Identifying Figurate Lesson 7-9 Number Patterns DATE TIME

SRB 1 Draw the next three rectangular numbers. 58-61

2 a. Complete the list of the first 10 rectangular numbers.

2, 6, 12, 20, 30, 42 56,EM4_MJ2_G4_U07_L09_001A.ai 72, 90, 110 b. How did you get your answers? Sample answer: I kept multiplying the next 2 counting numbers. I knew 42 = 6 ⁎ 7, so to find the

next rectangular number, I multiplied 7 ⁎ 8 = 56.

3 a. Continue the following pattern: 2 = 2 2 + 4 = 6 2 + 4 + 6 = 12 2 + 4 + 6 + 8 = 20 2 + 4 + 6 + 8 + 10 = 30 2 + 4 + 6 + 8 + 10 + 12 = 42 b. Describe the pattern. Sample answer: Each rectangular number is the sum of the even numbers in order, starting with 2.

c. What pattern do you notice about the number of addends and the rectangular number? The number of addends is the same as the “number” of the

rectangular number. For example, 30 is the fifth rectangular

number, and it has 5 addends. d. Describe a similar pattern with numbers. Sample answer: Each is the sum of the odd numbers in order, starting with 1. 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 = 16, and so on. 252 4.OA.5, 4.NBT.6, SMP7, SMP8 Identifying Figurate Lesson 7-9 DATE TIME Number Patterns (continued)

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4 Triangular numbers are numbers that are the sum of consecutive counting numbers. For example, the 3 is the sum of 1 + 2, and the triangular number 6 is the sum of 1 + 2 + 3.

a. Continue the patterns in the table below to find a connection between triangular numbers and rectangular numbers.

Triangular Number 1 3 6 10 15

Model

EM4_MJ2_G4_U07_L09_004A.ai Rectangular Number EM4_MJ2_G4_U07_L09_003A.ai2 6 EM4_MJ2_G4_U07_L09_005A.ai12 EM4_MJ2_G4_U07_L09_006A.ai EM4_MJ2_G4_U07_L09_002A.ai 20 30

Array

b. What patterns doEM4_MJ2_G4_U07_L09_007A.ai you notice?EM4_MJ2_G4_U07_L09_008A.ai SampleEM4_MJ2_G4_U07_L09_009A.ai answer:EM4_MJ2_G4_U07_L09_010A.ai Each EM4_MJ2_G4_U07_L09_011A.aitriangular number is always half of the corresponding rectangular number. For example, the fourth triangular number is 10 and the fourth rectangular number is 20.

c. The 20th rectangular number is 420. What is the 20th triangular number? 210 Explain how you got your answer. Sample answer: I divided 420 by 2.

d. Draw an array to show the rectangular number 20. Divide the array with a line to show the connection between rectangular and triangular numbers.

EM4_MJ2_G4_U07_L09_012A.ai

4.OA.5, 4.NBT.6, SMP7, SMP8 253