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. Calculate the following: 4.5 0.4 x 𝟏𝟎 𝟐 Multiply by 𝟏𝟎 𝟐 0.4 ÷ 𝟏𝟎 𝟐 4.5 x 𝟏𝟎 𝟐 = 450 3.895 x 𝟏𝟎 𝟑 3.895 ÷ 𝟏𝟎 𝟑

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 ____ = ____ 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 ____ = ____ 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? 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 48 ft. 56 ft.

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 multiply by $565. We have to first find the area of the office space then multiply by $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? 48 ft. 56 ft. 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? A = 2,688 ft² Have we answered the question? No. We need to multiply the area by the cost of one square foot, $565, to find the total cost. Solve and express your answer using a statement of solution. 48 ft. 56 ft. 2, 6 8 8 X 5 6 5 1 3, 4 4 0 1 6 1, 2 8 0 +1, 3 4 4, 0 0 0 1, 5 1 8, 7 2 0 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. Each necklace they make has exactly 104 beads on it. How many beads did both girls use while making their necklaces? 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. Each necklace they make has exactly 104 beads on it. How many beads did both girls use while making their necklaces? 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? Draw and label your tape diagrams. What is the question asking? We have to find the total number of beads on all the necklaces. What do we need to think about to solve this problem? What do you notice about it? It is a multi-step problem. We need to know how many necklaces Leah made before we can find the total number of necklaces. Then we need to find the number of beads. Work with your table to complete the first steps by finding the total number of necklaces. 39 Gemma 106 Leah ? Leah = 106 + 39 =145

Concept Development – Problem 2: Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces. Leah made 39 more necklaces than Gemma. Each necklace they make has exactly 104 beads on it. How many beads did both girls use while making their necklaces? 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? 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 39 Gemma 106 Leah ? Leah = 106 + 39 =145 necklaces Gemma = 106 necklaces

Concept Development – Problem 2: Gemma and Leah are both jewelry makers. Gemma made 106 beaded necklaces. Leah made 39 more necklaces than Gemma. Each necklace they make has exactly 104 beads on it. How many beads did both girls use while making their necklaces? 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 2 5 1 X 1 0 4 1 0 0 4 + 2 5 1 0 0 2 6, 1 0 4 39 Gemma 106 Leah ? Leah = 106 + 39 =145 necklaces Gemma = 106 necklaces 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. Each necklace they make has exactly 104 beads on it. How many beads did both girls use while making their necklaces? 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? 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 =145 necklaces Gemma = 106 necklaces 39 Gemma 106 Leah ? 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 Gemma and Leah used 26,104 beads altogether. Leah made $1,996 more than Gemma at the craft fair.

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Problem Set