Illuminations: Powerful Patterns

Powerful Patterns


Exploring Other Number Patterns

Students make and extend numerical patterns using hundred charts. They also explore functions at an intuitive level. This lesson integrates technology.

Learning Objectives

 
Students will:
  • describe number patterns in a hundred chart
  • skip count by 2’s, 5’s and 10’s

Materials

 
Computer with Internet Connection
Crayons or Markers
Hundred Chart
Calculators

Instructional Plan

To begin the lesson, display a table such as the following on which data can be recorded.

 

Number of People
Body Part 1  2  3  4  5  6 
Eyes      
Toes on 1 Foot      
Toes on 2 Feet      

 

Ask students to suggest entries for the first row. Then ask how the numbers in the answers are changing. Repeat with other rows. Explain that each row shows a number pattern because when you add the same number over and over, you create a pattern. Tell students you can use a hundred chart to show how these numbers create patterns.

Access the NCTM E-Example regarding Hundred Boards found on the NCTM Standards Web site. Ask a volunteer to enter 2, +, 2, =, =, =, = into the online calculator and to describe what he or she sees on the display. Make sure students understand that each time they press the = sign, the calculator adds 2 to the previous answer. Ask another student to describe what happened on the hundred chart. Have students check the numbers displayed on the hundred chart with the answers from the chart above. Repeat this process for 5 and 10. Ask students how they would use a calculator to find the pattern for a different number.

Now put the students into pairs. Allow some pairs to continue exploring patterns online and give each of the other pairs a calculator, crayons, and a copy of the Hundreds Chart. Have these students use the calculators to skip count by 3 and then circle the patterns they find on their paper hundred chart.

Hundred Chart Hundreds Chart

Rotate students so that they all get to explore patterns on the computer.

Questions for Students

 
If there were 2 boys, how many eyes would there be? How many noses? How many toes?
[Two boys have 4 eyes. Two boys have 2 noses. Two boys have 20 toes.]

What would come next in the pattern 5, 10, 15, 20, 25, 30, …?

[The next number would be 35.]

In the pattern 2, 4, 6, 8, 10, what will come next? And then what?

[The next number will be 12, then 14.]

My pattern is 6, 16, 26, 36, 46. What are the next three numbers in my pattern? How are the numbers changing?

[The next three numbers will be 56, 66, 76. Each number is 10 more than the last number. Students may also suggest that the tens place increases by one in each number.]

Tell about one pattern you found on the hundred chart. How would you describe it to a friend?

[Answers will vary.]

Assessment Options

 
  1. Provide each student with a calendar for the present month and ask the students to color one number pattern they notice. After students have had time to find a pattern, call on a volunteer to read her pattern. Then ask what other patterns the students found. See if students are able to replicate the patterns mentioned in class or find new patterns.
  2. Provide students with a hundreds chart with the numbers 1, 3, 5, 7 shaded in. Ask students to continue this pattern. You can have students write one sentence at the bottom of the paper telling how they found the pattern or discuss how they found the pattern. [Students may suggest any of the following explanations for how they determined which numbers to color: I colored the odd numbers. I added 2 to each number. I did an AB pattern. I left one box blank and colored the next block.]

Teacher Reflection

 
  • Were students able to connect the Number of People chart to skip counting on the calculator? If not, what could you do next time to help them make the connection?
  • Were students able to skip count on the calculators? If not, what was confusing?
  • Were students able to describe how numbers changed in a skip counting pattern?
  • Which students were able to skip count without calculators?
  • Did students make connections to prior experiences, such as adding 10 to a number or calendar patterns? How can I encourage students to make additional connections?
  • Did I help students use what they know about patterns to recognize their own mistakes in hundred chart patterns?

NCTM Standards and Expectations

 
Algebra Pre-K-2
  1. Analyze how both repeating and growing patterns are generated.
  2. Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
This lesson prepared by Grace M. Burton.
  
1 period   

NCTM Resources

Principles and Standards for School Mathematics

Web Sites


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