Fairfax County Public Schools Program of Studies: 3.5.a.1, 3.5.a.2, Students pract ice. мин

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1 1 План урока Multiplication Expand ed Algorithm Возрастная группа: 4, 5 Virginia - Mathematics Standards of Learning (2009): 3.5, 3.6, 5.4 Virginia - Mathematics Standards of Learning (2016): 3.3.b, 3.4.a, 3.4.b, 3.4.d Fairfax County Public Schools Program of Studies: 3.5.a.1, 3.5.a.2, 3.6.a.1, 3.6.a.3, 3.6.a.4, 3.6.a.5, 3.6.a.6, 5.4.a.6 Онлайн ресурсы: M ul t i pl i c at i o n Al go ri t hms Opening Teacher present s Students pract ice Class discussion Closing M at h Obj ect ives E xpe ri e nc e an application of the Distributive Property P rac t i c e multiplication facts Learn to use the expanded algorithm to multiply 2-digit numbers De vel o p algebra skills

2 2 Ope ni ng 6 Display the following rectangle: Ask: What is the rectangle s area? How do you find its area? The area of the rectangle is 6 square units. We can find it by multiplying its length by its width (2 by 3). Display the following rectangle: Ask: What is this rectangle s area? How do you find its area? The area of the rectangle is 21 square units. We multiply 3 by 7 to find its area. Display the following polygon: Ask: What is the area of this polygon? How do you know? The polygon has area 12 square units. There are 2 squares on the top. They are sitting on top of a rectangle that is 2 by 5. That rectangle has area 10. Adding the two parts together, we add 2 to 10 to get 12 square units. So to find the area of the whole shape, we found the area of both parts and added them together. That will be helpful in today s

3 3 episode. T e ac he r prese nt s M at h game : M ul t i pl i c at i o n Al go ri t hms - E xpande d Al go ri t hm 12 Present Matific s episode M ul t i pl i c at i o n Al go ri t hms - E xpande d Al go ri t hm to the class, using the projector. The goal of the episode is to practice using the expanded algorithm for multiplication. Example : Please read the question that the episode is asking. The question is, How many of the grid squares are yellow? Ask: What is the multiplication problem on the right of the episode? Students can respond based on the episode. Ask: How do the yellow squares relate to the multiplication problem? The number of yellow squares is equal to the answer to the multiplication problem. The length and width of the whole

4 4 rectangle are the f ac t o rs of the multiplication problem. When we multiply the factors, we get the answer to the multiplication problem and we get the area of the whole rectangle. Ask: How is the whole rectangle broken up? The rectangle has been divided into 4 smaller rectangles because vertical and horizontal lines have been drawn at the 10-mark on both the x- and y-axis. Ask: What is the area of each of the small rectangles? Enter the values that the students suggest by clicking on each. If the answer is correct, a copy of the answer will float to the multiplication problem. If the answer is incorrect, the answer will be colored brown. Ask the students to add the areas of all 4 rectangles to find the total area (and final pro duc t ). Enter this answer by clicking on the. If the answer is correct, the episode will proceed to the next problem. If the answer is incorrect, the question will wiggle. The episode will present a total of six problems. Only for the first problem is the rectangle drawn. Drag the mouse to create a rectangle for all the other problems.

5 5 St ude nt s prac t i c e M at h game : M ul t i pl i c at i o n Al go ri t hms - E xpande d Al go ri t hm 12 Have the students play M ul t i pl i c at i o n Al go ri t hms - E xpande d Al go ri t hm on their personal devices. Circulate, answering questions as necessary. Cl ass di sc ussi o n 12 Display the following problem: 17 x 12 = Ask a student to come to the board to draw a rectangle that represents this problem. Ask a different student to come to the board to break this rectangle up into 4 smaller rectangles. Ask for the area of each of the smaller rectangles and write it in the appropriate place.

6 6 Ask: What is the product of 12 and 17? The product is 204. Display the following calculation: Ask: Why is one of the products within the work 30? Why isn t it just 3? We are multiplying 3 by 10. Although it is just a 1 in the problem, it is in the tens place. So it represents 1 ten. When we multiply by 3, we get 30, not 3. Ask: Why is one of the products within the work 100? Where does that come from? The 100 appears when we multiply 10 by 10. Each of the ones in the problem is in the tens place. They each stand for 1 ten. So when we multiply 10 by 10, we get 100. Ask: Why then is 12 just 12 in the work? Why doesn t it also change place values? We get 12 when we multiply 3 by 4. Both 3 and 4 are in the ones place. They represent 3 and 4, nothing greater. The product of 3

7 7 and 4 is 12, so 12 appears in our work. Let s say I multiply two 2-digit numbers together. One number has 2 in the ones place and the other has a 3 in the ones place. What number is in the ones place in the product? How do you know? A 6 will be in the ones place. Two and 3 multiply to 6. Since they are both in the ones place, the result is also in the ones place. Ask: So if I have a 6 in the product, does that mean that the factors ended in 2 and 3? Not necessarily. There are other pairs that, when multiplied, produce a 6 in the ones place: 1 and 6, 2 and 8, 4 and 4, 4 and 9, 6 and 6, and 7 and 8. Let s say I multiply two 2-digit numbers and I get the following four smaller products: 100, 30, 80, and 24. What are my two factors? How do you know? The two factors are 18 and 13. Eighteen gets split into 10 and 8. Thirteen gets split into 10 and 3. Multiplying all the parts (10 by 10, 10 by 3, 8 by 10, and 8 by 3) gives 100, 30, 80, and 24. Let s say I multiply two 2-digit numbers. Two of the four smaller products are 100 and 60. What could my two factors be? How do you know? One of them must be 16 and the other can be anything between 11 and 19 inclusive. We need ones in both tens places to get the 100. We need 6 in a ones place to get the 60. We know that neither factor can be 10, because then there would not be 4 smaller products, only 2. Let s say I multiply two 2-digit numbers. Two of the four smaller products are 100 and 90. What could my two factors be? One must be 19, and the other can be anything between 11 and 19.

8 8 Cl o si ng 5 Let s expand the problem 8 times 27 into two easier problems. We could break 27 into 20 and 7. What would we do next? We would multiply 8 by 20 and 8 by 7 to get 160 and 56. Then we add these two numbers to get the final product, 216. Instead, let s break 27 up into 25 and 2. Now what would we do? We would multiply 8 by both 25 and 2. So 8 times 25 is 200 and 8 times 2 is 16. We add 200 to 16 and get 216, our product. It is also possible to break 27 into three pieces. Let s use 10, 10, and 7. Then we would have to multiply 8 by all three pieces. How would this work? We multiply 8 by 10, 8 by 10 again, and 8 by 7. So we get 80, 80, and 56. We add these three numbers together to get 216, our product. So we split 27 three different ways, but each time we got 216 as our product. So we can split the numbers any way we want. How would you use this method to multiply 32 by 5? Responses may vary. Most students will suggest splitting 32 into 30 and 2, multiplying each of these numbers by 5, and adding the sums. Ask the students to come up with other ways to break up the numbers 32 and 5. Discuss which ways make the problem easier and which make it harder.