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MODULE 1 LESSON 2 Relate multiplication to the array model.

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SPRINTS Today you’re going to learn about and do your first set of sprints. There are 2 sprints – A and B You will have 60 seconds to do as many problems as you can. I do not expect you to finish all of them, just as many as you can, trying for your personal best. Your sprint will be placed face down on your desk – do not look at your sprint until I give you the signal. Thumbs up if you understand. 1 minute

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SPRINTS Stop! Circle the last problem you completed. I will read just the answers. If you got the answer right, call out “Yes!” If you made a mistake, circle it (no noise). Touch your nose if you understand or raise your hand if you have any questions. Now, at the top of the page, write the number of problems you got correct. This is your personal goal for Sprint B. Thumbs up when you’re done.

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SPRINTS Time to do Sprint B. Once again, you will have 60 seconds to do as many problems as you can. I do not expect you to finish all of them, just as many as you can, trying for your personal best. Remember – try to meet or beat your number correct from Sprint A. Do not flip sprint B over until you have been given the signal. Thumbs up if you’re ready. 1 minute

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SPRINTS Stop! Circle the last problem you completed. I will read just the answers. If you got the answer right, call out “Yes!” If you made a mistake, circle it (no noise). Touch your nose if you understand or raise your hand if you have any questions. Stand up if you got more correct on the second Sprint than on the first. (For example if I got 20 right on Sprint A and 26 right on Sprint B– I got 6 more right than Sprint A). Keep standing until I say the number that tells how many more you got right on Sprint B. If you got exactly three more right on Sprint B than on Sprint A, when I say three, you sit down. Cross your arms if you’re ready.

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Group Counting Let’s count to 18 forward and backward. I want you to whisper, whisper, and then speak numbers. Example: whisper number 1, whisper number 2, and speak number 3. Watch my fingers to know whether to count up or down. A closed hand means stop. Thumbs up if you’re ready. 123456789 10 111213 14 15 16 17 18

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Group Counting Cont. Let’s count to 18 forward and backward again. This time, think every number instead of whispering. I will not show the numbers – so you really need to THINK Thumbs up if you understand. What did we just count by? Turn and talk to a partner. What did we just count by? Turn and talk to a partner.

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Group Counting Cont. Let’s count by threes. Remember I can change direction any time. Hold up three fingers if you’re ready.

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Add Equal Groups How many groups are circled? How many are in each group? Write as an addition sentence. Write a multiplication sentence for 3 twos equals 6.

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Add Equal Groups How many groups are circled? How many are in each group? Write as an addition sentence. Write a multiplication sentence for 3 fives equals 15.

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Problem of the Day Jordan uses 3 lemons to make 1 pitcher of lemonade. He makes 4 pitchers. How many lemons does he use altogether? Use the RDW process to show your solution.

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Concept Development Before we get started make sure you have: A 3s template (vertically like picture shown to the right) A blank piece of paper Thumbs up when you have everything

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Look back at Jordan’s lemons. Compare the way his lemons are organized with the groups of 3 circles on your template. (Touch your nose if you want to share your thinking) Many students are noticing straight lines on the template. Let’s call a straight line going across a row. Use your blank paper to cover all but the top row.

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Uncover 1 row at a time in the picture. As you uncover each row, write the new total number of circles to the right of it. When the picture pops up on the screen say how many circles you counted.

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Let’s Check Our Work Take 10 seconds to find how many rows of 3 you counted. At the signal WHISPER how many. 10 ROWS TRUE OR FALSE – 10 rows of 3 circles equals 30 circles. Stand up when you have your answer.

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10 x 3 = 30 Use the picture on your template to talk with a partner about why this equation is true. We call this type of organized picture an array.

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Take a look at this array. At the signal, tell how many rectangles are in the top row. 4 RECTANGLES! The size of 1 row is 4 rectangles. Each row of 4 can also be called a group of 4. At the signal, tell how many groups of four are in the array. 3 groups of four!

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_____ x ____ = _____ To write this as an equation, we first write the number of groups. How many groups? Next, we write the size of the group. How many rectangles are in each group? 3 GROUPS 4 IN EACH GROUP Skip-count to find the total number of rectangles in the array. 4 8 12

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Redraw Equal Groups as Arrays The drawing shows 3 equal groups of 5. On your personal white board or your math notebook, re-draw the picture as an array with 3 rows of 5. Do 2 jumping jacks when you’re done. Write a multiplication expression to describe your array. Remember, an expression is different from an equation because it doesn’t have an equal sign. Do 4 jumping jacks when you’re done. 3 x 5 3 (groups) of 5 (in each group) SKIP COUNT TO FIND THE TOTAL NUMBER OF TRIANGLES IN THE ARRAY 5 10 15 With a partner, compare my drawing with your array. Which is easier to count? Why? MY DRAWING

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PROBLEM SET

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