Exploring Other Number Patterns

Pre-K-2,3-5
1

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

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 E-Example regarding Hundred Boards. 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 hundreds chart.

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

• Computer with Internet Connection
• Crayons or Markers
• Hundreds Chart
• Calculators

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.]
Extension
Move on to the next lesson, Growing Patterns.

Questions for Students

1. 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.]

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

[The next number would be 35.]

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

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

4. 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.]

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

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?

Order, Order

Pre-K-2

In this lesson students seriate objects and review the meaning of ordinal numbers. They describe orderings in words and in pictures. [This lesson gives you an opportunity to review or teach vocabulary such as before, after, and next.] At the conclusion of the lesson, students make an entry in their portfolios. A Science extension is suggested.

Sorting Time

Pre-K-2
Students sort objects and symbols and make patterns with sorted objects. They make Venn diagrams and use their sortings to create linear patterns. They extend a pattern created by the teacher. Students will begin identifying pattern cores and reading patterns. A Social Studies connection is suggested as an extension.

What’s Next?

Pre-K-2, 3-5
In this lesson, students make patterns with objects, read patterns and find patterns in the environment. They should be encouraged to classify patterns by type (i.e. AAB, ABC). They continue learning about patterns by extending a given pattern, identifying missing elements in a pattern, and recording a pattern.

Playing With Patterns

Pre-K-2
Students use objects and symbols to make repeating linear patterns. They extend patterns and translate patterns from one modality (auditory, visual, and kinesthetic) to another. A Physical Education connection is suggested as an extension. This lesson is intended to take two class periods to ensure that all students have multiple opportunities to create original patterns.

More Patterns

Pre-K-2
Students extend their knowledge of linear patterns by recognizing and discussing familiar patterns. Students make auditory and visual patterns from names. An art activity is suggested as an extension.

Multiple Patterns

Pre-K-2
Students explore patterns which involve doubling. They use objects and numbers in their exploration and record them using a table.

Growing Patterns

Pre-K-2, 3-5
Students explore growing patterns. They analyze, describe, and justify their rules for naming patterns. Since students are likely to see growing patterns differently, this is an opportunity to engage them in communicating about mathematics.

Looking Back and Moving Forward

Pre-K-2
This final lesson reviews the work of the previous lessons. Students explore patterns in additional contexts and record their investigations. Students will rotate through center activities. Teachers may add other centers they feel will benefit the students.

Learning Objectives

Students will:

• Analyze numeric patterns.
• Record numeric patterns.
• Use a table to record and analyze patterns.

NCTM Standards and Expectations

• Recognize, describe, and extend patterns such as sequences of sounds and shapes or simple numeric patterns and translate from one representation to another.
• Analyze how both repeating and growing patterns are generated.