Patterns that Grow
10 min
Narrative
This Warm-up prompts students to analyze a visual pattern and the mathematics involved in how each step in the pattern changes. Students also familiarize themselves with a kind of pattern they will investigate closely later in the lesson.
Launch
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The number of circles is increased by 3 each time.
- The circles are organized in rows and columns like an array.
- The total number of circles is 3 times the step number.
Students may wonder:
- Is this a pattern?
- How many circles are there altogether?
- Why is it labeled “step 1,” “step 2,” “step 3,” and “step 4”?
Activity Synthesis (Teacher Notes)
- “This image shows a pattern. The rule for this pattern is to add a row of 3 circles in each step.”
- “What else do you notice about the number of circles in each step? Why do you think this happens?” (It starts as an odd number of circles, and then changes to even, then odd, over and over again because you’re adding an odd number each time. You can use multiplication to find the total number because you’re adding a group of 3 each time. Step 4 is 4 x 3, so step 5 would be 5 x 3.)
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 Grow
10 min
Narrative
This Warm-up prompts students to analyze a visual pattern and the mathematics involved in how each step in the pattern changes. Students also familiarize themselves with a kind of pattern they will investigate closely later in the lesson.
Launch
- Display the image.
- “What do you notice? What do you wonder?”
- 1 minute: quiet think time
Teacher Instructions
- “Discuss your thinking with your partner.”
- 1 minute: partner discussion
- Share and record responses.
Student Task
What do you notice? What do you wonder?
Sample Response
Students may notice:
- The number of circles is increased by 3 each time.
- The circles are organized in rows and columns like an array.
- The total number of circles is 3 times the step number.
Students may wonder:
- Is this a pattern?
- How many circles are there altogether?
- Why is it labeled “step 1,” “step 2,” “step 3,” and “step 4”?
Activity Synthesis (Teacher Notes)
- “This image shows a pattern. The rule for this pattern is to add a row of 3 circles in each step.”
- “What else do you notice about the number of circles in each step? Why do you think this happens?” (It starts as an odd number of circles, and then changes to even, then odd, over and over again because you’re adding an odd number each time. You can use multiplication to find the total number because you’re adding a group of 3 each time. Step 4 is 4 x 3, so step 5 would be 5 x 3.)
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>