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Engage NY Math Module 2
Lesson 9: Fluently multiply multi-digit whole numbers using the
standard algorithm to solve multi-step word problems.
Multiply and Divide by Exponents
 Write 45 tenths as a decimal.
 4.5
 Multiply by 
 4.5 x  = 450
 Calculate the following:




0.4 x 
0.4 ÷ 
3.895 x 
3.895 ÷ 
Estimate the Product
• 421 x 231 ≈ ____ x ____ = ____
• Round both factors to the nearest hundred.
• 421 x 231 ≈ 400 x 200 = ____
• What’s 400 x 200?
• 80,000
• 523 x 298 ≈ ____ x ____ = ____
• Round both factors to the nearest hundred.
• 523 x 298 ≈ 500 x 300 = ____
• What’s 500 x 300?
• 150,000
Estimate the Product
• 684 x 347 ≈ ____ x ____ = ____
• Round both factors to the nearest hundred.
• 684 x 347 ≈ 700 x 300 = ____
• What’s 700 x 300?
• 210,000
• 908 x 297 ≈ ____ x ____ = ____
• Round both factors to the nearest hundred.
• 908 x 297 ≈ 900 x 300 = ____
• What’s 900 x 300?
• 270,000
Concept Development – Problem 1:
• An office space in New York City measures 48 feet by 56 feet. If it sells
for $565 per square foot, what is the selling price of the office space?
• We will work Problem 1 together. Let’s read the word problem aloud.
• Now let’s reread the problem sentence by sentence and draw as we go.
• “An office space in New York City measures 48 feet by 56 feet.”
• What do you see? Can we draw something?
48 ft.
56 ft.
• Read the next sentence.
• “If it sells for $565 per square foot, what is the selling price of the
office space?”
• What is the important information and how can we show this in our
drawing?
• The office square sells for $565 for each square foot. We can draw
a single square unit inside our rectangle to remind us.
• We can write that 1 unit = $565
Concept Development – Problem 1:
• An office space in New York City measures 48 feet by 56 feet. If it sells
for $565 per square foot, what is the selling price of the office space?
• How do we solve this problem? Turn and talk.
• We have to multiply.
• We have to find the total square feet of the office space then
48 ft.
multiply by $565.
56 ft.
• We have to first find the area of the office space then multiply by
$565.
1 unit = $565
• What information are we given that would help us figure out the area?
• We can multiply the length times the width.
• Find the area of the office space.
• A = LxW
• A = 56 x 48
• A = 2,688 ft²
• Have we answered the question?
Concept Development – Problem 1:
• An office space in New York City measures 48 feet by 56 feet. If it sells
for $565 per square foot, what is the selling price of the office space?
• A = 2,688 ft²
• Have we answered the question?
• No. We need to multiply the area by the cost of one square foot, 48 ft.
$565, to find the total cost.
• Solve and express your answer using a statement of solution.
2, 6
X
5
1 3, 4
1 6 1, 2
+1, 3 4 4, 0
1, 5 1 8, 7
8
6
4
8
0
2
8
5
0
0
0
0
56 ft.
1 unit = $565
2,688 units = 2,688 x 565
The selling price of the office space was $1,518,720.
Concept Development – Problem 2:
• Gemma and Leah are both jewelry makers. Gemma made 106 beaded
necklaces. Leah made 39 more necklaces than Gemma.
a. Each necklace they make has exactly 104 beads on it. How many
beads did both girls use while making their necklaces?
b. At a recent craft fair, Gemma sold her necklaces for $14 each. Leah
sold her necklaces for $10 more. Who made more money at the
craft fair? How much more?
• Reread the problem sentence by sentence.
• What do you see? Can we draw something?
• Yes.
• What can we draw?
• A bar for Gemma’s necklaces and a second, longer bar for Leah’s.
• Draw and label your tape diagrams.
Concept Development – Problem 2:
• Gemma and Leah are both jewelry makers. Gemma made 106 beaded
necklaces. Leah made 39 more necklaces than Gemma.
a. Each necklace they make has exactly 104 beads on it. How many
beads did both girls use while making their necklaces?
b. At a recent craft fair, Gemma sold her necklaces for $14 each. Leah
sold her necklaces for $10 more. Who made more money at the
craft fair? How much more?
• What is the question asking?
• Draw and label your tape diagrams.
• We have to find the total number of
beads on all the necklaces.
39
• What do we need to think about to solve
106
Gemma
this problem? What do you notice about it?
• It is a multi-step problem. We need to
?
Leah
know how many necklaces Leah made
before we can find the total number of
Leah = 106 + 39
necklaces. Then we need to find the
=145
number of beads.
• Work with your table to complete the first
steps by finding the total number of
necklaces.
Concept Development – Problem 2:
•
Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces.
Leah made 39 more necklaces than Gemma.
a. Each necklace they make has exactly 104 beads on it. How many beads did
both girls use while making their necklaces?
b. At a recent craft fair, Gemma sold her necklaces for $14 each. Leah sold her
necklaces for $10 more. Who made more money at the craft fair? How
much more?
39
Gemma
Leah
106
?
Leah = 106 + 39
=145 necklaces
Gemma = 106 necklaces
• We haven’t answered the question yet. Turn
and talk to your table about how we can finish
solving part a.
• We have to find the total beads for both
girls so we need to multiply Gemma’s
necklaces by 104 beads and Leah’s by 104
and then add them together.
• We also could add Gemma’s and Leah’s
necklaces together then multiply by 104.
• Use an expression to show your strategy for
solving.
• (106 x 104) + (145 x 104)
OR
• (106 + 145) x 104
Concept Development – Problem 2:
•
Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces.
Leah made 39 more necklaces than Gemma.
a. Each necklace they make has exactly 104 beads on it. How many beads did
both girls use while making their necklaces?
b. At a recent craft fair, Gemma sold her necklaces for $14 each. Leah sold her
necklaces for $10 more. Who made more money at the craft fair? How
much more?
• Solve the problem with your partner and make
a statement to answer the question.
• 106 + 145 = 251 necklaces
39
Gemma
Leah
106
?
Leah = 106 + 39
=145 necklaces
Gemma = 106 necklaces
2 5
X 1 0
1 0 0
+2 5 1 0
2 6, 1 0
1
4
4
0
4
Gemma and Leah used 26,104 beads
altogether.
Concept Development – Problem 2:
•
Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces.
Leah made 39 more necklaces than Gemma.
a. Each necklace they make has exactly 104 beads on it. How many beads did
both girls use while making their necklaces?
b. At a recent craft fair, Gemma sold her necklaces for $14 each. Leah sold her
necklaces for $10 more. Who made more money at the craft fair? How
much more?
Leah =145 necklaces
Gemma = 106 necklaces
39
Gemma
Leah
106
?
Gemma and Leah used 26,104 beads
altogether.
Leah made $1,996 more than Gemma
at the craft fair.
• Let’s read part (b) together.)
• Who made more money? Without calculating
can we answer this question? Turn and talk.
• Leah made more necklaces than Gemma,
and she charged more per necklace, so it
makes sense that she made more money.
• Find out how much more money Leah made.
LEAH
1 4 5
X 2 4
5 8 0
+ 2, 9 0 0
$3, 4 8 0
GEMMA
1 0 6
X 1 4
4 2 4
+ 1, 0 6 0
$1, 4 8 4
DIFFERENCE
$ 3 4 8 0
- 1 4 8 4
$1, 9 9 6
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