## 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.

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. 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.

Hundreds Chart |

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

- Computer with Internet Connection
- Crayons or Markers
- Hundred Chart
- Calculators

Assessments

- 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.
- 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.]

**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?

[Answers will vary.]

**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

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.

[At this point you may wish to make pretty pasta for the students to use in this unit. Simply place uncooked pasta of various shapes in a plastic bag; add a few drops of food color and a few drops of rubbing alcohol. Shake the bag until the pieces are coated, then spread them out to dry.]

### Sorting Time

### What’s Next?

### Playing With Patterns

### More Patterns

### Multiple Patterns

### Growing Patterns

### Looking Back and Moving Forward

### Learning Objectives

Students will:

- Analyze numeric patterns
- Record numeric patterns
- Use a table to record and analyze patterns

### Common Core State Standards – Mathematics

Grade 4, Algebraic Thinking

- CCSS.Math.Content.4.OA.C.5

Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule ''Add 3'' and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way.