C1.4 Create and describe patterns to illustrate relationships among whole numbers up to 1000.

Activity 1: Finding Relationships Using Place Value


Have students represent each of the following in the table using base-10 blocks.

580

5 hundreds

+ 8 tens

image Numbers represented by blocks with hundredths and tenths. 580: 5 hundredths and 8 tenths, 580: 4 hundredths and 18 tenths, 580: 3 hundredths and 28 tenths, 580: 2 hundredths and 38 tenths, 580: one hundredth and 48 tenths, 580: 58 tenths

580

4 hundreds

+ 18 tens

580

3 hundreds

+ 28 tens

580

2 hundreds

+ 38 tens

580

1 hundred

+ 48 tens

580

0 hundred

+ 58 tens

Ask students to describe this number pattern. Ask questions such as:

  • What do you notice? What is different in each representation?
  • What relationships exist between the numbers? Explain your reasoning.

Invite students to create a similar pattern by choosing a number from 0 to 100.

Activity 2: Create a Pattern and Show the Relationship Between the Multiplication and Division Facts


Present the ordered list below to students.

2 × 1 = 2

2 × 2 = 4

2 × 3 = 6

2 × 4 = 8

2 × 5 = 10

2 × 6 = 12

2 × 7 = 14

2 × 8 = 16

2 × 9 = 18

2 × 10 = 20

From the list presented above, have students create an ordered list of related operations to represent the relationships that exist between multiplication and division.

Ask students questions such as:

  • What do you notice when you compare the ordered list for division with the ordered list for multiplication?
  • What relationships exist between the numerical facts? Justify your answer.