**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 ≈ 500x 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 ≈ 700x 300= ____ • What’s 700 x 300? • 210,000 • 908 x 297 ≈ ____ x ____ = ____ • Round both factors to the nearest hundred. • 908 x 297 ≈ 900x 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. 39 106 Gemma ? 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 39 106 Gemma ? 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 39 106 Gemma ? 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 39 106 Gemma ? Leah GEMMA 1 0 6 X 1 4 4 2 4 + 1, 0 6 0 $1, 48 4 LEAH 1 4 5 X 2 4 5 8 0 + 2, 9 0 0 $3, 48 0 • 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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