Illuminations: Patterns That Grow

Patterns That Grow

Patterns on Charts

 Students find, record, and analyze patterns on hundred and multiplication charts. They also use an online calculator to generate patterns and then record the patterns on a chart.

Learning Objectives

 Students will: find and record patterns on hundreds and multiplication charts analyze patterns on hundreds and multiplication charts use a calculator to generate patterns

Instructional Plan

 As a way of reviewing yesterday's lesson, display the Shape Tool and model how to make a pattern using this Tool. After the students have made and recorded the patterns, call them together to describe their patterns. Now show the Web site, Calculator and Hundreds Board Tool. Ask a volunteer to enter 2, +, 2, =, =, =, = into the online calculator and to describe what he or she sees on the calculator display. Ask another student to describe what happened on the online hundred chart. [The squares containing 2, 4, 6, etc. will be colored to correspond with the numbers showing on the online calculator.] Next, place the students in pairs, and give each pair one copy of the Hundreds Chart and some crayons. While some students explore patterns online, have the other students circle the patterns they find on their paper hundred chart. When the groups have located several patterns, call on volunteers to describe patterns they found. Encourage the students to find skip-counting patterns for 2’s, 5’s, and 10’s [a preparation for multiplication] and the pattern of odd and even numbers. Also encourage them to notice patterns in the tens and ones places. For independent practice, give students copies of the Multiplication Chart and ask them to color any number patterns that they notice. After students have found several patterns, call on volunteers to read one of their patterns. Then ask what other patterns the students found. You may wish to have the students record some of the patterns at the bottom of their charts.

Questions for Students

 Listen to this pattern (3, 6, 9, 12). Can you find it on the multiplication chart? What three numbers will come next when you extend this pattern? [15, 18, 21.] Tell about one pattern that you found on the hundred chart. How would you describe it to a friend? Did anyone find another pattern? How would you describe that pattern to a friend? [Student responses may vary.] How would you use a calculator to generate the pattern 1, 12, 23, 34 … ? [Add 11 to each previous number.] Suppose that you wanted to find a pattern of even numbers. Where would you look? [Both charts contain this pattern.] How would you tell a younger student to find a pattern on a hundreds chart? [Student responses may vary.]

Assessment Options

 At this stage of the unit, it is important for students to know how to: find patterns on a chart; analyze patterns on a chart. Collect the students' multiplication charts with their observations about their patterns.

Teacher Reflection

 Which students can analyze a pattern on a chart? What activities are appropriate for those who cannot do so yet? Can most of the students read a pattern? What extension activities are appropriate for those who do this well? What adjustments would I make the next time that I teach this lesson?

NCTM Standards and Expectations

 Algebra 3-5Describe, extend, and make generalizations about geometric and numeric patterns. Represent and analyze patterns and functions, using words, tables, and graphs.
 This lesson prepared by Grace M. Burton.

1 period

NCTM Resources

Principles and Standards for School Mathematics

Web Sites

 More and Better Mathematics for All Students
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