Patterns that Repeat
10 min
Narrative
This Warm-up encourages students to look for structure in the ways the symbols or colors repeat and to use grouping strategies or the structure they see (MP7) to quantify something that would be tedious to count individually. The work in this lesson prepares students to analyze and describe patterns formed by repetition later in the lesson.
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash image.
- 30 seconds: quiet think time
Teacher Instructions
- Display image.
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Task
How many tiles do you see? How do you see them?
pattern of tiles. First tile, red, asterisk. Second tile, blue, question mark. Third tile, green, exclamation mark. Fourth tile, yellow, number sign. The pattern repeats with these four tiles 4 more times. Twenty first tile, red, asterisk. Twenty second tile, blue, question mark.
Sample Response
22 tiles. Sample responses:
- I see the colors (or symbols) repeating every four tiles. It repeats 6 times and there are 2 extra tiles. 5×4 is 20, and 2 more makes 22.
- I see 6 reds (*) and 6 blues (?), and 5 greens (!) and 5 yellows (#). 6+6+5+5=22.
- I see multiple sets of red, blue, green, and yellow. Each set always starts with red and ends with yellow. There are 5 full sets and one incomplete set with only 2 tiles.
Activity Synthesis (Teacher Notes)
- “These tiles are in a pattern that follows a rule that repeats red, blue, green, yellow.”
- “How might knowing that rule help you count the tiles?” (I could just look for the yellow tiles and count by 4. I could count the number of yellow tiles and multiply by 4. Then add on how many are left.)
Standards
Building Toward
- 4.OA.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. <em>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.</em>
- 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. <span>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.</span>
15 min
20 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Patterns that Repeat
10 min
Narrative
This Warm-up encourages students to look for structure in the ways the symbols or colors repeat and to use grouping strategies or the structure they see (MP7) to quantify something that would be tedious to count individually. The work in this lesson prepares students to analyze and describe patterns formed by repetition later in the lesson.
Launch
- Groups of 2
- “How many do you see? How do you see them?”
- Flash image.
- 30 seconds: quiet think time
Teacher Instructions
- Display image.
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Record responses.
Student Task
How many tiles do you see? How do you see them?
pattern of tiles. First tile, red, asterisk. Second tile, blue, question mark. Third tile, green, exclamation mark. Fourth tile, yellow, number sign. The pattern repeats with these four tiles 4 more times. Twenty first tile, red, asterisk. Twenty second tile, blue, question mark.
Sample Response
22 tiles. Sample responses:
- I see the colors (or symbols) repeating every four tiles. It repeats 6 times and there are 2 extra tiles. 5×4 is 20, and 2 more makes 22.
- I see 6 reds (*) and 6 blues (?), and 5 greens (!) and 5 yellows (#). 6+6+5+5=22.
- I see multiple sets of red, blue, green, and yellow. Each set always starts with red and ends with yellow. There are 5 full sets and one incomplete set with only 2 tiles.
Activity Synthesis (Teacher Notes)
- “These tiles are in a pattern that follows a rule that repeats red, blue, green, yellow.”
- “How might knowing that rule help you count the tiles?” (I could just look for the yellow tiles and count by 4. I could count the number of yellow tiles and multiply by 4. Then add on how many are left.)
Standards
Building Toward
- 4.OA.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. <em>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.</em>
- 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. <span>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.</span>