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Patterns and Relations
P3.1 Demonstrate understanding of increasing and decreasing patterns including:• observing and describing• extending• comparing• creating patterns using manipulatives, pictures, sounds, and actions.
Visualize and create oral, concrete, physical, pictorial, or symbolic representation for a given increasing or decreasing pattern rule and explain how the representations are related.
Research ﴾e.g., through Elders, traditional knowledge keepers, naturalists, and media﴿ and present about the role and significance of increasing and decreasing patterns in First Nations and Métis practices, lifestyles, and worldviews ﴾e.g., making of a star blanket, beading, music, and patterns found in nature﴿.
Create a concrete, physical, pictorial, or symbolic pattern ﴾increasing or decreasing﴿ and describe the pattern rule.
Describe strategies used to solve situational questions involving increasing or decreasing patterns, including determining missing elements within the pattern.
P2.2 Demonstrate understanding of increasing patterns by:• describing• reproducing• extending• creating patterns using manipulatives, pictures, sounds, and actions (numbers to 100).
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Use the colored tiles to represent the pattern.
Describe this pattern to your partner.What shape does it make?
Share in full group.
What is the pattern rule?
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The Human PyramidA group of children were forming a pyramid by kneeling on each other's backs. How many children would it take to make a pyramid with 5 children on the bottom?
Use blocks or cubes to help you solve this problem.
There are 20 children in Mrs. Muir's class. Can her students make a pyramid with 6 children on the bottom row?
Prove your answer with a representation of your work.
Be prepared to explain to the class how you solved this problem.
Problem
Record your work in your math notebook.
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There are 20 children in Mrs. Muir's class. Can her students make a pyramid with 6 children on the bottom row?
Prove your answer with a representation of your work.
Be prepared to explain to the class how you solved this problem.
Concrete Manipulatives Virtual Manipulatives
Pencil and Paper
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Pyramid # Number of students added
Total number of students
1 2 3
2 3 6
3 4 10
4 5 15
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6
7
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Pyramid # Number of students added
Total number of students
1 2 3
2
3
4
5
6
7
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TriangleNumber
Number of Blocks Added
Total Number of Blocks
1 1 1
2 2 3
3 3 6
4 4 10
5 5 15
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Figure 1
Figure 2
Figure 3
Figure 4
Figure Number
Number of Blocks Added
Total number of blocks
1 2 2
2 2 4
3 2 6
4 2 8
5 2 10
15 ? ?
Input Functionor Pattern Rule Output
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http://teams.lacoe.edu/documentation/classrooms/amy/algebra/34/activities/functionmachine/functionmachine3_4.html
In Out
1 2
2 4
3 6 Pattern Rule
The Pattern Rule is the Function
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http://standards.nctm.org/document/eexamples/chap4/4.5/index.htm#applet
Hundreds Chart and Calculator to Show number Patterns
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Hexagon Dragons
Students in Mr. Koberinski ’s class are making up their own growing patterns.
Sara uses pattern blocks to make a growing dragon.
• Use pattern blocks to build and draw the next two dragons in this pattern.• Complete the table of values.
• Predict what the tenth dragon will look like and tell how many blocks you wouldneed to build it. Explain any pattern you used to find this answer.
• CHALLENGE: Sara would like to figure out how many blocks he would need tobuild the 25th dragon without actually building it. He knows that there is a patternto his hexagon dragons.
Can you write a rule in words or a math expression thatSara can use to figure out the total number of blocks for any dragon without havingto build it?
Explain how your rule works.
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Dragon # Number of blocks added
Total number of blocks
0
1
2
3
4
5
Dragon #1
Dragon #2
Dragon #3
Input OutputFunction or Pattern Rule
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These can be printed off to use as manipulatives if needed.
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![Sky Patterns [2nd grade] - Trinity University](https://img.pdfslide.us/doc/110x75/621143fdac95da672a152fc8/sky-patterns-2nd-grade-trinity-university.jpg)