Developing Mathematical Thinking Institute PMA Grade 2 Sequencing

Developing Mathematical Thinking Institute

PMA – Grade 2 Sequencing – Counting © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 2

Sequencing What’s involved: • Finding patterns • Counting forward and backward • Recognizing numbers • Determining quantity Why it matters: • Builds one-to-one correspondence • Begins to build proportional reasoning, which is important for many math ideas and STEM careers • Leads to efficient computation and stronger number sense and flexible thinking © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 3

Sequencing: Counting Materials • Paper or writing space © DMTI (2019) | RESOURCE MATERIALS DMTINSTITUTE. COM 4

Sequencing: Counting Activity I • Have the child practice counting by 1’s. 1. Follow the bar model example below. 2. Count forward from 0 to 10 by 1’s. 3. Now count from 10 backwards to 0 0 1 2 3 4 5 6 7 © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 8 9 10 5

Sequencing: Counting Activity I • Have the child practice drawing a bar model by iterating (copying) units of 1. 1. Draw a rectangle and label it 0 on the left and 1 on the right. 2. Iterate another unit of 1 by drawing the same size rectangle connected and to the right of the first one. Label the end of this unit 2. 3. Continue iterating units of 1 until the child gets to 10. 4. Now practice counting the numbers from 0 to 10 and back down to 0 0. 1 2 © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 6

Sequencing: Counting Activity II • Have the child practice counting by 1’s forwards and backwards given the following situations: (0 to 7 to 0) (2 to 10 to 2) (0 to 12 to 0) (10 to 19 to 10) (20 to 29 to 20) (25 to 45 to 25) (0 to 25 to 0) 50 to 30) (50 to 75 to 50) (75 to 100 to 75) (0 to 100) © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com (30 to (100 to 0) 7

Sequencing: Counting Activity II • Have the child practice drawing bar models to represent the following situations. (0 to 7 to 0) (0 to 12 to 0) (20 to 29 to 20) (25 to 45 to 25) (50 to 75 to 50) (75 to 100 to 75) © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 8

Sequencing: Counting Activity III • Count by 5’s from 0 to 50 and back down to 0. 1. Follow the bar model example below. 2. Count forward from 0 to 50 by 5’s. 3. Now count from 50 backwards by 5’s to 0. 0 5 10 15 20 25 30 35 © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 40 45 50 9

Sequencing: Counting Activity III • Have the child practice drawing a bar model by iterating (copying) units of 5. 1. Draw a rectangle and label it 0 on the left and 5 on the right. 2. Iterate another unit of 5 by drawing the same size rectangle connected and to the right of the first one. Label the end of this unit 5. 3. Continue iterating units of 5 until you get to 50. 4. Now practice counting the numbers from 0 to 50 and back down to 0 0 by 5 5’s. 10 © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 10

Sequencing: Counting Activity III • Ask the following questions based on the bar model of counting by 5’s to 50. 1. What patterns do you notice when counting by 5’s? 2. What is staying the same and what is changing? Why? 0 5 10 15 20 The ones digit will always be a 0 or 5. 25 30 35 40 45 50 The tens digit keeps changing every other number. These patterns happen because every time you add 5 + 5 you compose a new unit of ten. © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 11

Sequencing: Counting Activity IV • Create a bar model by 10’s from 0 to 50. • Create a bar model by 10’s from 25 to 105. 1. What patterns do you notice when counting by 10’s? 2. What is staying the same and what is changing? Why? • Create a bar model by 2’s from 0 to 20. 1. What patterns do you notice when counting by 2’s? 2. What is staying the same and what is changing? Why? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 12

Sequencing: Counting Activity V • Have the child practice counting by 1’s forwards and backwards given the following situations: (50 to 100 to 50) (75 to 120 to 75) (0 to 120 to 0) • Have the child practice counting by 10’s forwards and backwards given the following situations: (50 to 100 to 50) (75 to 120 to 75) (0 to 120 to 0) • Have the child practice counting by 5’s forwards and backwards given the following situations: (50 to 100 to 50) (75 to 120 to 75) (0 to 120 to 0) © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 13

Sequencing: Counting Activity VI • Create a bar model by 4’s from 0 to 40. 1. What patterns do you notice when counting by 4’s? 2. Count by 4’s from 0 to 40 and back down to 0. 3. What is staying the same and what is changing? 4. What is the pattern happening with the ones digit? 5. What is the pattern happening with the tens digit? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 14

Sequencing: Counting Activity VI • Create a bar model by 8’s from 0 to 80. 1. What patterns do you notice when counting by 8’s? 2. Count by 8’s from 0 to 80 and back down to 0. 3. What is staying the same and what is changing? 4. What is the pattern happening with the ones digit? 5. What is the pattern happening with the tens digit? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 15

Sequencing: Counting Activity VI • Create a bar model by 3’s from 0 to 30. 1. What patterns do you notice when counting by 3’s? 2. Count by 3’s from 0 to 30 and back down to 0. 3. What is staying the same and what is changing? 4. What is the pattern happening with the ones digit? 5. What is the pattern happening with the tens digit? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 16

Sequencing: Counting Activity VI • Create a bar model by 6’s from 0 to 60. 1. What patterns do you notice when counting by 6’s? 2. Count by 6’s from 0 to 60 and back down to 0. 3. What is staying the same and what is changing? 4. What is the pattern happening with the ones digit? 5. What is the pattern happening with the tens digit? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 17

Sequencing: Counting Activity VI • Create a bar model by 9’s from 0 to 90. 1. What patterns do you notice when counting by 9’s? 2. Count by 9’s from 0 to 90 and back down to 0. 3. What is staying the same and what is changing? 4. What is the pattern happening with the ones digit? 5. What is the pattern happening with the tens digit? © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 18

Sequencing: Counting Activity VII • Have the child practice counting by 5’s, 10’s, and 100’s forwards and backwards given the following situations: (100 to 900 to 100 by 100’s) (500 to 1000 to 500 by 100’s) (750 to 1000 to 750 by 10’s) (895 to 1000 to 895 by 5’s) (353 to 453 to 353 by 10’s) (284 to 984 to 284 by 100’s) (96 to 146 to 96 by 5’s)© DMTI (2019) | RESOURCE MATERIALS | (929 to 1009 to 929 by www. DMTinstitute. com 19

“The Developing Mathematical Thinking Institute (DMTI) is dedicated to enhancing students’ learning of mathematics by supporting educators in the implementation of researchbased instructional strategies through high-quality professional development, curricular resources and assessments. " For more information contact Dr. Brendefur at jonathan@dmtinstitute. com © DMTI (2019) | RESOURCE MATERIALS | www. DMTinstitute. com 20