grade 4 supplement - the math learning center geoboards and geobands or geoboard app (online or...
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GRADE 4 SUPPLEMENTSet A10 Number & Operations: Multiplying Whole Numbers by Fractions
Includes H Activity 1: Multiplying Fractions on the Geoboard A10.1
H Activity 2: Quick Sketches & Fraction Arrays A10.9
H Activity 3: Fraction Word Problems & Arrays A10.13
H Independent Worksheet 1: Pizza Party Planning A10.17
H Independent Worksheet 2: Brownie Dessert A10.19
H Independent Worksheet 3: Multiplying Fractions with Arrays A10.21
H Independent Worksheet 4: Company’s Coming! A10.23
Skills & Concepts H Add fractions with like denominators
H Write an equation showing a fraction a⁄b as the sum of a number of the unit fraction 1⁄b
H Write an equation to show a fraction as the sum of other fractions with the same denominator
H Demonstrate an understanding that a fraction a⁄b is a multiple of the unit fraction 1⁄b
H Write an equation showing that a fraction a⁄b is the product of a × 1⁄b
H Multiply a fraction by a whole number
H Solve word problems in which fractions are multiplied by a whole number
H Use a visual area model to multiply a whole number by a fraction
P0213
Bridges in Mathematics Grade 4 Supplement
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
The Math Learning Center, PO Box 12929, Salem, Oregon 97309. Tel. 1 800 575–8130.
© 2012 by The Math Learning Center
All rights reserved.
Prepared for publication on Macintosh Desktop Publishing system.
Printed in the United States of America.
P0213
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masters in appropriate quantities for their classroom use.
Bridges in Mathematics is a standards-based K–5 curriculum that provides a unique blend
of concept development and skills practice in the context of problem solving. It incorpo-
rates the Number Corner, a collection of daily skill-building activities for students.
The Math Learning Center is a nonprofit organization serving the education community.
Our mission is to inspire and enable individuals to discover and develop their mathematical
confidence and ability. We offer innovative and standards-based professional development,
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visit us at www.mathlearningcenter.org.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.1
Set A10 H Activity 1
ACTIVITY
Multiplying Fractions on the GeoboardOverview Students re-examine problems from Bridges Unit 6: Ses-
sion 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.
Skills & Concepts H Write an equation showing a fraction a⁄b as the sum of
a number of the unit fraction 1⁄b (CCSS 4.NF.3)
H Express a fraction as the sum of other fractions with the
same denominator in more than one way (CCSS 4.NF.3b)
H Demonstrate an understanding that a fraction a⁄b is a
multiple of the unit fraction 1⁄b (CCSS 4.NF.4a)
H Write an equation showing that a fraction a⁄b is the
product of a × 1⁄b (CCSS 4.NF.4a)
H Use an area model to multiply a fraction by a whole
number (CCSS 4.NF.4b)
H Explore fraction relationships and operations using a
visual model
H Find equivalent fractions
Recommended TimingUse anytime after Unit 6 Session 3
You’ll need H Fractions on a Geoboard: Multiplying Fractions, pages
A10.5–A10.7 (run a class set.)
H Geoboards and geobands or Geoboard App (online
or iPad) for display
H Geoboards and geobands for students, optional
H Paper/pen for use on the display
H Colored pencils, optional
Note When you represent the symbolic form for a fraction,
please use a horizontal bar.
Instructions for Multiplying Fractions on the Geoboard1. Distribute copies of Fractions on a Geoboard: Multiplying Fractions and display the top portion. Give stu-dents time to build all the regions on their geoboards.
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Fractions on a Geoboard Multiplying FractionsIn 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
C C
C C
A
c
(continued on next page)
D D D D
D D D D
A
18 =2 x 1
4There are 2 C’s in Part B
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 be-tween regions B and C.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
A10.2 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
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.
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Fractions on a Geoboard Multiplying FractionsIn 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
C C
C C
A
c
(continued on next page)
D D D D
D D D D
A
18 =2 x 1
4There are 2 C’s in Part B
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.
116
116 = 1
2+1
16 +116 +1
16 +116 +1
16 +116 +
416
416 = 1
2+
216
216 = 8
16+2
16 +216 +
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.
Activity 1 Multiplying Fractions on the Geoboard cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.3
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.
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Fractions on a Geoboard Multiplying FractionsIn 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
C C
C C
A
c
D D D D
D D D D
(continued on next page)
18 =
There are 8 D’s in Part A
2 x 14
There are 4 C’s in Part A
There are 2 C’s in Part B
A
116 =8 x 8
16
116 =8 x 1
2
18 =4 x 1
2
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Visual Model Explanation Multiplication Equation
d
CEE
EE
e
B
f
C C
C
C
C
C
g
D D
D D
(continued on next page)
Fractions on a Geoboard Multiplying Fractions cont.
The whole geoboard can be split into 32 E’s. C can be split into 4 E’s.
132 =4 x 1
8
14 =2 x 2
4
18 =6 x 6
8
116 =4 x 4
16
The whole geoboard can be split into 4 B’s. Two shaded parts is or 2
412
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.
14 =2 x 1
2
34
14
or
or
B
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. Re-serve time at the end of the session for volunteers to prove their thinking.
Activity 1 Multiplying Fractions on the Geoboard cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
A10.4 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
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.
Activity 1 Multiplying Fractions on the Geoboard cont.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.5
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Fractions on a Geoboard Multiplying FractionsIn 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)
A10.6 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
Visual Model Explanation Multiplication Equation
d
CEE
EE
e
B
B
f
C C
C
C
C
C
g
D D
D D
(continued on next page)
Fractions on a Geoboard Multiplying Fractions cont.
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.7
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set.
CHALLENGE
2 Create a sketch that could be used to solve the following unknowns:
Problem Labeled Sketch Answer
a 3 × _______ = 3 4
b 5 × ______ = 5 16
c 7 × ______ = 7 8
d 2 × ______ = 1 4
Fractions on a Geoboard Multiplying Fractions cont.
A10.8 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.9
Set A10 H Activity 2
ACTIVITY
Quick Sketches & Fraction Arrays
OverviewThe teacher models how to sketch an array for 1/4 × 3.
Together as a class, students use this quick-sketch method
to find the product of 2/3 × 5. Then, students work inde-
pendently on 3 more combinations.
Skills & Concepts H Write an equation showing a fraction a/b as the sum of
a number of the unit fraction 1/b (CCSS 4.NF.3)
H Express a fraction as the sum of other fractions with the
same denominator in more than one way (CCSS 4.NF.3b)
H Write an equation to show a fraction as the sum of other
fractions with the same denominator (CCSS 4.NF.3b)
H Add fractions with like denominators
H Demonstrate an understanding that a fraction a/b is a
multiple of the unit fraction 1/b (CCSS 4.NF.4a)
H Write an equation showing that a fraction a/b is the
product of a × 1/b (CCSS 4.NF.4a)
H Multiply a fraction by a whole number (CCSS 4.NF.4b)
Recommended TimingUse after Supplement Set A10, Activity 1
You’ll Need H Paper for sketching
Note When you represent the symbolic form for a fraction,
please use a horizontal bar.
Instructions for Quick Sketches & Fraction Arrays1. 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.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
A10.10 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
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.
314
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?
David You 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.
Activity 2 Quick Sketches & Fraction Arrays cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.11
5. Ask students to determine the closest whole numbers for 2/3 and 5. Have students draw a 1 × 5 rect-angle, divide it into 3 fractional parts, label the drawing, and shade in the area. If students find 2/3 con-fusing, you may want to first label each row with 1/3, or thirds, then erase and label the top two rows with 2/3.
523
6. Again, have students pair-share to determine the area of 2/3 × 5. Then work with student input to la-bel 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:
523
13
1 1 1
33
1
1333
333
1
+ + + =13
1 133+ =1
3+ +
• Students may observe that each column shows 2/3 of 1 whole:
523
23
23 5 10
3× =103+ =+ +2
323
23
23+2
3
23
23
23
23
• They may also notice that 2/3 × 5 is the same as 1/3 × 10.
523
13
23 5× = (2 × 5) × 1
3
10 × 13
or
13
13
13
13
13
13
13
13
13
• 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-on-numbers/PON_S12_01.asp
Activity 2 Quick Sketches & Fraction Arrays cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
A10.12 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
INDEPENDENT WORKSHEET
See Brownie Dessert on pagesA10.19 and A10.20 for more practice with equivalent fractions and word problems.
Activity 2 Quick Sketches & Fraction Arrays cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.13
Set A10 H Activity 3
ACTIVITY 3
Fraction Word Problems & Arrays
OverviewToday’s session extends work using array models to
multiply a whole number by a fraction. Students sketch,
discuss, and solve four story problems.
Skills & Concepts: H Write an equation showing a fraction a/b as the sum of
a number of the unit fraction 1/b (CCSS 4.NF.3)
H Write an equation to show a fraction as the sum of other
fractions with the same denominator (CCSS 4.NF.3b)
H Add fractions with like denominators
H Demonstrate an understanding that a fraction a/b is a
multiple of the unit fraction 1/b (CCSS 4.NF.4a)
H Write an equation showing that a fraction a/b is the
product of a × 1/b (CCSS 4.NF.4a)
H Multiply a fraction by a whole number (CCSS 4.NF.4b)
H Solve word problems in which fractions are multiplied
by a whole number
H Use a visual fraction area model to understand multi-
plication of fractions by a whole number
Recommended TimingUse after Supplement Set A10, Activity 2
You’ll need: H pens and paper to record on the display
H Pencil/paper for each student
H 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.
Instructions for Fraction Word Problems & Arrays1. 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.
Set A
10 Nu
mb
er &
Op
eratio
ns: M
ultip
lying W
ho
le Nu
mb
ers b
y Fraction
s Blacklin
e
NAME DATE
Story Problems Multiplying Fractions
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 1
4 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 1
8 of a bag of dog treats. How much of the bag is eaten?
3 The cookie recipe calls for 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 hamburger do we need?
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
A10.14 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
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 deter-mine 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.
214
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 num-ber. So I said 2/1 × 1/4 and just multiplied them across. That’s 2/4.
Set A
10 Nu
mb
er &
Op
eratio
ns: M
ultip
lying W
ho
le Nu
mb
ers b
y Fraction
s Blacklin
e
NAME DATE
Story Problems Multiplying Fractions
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 1
4 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 1
8 of a bag of dog treats. How much of the bag is eaten?
3 The cookie recipe calls for 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 hamburger do we need?
214
12
• How are we seeing the area of this rectangle? » 1⁄4 + 1⁄4 = 2⁄4 » 1⁄4 + 1⁄4 = 1⁄2 » 1⁄2 × 14 = 2⁄4
4. With student input, label the area of each rectangle.
214
14
14
Activity 3 Fraction Word Problems & Arrays cont.
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.15
Activity 3 Fraction Word Problems & Arrays cont.
5. Repeat this process with the three other problems on the projector as students complete the prob-lems 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.
A10.16 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
NA
ME
DA
TE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline Run a class set, plus 1 for display.
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© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.17
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 1.
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.
2 Carlos said that Mariah ate 1 6 of a pizza. Explain why you agree or disagree.
3 Mariah’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)
A10.18 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME DATE
4 Tony 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.
b Write an equation to show what fraction of the pizza they ate together.
5 Lionel’s table group drank 1 1 2 liters of juice with their pizza. How many milliliters
did they drink?
Independent Worksheet 1 Pizza Party Planning (cont.)
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.19
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 2.
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 brownie did she eat? Draw a sketch to show your thinking.
2 Jorge ate one piece more than Tori. Write two equivalent fractions to show how much Jorge ate.
3 Ford’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 brownie pan was eaten.
4 April 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.
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A10.20 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME DATE
b What fraction of the large brownie pan did they eat together?
5 Frederick had 2 of the brownies from the large pan. His brother said that he ate 1
8 of the pan of brownies. Explain why you agree or disagree.
CHALLENGE
6 In a 12-egg carton, 1 6 equals 2 eggs. Use the grids below to help you imagine
Independent Worksheet 2 Brownie Dessert (cont.)
and draw cartons where:
a 1 6 is 3 eggs b 5
6 is 25 eggs
c How did you decide on the sizes of the cartons for a and b?
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.21
NAME DATE
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 3.
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 Equation
a 3 8 × 3
b 2 6 × 2
c 1 7 × 5
d 1 5 × 10
2 Write a story problem to match one of the combinations above.
A10.22 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
© The Math Learning Center Bridges in Mathematics Grade 4 Supplement • A10.23
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(12ounce)bagoffreshcranberries• 3
4 cup orange juice• 2
3 cup. brown sugar• 1
4 cup white sugar
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.
b Jamie’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.
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Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline For use anytime after Supplement Set A10, Activity 3.
A10.24 • Bridges in Mathematics Grade 4 Supplement © The Math Learning Center
Set A10 Number & Operations: Multiplying Whole Numbers by Fractions Blackline
NAME DATE
Independent Worksheet 4 Company’s Coming! (cont.)
2 Jamie 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 1 Serving Show Your Work and Write an Equation for 8 Servings
a Vegetables 1 2 cup
b Turkey 3 ounces
c Gravy 1 4 cup
d Potatoes 1 2 cup
e Stuffing 1 3 cup
f Green Salad 3 4 cup
g Cranberry Sauce
1 4 cup
h Apple Pie 1 8 pie