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Patterns on Charts

3-5
1
Algebra
Grace M. Burton
Location: unknown

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.

As a way of reviewing yesterday's lesson, display the Shape Tool and model how to make a pattern using this Tool.

appicon Shape 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.

appicon 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.

pdficon  Hundreds Chart 

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.

pdficon  Multiplication Chart 

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.

Assessments 

  1. 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.
     
  2. Collect the students' multiplication charts with their observations about their patterns.
 

Questions for Students 

1. 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.]

2. 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.]

3. How would you use a calculator to generate the pattern 1, 12, 23, 34 … ?
 

[Add 11 to each previous number.]

4. Suppose that you wanted to find a pattern of even numbers. Where would you look?

[Both charts contain this pattern.]

5. How would you tell a younger student to find a pattern on a hundreds chart?

[Student responses may vary.]

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?
 
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What’s Next?

3-5
Students begin their study of growing patterns by making linear patterns with pattern block shapes using several pattern cores. They extend a partner’s pattern and find the missing element in a pattern.

Growing Patterns

3-5
Students use numbers to make growing patterns. They create, analyze, and describe growing patterns and then record them. They also analyze a special growing pattern called Pascal’s triangle.
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Exploring Other Number Patterns

3-5
Students analyze numeric patterns, including Fibonacci numbers. They also describe numeric patterns and then record them in table form.

Looking Back and Moving Forward

3-5
In this final lesson of the Unit, students use logical thinking to create, identify, extend, and translate patterns. They make patterns with numbers and shapes and explore patterns in a variety of mathematical contexts.

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

Common Core State Standards – Mathematics

Grade 3, Algebraic Thinking

  • CCSS.Math.Content.3.OA.D.9
    Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.

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.