh, could you show us on the geoboard?
Josh Sure. Look at the 8 D’s that are shaded in. That makes 8 sixteenths. But the entire part that’s
shaded in shows 1⁄2 of the whole geoboard. So 8 sixteenths is 1⁄2. Or 8 × 1⁄16 = 1⁄2.
8. Continue having students look at parts in relationship to the entire area of the geoboard. Ask them to
write explanations and multiplication equations to represent the shaded portion of the geoboard.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
NAME
DATE
DATE
Fractions on a Geoboard Multiplying Fractions cont.
Fractions on a Geoboard Multiplying Fractions
Visual Model
In the illustration below, the whole geoboard has an area of 1.
E
A
E
E
E
C
B
C
D E
1
Look at the visual models below and think about what you notice about the
relationships between the regions on the geoboard. How could you express your
observations using multiplication? Explain your thinking in words and record
your observations in a multiplication equation.
Visual Model
Explanation
Explanation
Multiplication Equation
d
e
B
B
Multiplication Equation
The whole geoboard can
be split into 32 E’s.
C can be split into 4 E’s.
4x
1
32
=
1
8
The whole geoboard can
be split into 4 B’s. Two
shaded parts is 42 or 21
2x
1
4
=
2
4
2x
1
4
=
1
2
6x
1
8
=
6
8
or
3
4
=
4
16
or
1
4
a
There are 2 C’s in Part B
2x
1
8
=
1
4
f
B
C
C
b
D
D
D
D
D
D
D
D
There are 8 D’s in Part A
A
=
8
16
8x
1
16
=
1
2
4x
1
8
=
1
2
8x
1
16
C
C
C
C
C
C
g
D
D
D
D
The whole geoboard can
be split into 8 C’s. 6 of
the 8 parts are shaded.
The whole geoboard can
be split into 16 D’s. 4 of 16
are shaded.
4x
1
16
c
C
C
C
C
There are 4 C’s in Part A
A
(continued on next page)
(continued on next page)
9. As students feel comfortable, encourage them to continue the problems on their own. If they finish
the models you’ve created, ask them to solve for an unknown on the challenge problems provided. Reserve time at the end of the session for volunteers to prove their thinking.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.3
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 1 Multiplying Fractions on the Geoboard cont.
INDEPENDENT WORKSHEET
See Pizza Party Planning on pages A10.17 and A10.18 for more practice with multiplying fractions by a
whole number in the context of word problems.
A10.4 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
DATE
Fractions on a Geoboard Multiplying Fractions
In the illustration below, the whole geoboard has an area of 1.
A
B
C
D E
1 Look at the visual models below and think about what you notice about the
relationships between the regions on the geoboard. How could you express your
observations using multiplication? Explain your thinking in words and record
your observations in a multiplication equation.
Visual Model
Explanation
Multiplication Equation
a
B
C
C
b
D
D
D
D
D
D
D
D
A
c
C
C
C
C
A
(continued on next page)
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.5
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
DATE
Fractions on a Geoboard Multiplying Fractions cont.
Visual Model
Explanation
Multiplication Equation
d
E
E
E
E
C
e
B
B
f
C
C
C
C
C
C
g
D
D
D
D
(continued on next page)
A10.6 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
NAME
DATE
Fractions on a Geoboard Multiplying Fractions cont.
CHALLENGE
2Create a sketch that could be used to solve the following unknowns:
Problem
Labeled Sketch
a 3 × _______ =
3
4
b5 × ______ =
5
16
c 7 × ______ =
7
8
d2 × ______ =
1
4
© The Math Learning Center Answer
Bridges in Mathematics Grade 4 Supplement • A10.7
A10.8 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Set A10 H Activity 2
ACTIVITY
Quick Sketches & Fraction Arrays
Overview
You’ll Need
The teacher models how to sketch an array for /4 × 3.
Together as a class, students use this quick-sketch method
to find the product of 2 /3 × 5. Then, students work independently on 3 more combinations.
1
HH Paper for sketching
Note When you represent the symbolic form for a fraction,
please use a horizontal bar.
Skills & Concepts
HH Write an equation showing a fraction a /b as the sum of
a number of the unit fraction 1 /b (CCSS 4.NF.3)
HH Express a fraction as the sum of other fractions with the
same denominator in more than one way (CCSS 4.NF.3b)
HH Write an equation to show a fraction as the sum of other
fractions with the same denominator (CCSS 4.NF.3b)
HH Add fractions with like denominators
HH Demonstrate an understanding that a fraction a /b is a
multiple of the unit fraction 1 /b (CCSS 4.NF.4a)
HH Write an equation showing that a fraction a /b is the
product of a × 1 /b (CCSS 4.NF.4a)
HH Multiply a fraction by a whole number (CCSS 4.NF.4b)
Instructions for Quick Sketches & Fraction Arrays
1. Ask students to imagine the outline of a 1/4 × 3 array. Following a moment of private think-time, ask
a couple of students to describe what they see in their mind’s eye.
Teacher Yesterday we made rectangular regions on a geoboard to multiply fractions. I wonder
if we could make a quick sketch to multiply fractions if we didn’t have a geoboard with us? What
would a 1/4 × 3 array look like? We’ll share after some think-time.
Devon I see a rectangle with a tiny piece on the side and then a long piece across the top.
Misty Me, too. The little piece on the side is 1/4. In my mind I saw the piece on top divided into 3 sections.
Teacher Let’s draw this model. I’ll make an array just like we did for multiplying 2-digit numbers.
2. Draw a rectangle using the closest whole numbers, 1 × 3. Ask students how this could help you to make
a 1/4 × 3 array. With student guidance, split the array into fractional subsections and label the dimensions.
Teacher When I begin thinking about my rectangle, I’m going to use the closest whole numbers. So
if the problem is 1/4 × 3, I’m going to make a 1 × 3 rectangle.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.9
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 2 Quick Sketches & Fraction Arrays cont.
3
1
Teacher Turn to your partner and discuss how I could use this array to help me find 1/4 × 3. Who
would like to volunteer an idea?
Jodi You can just cut the rectangle into fourths.
Teacher Can you show me what you mean?
Jodi Sure. (Points on grid.) You can just draw a line to divide the length of your rectangle in half.
That shows the two halves or 1/2 of 3. Then split each half to make fourths.
Teacher I’m going to add the lines that Jodi mentioned to our grid. In my drawing, where do you see
1
/4 × 3? Take a moment to tell your partner where you see the 1/4 × 3 array. Who would like to share?
3
1
Megan I see it across the top row. The top row just shows 1/4, so you could write 1/4 next to the top row.
Teacher I’m going to erase the 1, label our array with 1/4, and shade in the top of my drawing to
show the problem we’re discussing.
3
1
4
3. Have students pair-share how they see the area pieces to determine the product of 1/4 × 3. Is it the
same as 3 × 1/4 ? Can they prove it?
Students may notice that they can multiply straight across. Record their thoughts.
Joe I know you can put any number over 1 and it’s still the same number. 3 over 1, that’s like just 3.
So I put 3 over 1 and multiplied straight across. 3/1 × 1/4= 3/4
Liz Hey, that’s cool. I wonder if it works every time?
DavidYou don’t even need the 1 under the 3. You can just look at 3 × 1/4 and in your head go (3 × 1)/4.
4. Write another multiplication combination on the board, 2 /3 × 5, and repeat the process. This time,
begin by having students make and share estimates, first in pairs and then as a class.
Joy I think the answer is going to be more than one. Like somewhere between 2 1/2 and 4.
1
/2 of 5 would be 2 1/2 and I know 2 /3 of 5 is more than that.
A10.10 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 2 Quick Sketches & Fraction Arrays cont.
5. Ask students to determine the closest whole numbers for 2 /3 and 5. Have students draw a 1 × 5 rectangle, divide it into 3 fractional parts, label the drawing, and shade in the area. If students find 2 /3 confusing, you may want to first label each row with 1/3, or thirds, then erase and label the top two rows
with 2 /3.
5
2
3
6. Again, have students pair-share to determine the area of 2 /3 × 5. Then work with student input to label the sub-regions, recording the product and one or more equations to show how students figured it out.
• Students may look for groups of fractions that equal 1:
5
2
3
1
1
+ 33 +
3
3
3
3
1
3
1
+ 31 = 3 31
1 + 1 + 1 + 31 = 3 31
• Students may observe that each column shows 2 /3 of 1 whole:
5
2
3
2
3
2
3
2
3
2
3
2
3
× 5 = 103
+ 23 + 23 + 23 = 103
2
3
2
3
+
2
3
• They may also notice that 2 /3 × 5 is the same as 1/3 × 10.
2
3
1
3
1
3
1
3
1
3
2
3
5
1
3
1
3
1
3
1
3
× 5 = (2 × 5) ×
or
10 × 31
1
3
1
3
1
3
• Or 5 × 2 /3 could be understood as 5 times 2 groups of 1/3.
» n × (a /b) = (n × a)/b
» In this case, 5 × 2 /3 = (5 × 2)/3
7. If students need additional modeling, do another problem together: 4 × 1/3.
Additional Resource
• On The Math Learning Center website, visit “A Play on Numbers” by Eugene Maier and read
Scene 12: Multiplying/Dividing Fractions. http://www.mathlearningcenter.org/media/gene/play-onnumbers/PON_S12_01.asp
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.11
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 2 Quick Sketches & Fraction Arrays cont.
INDEPENDENT WORKSHEET
See Brownie Dessert on pagesA10.19 and A10.20 for more practice with equivalent fractions and
word problems.
A10.12 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Set A10 H Activity 3
ACTIVITY 3
Fraction Word Problems & Arrays
Overview
You’ll need:
Today’s session extends work using array models to
multiply a whole number by a fraction. Students sketch,
discuss, and solve four story problems.
HH pens and paper to record on the display
Skills & Concepts:
HH Write an equation showing a fraction a/b as the sum of
a number of the unit fraction 1/b (CCSS 4.NF.3)
HH Write an equation to show a fraction as the sum of other
fractions with the same denominator (CCSS 4.NF.3b)
HH Pencil/paper for each student
HH Story Problems: Multiplying Fractions page A10.16, run
a class set plus one for display
Note When you represent the symbolic form for a fraction,
please use a horizontal bar.
HH Add fractions with like denominators
HH Demonstrate an understanding that a fraction a/b is a
multiple of the unit fraction 1/b (CCSS 4.NF.4a)
HH Write an equation showing that a fraction a/b is the
product of a × 1/b (CCSS 4.NF.4a)
HH Multiply a fraction by a whole number (CCSS 4.NF.4b)
HH Solve word problems in which fractions are multiplied
by a whole number
HH Use a visual fraction area model to understand multiplication of fractions by a whole number
Instructions for Fraction Word Problems & Arrays
1. Give each student a copy of Story Problems: Multiplying Fractions while you display the same Teacher
Master. Read the first problem together, taking time to discuss and record students’ thoughts about what
the problem is asking them to do. Pair-share estimates and then ask volunteers to explain their reasoning
with the class. Encourage students to consider benchmark fractions.
DATE
Story Problems Multiplying Fractions
Estimate then draw an array to show your work.
Problem
Estimate
1
The principal hands out ice cream
bars and popsicles at field day. The
first class finished two bags of ice
cream bars. Only 14 of that amount
of ice cream bars were needed for the
second class. How much ice cream
did the second class eat?
2 I have 6 dogs. This week each dog
gets 18 of a bag of dog treats. How
much of the bag is eaten?
Array and Answer
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME
3 The cookie recipe calls for
© The Math Learning Center 1
3 cup
of sugar. I need to make a double
batch of cookies. How much sugar do
I need?
4 If everyone wants a
1
4
pound
hamburger, and we have six people
in our family, how many pounds of
Bridges in Mathematics Grade 4 Supplement • A10.13
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 3 Fraction Word Problems & Arrays cont.
Teacher When you estimate, sometimes it’s helpful to think about benchmarks or numbers that are easy
to imagine. In this problem I’m wondering if the answer will be closer to zero, one half, or one whole?
Scott It must be close to zero. 1/4 of 2 bags has to be a really small number.
Jacque It’s small, but I don’t think it’s that small. 1/4 of 1 bag is 1/4. So 1/4 of 2 bags has to be more.
My estimate would be closer to one half.
2. Next, work with the class to sketch an array to represent the problem 1/4 × 2. Ask students to determine the closest whole numbers. Have them draw a 1 × 2 rectangle, and coach you to divide it into 4
fractional parts, as they sketch the same model. Label the drawing, and shade in the area.
2
1
4
3. After students have had a chance to sketch the array, work with the class to connect to the original
problem. What do the two dimensions represent? What does the area represent? Then ask students to
find the area of the array they’ve drawn. Have students pair-share their thoughts before a volunteer
shares with the entire class. Record multiplication equations to match student strategies.
Elsie I saw 2 groups of 1/4. So I just added 1/4 and 1/4. That’s 2 /4.
Jeb
I did the same thing. But I said it equals 1/2. Because 2 /4 and 1/2 are equivalent.
Sarah I just multiplied. I know that you can put any number over a 1 and it’s still the same number. So I said 2 /1 × 1/4 and just multiplied them across. That’s 2 /4.
DATE
Estimate then draw an array to show your work.
Problem
Estimate
Array and Answer
1
The principal hands out ice cream
bars and popsicles at field day. The
first class finished two bags of ice
cream bars. Only 14 of that amount
of ice cream bars were needed for the
second class. How much ice cream
did the second class eat?
1
2
1
4
2 I have 6 dogs. This week each dog
gets 18 of a bag of dog treats. How
much of the bag is eaten?
• How are we seeing the area of this rectangle?
3 The cookie recipe calls for cup
» 1⁄4 + 1⁄4 = 2 ⁄4
of sugar. I need to make a double
1
1
1
batch of cookies. How much sugar do
» ⁄4 + ⁄4 = ⁄2
I need?
1
2
» ⁄2 × 14 = ⁄4
4 If everyone wants a pound
and we have six people
4. With student input, label thehamburger,
area
rectangle.
in our
family,of
howeach
many pounds
of
2
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME
Story Problems Multiplying Fractions
1
3
1
4
hamburger do we need?
2
1
4
A10.14 • Bridges in Mathematics Grade 4 Supplement
1
4
1
4
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
Activity 3 Fraction Word Problems & Arrays cont.
5. Repeat this process with the three other problems on the projector as students complete the problems on their own sheets.
INDEPENDENT WORKSHEET
See Multiplying Fractions with Arrays on page A10.21 for more practice with estimating and sketching
arrays for multiplying fractions by a whole number.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.15
A10.16 • Bridges in Mathematics Grade 4 Supplement
1
3
1
4
pound
hamburger, and we have six people
in our family, how many pounds of
hamburger do we need?
4If everyone wants a
cup
of sugar. I need to make a double
batch of cookies. How much sugar do
I need?
3The cookie recipe calls for
gets 18 of a bag of dog treats. How
much of the bag is eaten?
2I have 6 dogs. This week each dog
bars and popsicles at field day. The
first class finished two bags of ice
cream bars. Only 14 of that amount
of ice cream bars were needed for the
second class. How much ice cream
did the second class eat?
1 The principal hands out ice cream
Problem
Estimate then draw an array to show your work.
Story Problems Multiplying Fractions
NAME
Estimate
DATE
Array and Answer
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set, plus 1 for display.
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 1.
NAME
DATE
Set A10 H Independent Worksheet 1
INDEPENDENT WORKSHEET
Pizza Party Planning
A fourth grade class won a pizza party for contributing the most paper in the
recycling contest at school. Medium pizzas were cut into 8 slices and large pizzas
were cut into 12 slices.
1 Mariah ate 2 slices of a large pizza. What fraction of the pizza did she eat?
Draw a sketch to show your thinking.
2Carlos said that Mariah ate
1
6
of a pizza. Explain why you agree or disagree.
3Mariah’s table group seats four students. Each student ate 2 slices of a large
pizza. Write a multiplication equation that shows what fraction of a pizza was eaten.
(continued on next page)
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.17
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME
DATE
Independent Worksheet 1 Pizza Party Planning (cont.)
4Tony ate 3 slices of a medium pizza and his friend Conner ate 4 slices of the
same pizza.
a Write two equivalent fractions to tell how much pizza Conner ate.
bWrite an equation to show what fraction of the pizza they ate together.
5Lionel’s table group drank 1
1
2
liters of juice with their pizza. How many milliliters
A10.18 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
did they drink?
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 2.
NAME
DATE
Set A10 H Independent Worksheet 2
INDEPENDENT WORKSHEET
Brownie Dessert
A fourth grade class earned a brownie dessert party for the highest attendance
in one grading period. Smaller pans of brownies were cut into 9 pieces and large
pans were cut into 16 pieces.
1 Tori ate 2 pieces of brownie from the smaller pan. What fraction of the small
pan of brownies did she eat? Draw a sketch to show your thinking.
2Jorge ate one piece more than Tori. Write two equivalent fractions to show how
much Jorge ate.
3Ford’s table group seats five students. Each student ate 2 pieces from the large
brownie pan. Write an equation that shows what fraction of the large pan of
brownies was eaten.
4April ate 1 piece from the large pan and her friend Karissa ate 4 slices from the
same pan.
a Write two fractions to tell how much of the large brownie pan Karissa ate.
(continued on next page)
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.19
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME
DATE
Independent Worksheet 2 Brownie Dessert (cont.)
bWhat fraction of the large brownie pan did they eat together?
5Frederick had 2 of the brownies from the large pan. His brother said that he
1
8
ate
of the pan of brownies. Explain why you agree or disagree.
CHALLENGE
6In a 12-egg carton,
1
6
equals 2 eggs. Use the grids below to help you imagine
and draw cartons where:
a
1
6
is 3 eggs
b 56
is 25 eggs
c How did you decide on the sizes of the cartons for a and b?
A10.20 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 3.
NAME
DATE
Set A10 H Independent Worksheet 3
INDEPENDENT WORKSHEET
Multiplying Fractions with Arrays
1 Sketch each array below. Then write a multiplication equation to show how you
found the product.
Sketch This Array
a
3
8
×3
b 26
×2
c
×5
1
7
d 15
Equation
× 10
2 Write a story problem to match one of the combinations above.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.21
A10.22 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 3.
NAME
DATE
Set A10 H Independent Worksheet 4
INDEPENDENT WORKSHEET
Company’s Coming!
1 Jamie has three people in her family. For three people, they make a recipe for
Cranberry Sauce that calls for the following ingredients:
• 1 (12 ounce) bag of fresh cranberries
• 34 cup orange juice
• 23 cup brown sugar
• 1 cup white sugar
4
a Jamie’s grandparents are joining them for dinner. Double Jamie’s recipe for
Cranberry Sauce. Show your work and the new ingredient list below.
bJamie’s aunt, uncle and cousin are now coming for dinner as well. Triple the
original recipe. Show your work and the new ingredient list below.
(continued on next page)
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.23
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME
DATE
Independent Worksheet 4 Company’s Coming! (cont.)
2Jamie also needs to plan for the meal. The following portions are for one person. To
serve 8, how much of each food is needed? Write an equation to show your thinking.
Note: remember to label the units in your equation.
Food
a Vegetables
bTurkey
1 Serving
1
2
cup
3 ounces
c Gravy
1
4
cup
dPotatoes
1
2
cup
eStuffing
1
3
cup
f Green Salad
3
4
cup
gCranberry
1
4
cup
1
8
pie
Sauce
hApple Pie
Show Your Work and Write an Equation for 8 Servings
A10.24 • Bridges in Mathematics Grade 4 Supplement
© The Math Learning Center