Engage NY Math Module 7 Lesson 7: Connect area diagrams and the distributive property to partial products of the standard algorithm with renaming.

 2 x 10 = ____  12 x 10 = ____  12 x 100 = ____  4 x 10 = ____  34 x 10 = ____  34 x 100 = ____  7 x 10 = ____  27 x 10 = ____  27 x 100 = ____  3 x 10 = ____  3 x 2 = ____  3 x 20 = ____  13 x 20 = ____  13 x 100 = ____  13 x 200 = ____  2 x 4 = ____  22 x 4 = ____  22 x 40 = ____  22 x 400 = ____  33 x 2 = ____  33 x 20 = ____  33 x 200 = ____  24 x 10 = ____  24 x 20 = ____  71 x 2 = ____  71 x 20 = ____  82 x 20 = ____  15 x 300 = ____  71 x 600 = ____  18 x 40 = ____  75 x 30 = ____  84 x 300 = ____  87 x 60 = ____  87 x 600 = ____  79 x 800 = ____ Multiply by Multiples of 10 and 100 Multiply.

MULTIPLY USING THE AREA MODEL In your math journal, solve these two problems using the area model. 24 x x 15

The length of a school bus is 12.6 meters. If 9 school buses park end to end with 2 meters between each one, what’s the total length from the front of the first bus to the end of the last bus? Use a tape diagram to solve this problem and include a statement of solution. Application Problem: The total length is meters. 9 Buses: (12.6 x 10) – (12.6) space between: 8 x 2 = 16 m m = m ?

Concept Development – Problem 1: 524 x 136 Compare this problem with the problems in the last lesson. What do you notice? In the last lesson, we multiplied using only two-digit numbers as the number of units. The problems in the last lesson had a two-digit number in them. So which one of these factors should we designate as our unit? Turn and talk. It will be easier to count 136 units of 524 than 524 units of 136. It won’t matter this time because they are both three-digit numbers. Let’s designate 524 as our unit. How will the area model for this problem be different than yesterday’s models? There will be 3 columns and 3 rows. Yesterday we only had 2 rows because we used the smaller number to tell the number of units and our larger numbers yesterday as our units. Solve this problem using an area model and the standard algorithm.

Concept Development – Problem 1: 524 x ,000 2, , , ,400 15, ,144 71, X , Compare your solutions by matching your partial products and final product.

Concept Development – Problem 2: 4,519 x 326 What is different about this problem? We have a four-digit number this time. Which factor will be our unit? Is one more efficient to use than the other? Turn and talk. Does the presence of the fourth digit change anything about how we multiply? Why or why not? We will have an extra column in the area model, but we just multiply the same way. Before we solve this problem, let’s estimate our product. Round the factors and make an estimate. 5,000 x 300 = 1,500,000 Solve this problem using an area model and the standard algorithm.

Concept Development – Problem 2: 4,519 x 326 4, ,200, ,000 3,000 2,700 80,000 10, ,000 3, ,355,700 90, ,114 1,473,194 4, X , 4 7 3, Compare your solutions by matching your partial products and final product.

Concept Development – Problem 3: 4,509 x 326 Estimate the product of this problem. 5,000 x 300 = 1,500,000 Compare 4,519 and 4,509. How are they different? There’s a zero in the tens place in 4,509. What does 4,509 look like in expanded form? 4, Can you imagine what the length of our rectangle will look like? How many columns will we need to represent the total length? We will only need three columns. This is a four-digit number. Why only three columns? The rectangle shows area. So if we put a column in for the tens place, we would be drawing the rectangle bigger than it really is. We are chopping the length of the rectangle into three parts. The width of the tens column would be zero, so it has no area. Solve this problem using an area model and the standard algorithm.

Concept Development – Problem 3: 4,509 x 326 4, ,000 3, ,000 10, ,200, ,000 2,700 27,054 90, ,352,700 1,469,934 4, X , , , 3 5 2, , 4 6 9, Compare your solutions by matching your partial products and final product.

Concept Development – Problem 4: 4,509 x 306 Estimate the product of this problem. 5,000 x 300 = 1,500,000 How is this problem different from problem 3? There’s a zero in both factors this time. It’s going to be 20 units less of 4,509 than last time. Thinking about the expanded forms of the factors, imagine the area model. How will the length and width be decomposed? How will it compare to problem 3? Like problem 3, there are only 3 columns in the length again even though it’s a four digit number. The model doesn’t need three rows because there’s nothing in the tens place. We only need to show rows for hundreds and ones. Solve this problem using an area model and the standard algorithm.

Concept Development – Problem 3: 4,509 x 306 4, ,000 3, ,200, ,000 2,700 27, ,352,700 1,379,754 4, X , , 3 5 2, , 3 7 9, Compare your solutions by matching your partial products and final product.

Exit Ticket

Display Problem Set on the board. Allow time for the students to complete the problems with tablemates. Problem Set

Assign Lessons 6 and 7 Homework Tasks. Due Date: Tuesday, January 28. HOMEWORK TASK