Lesson 10.5Math is Boundless
Start hereWords, worked example, and sentence starters
Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| repetitionSpanish: repetición | The same object, shape, or form repeated multiple times. | The same tile, over and over, all the way along the border. |
| patternSpanish: patrón | A set of objects or shapes that are repeated and arranged in a regular order. | Circle, square, triangle, circle, square, triangle … |
| pattern unitSpanish: unidad del patrón | The smallest chunk of a pattern that repeats. | circle · square · triangle — the chunk that starts over. |
| rhythmSpanish: ritmo | A design element created by varying the placement, size, orientation, or order of the same objects or shapes. | The same circles, but sizes and spacing change as your eye travels. |
| predictabilitySpanish: previsibilidad | Being able to know what comes next because the design follows a rule. | Shape 25 must be a circle — the unit repeats every 3. |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A border repeats: pink circle, purple square, blue triangle, pink circle, purple square, blue triangle, ...
- The pattern unit is 3 shapes long: circle, square, triangle.
- To predict shape number 12, I divide: 12 ÷ 3 = 4 with no remainder, so shape 12 ends a complete unit — it is the blue triangle.
- The next three shapes after any complete unit will be a pink circle, a purple square, and a blue triangle.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
The pattern unit is still 3 shapes long.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The pattern unit is , so this is rather than .
- I have seen a geometric pattern on .
- Its pattern unit is .
- A design with only repetition feels .
Word bank repetitionpatternpattern unitrhythmpredictability
Watch outA common mistake
Calling every repeated design a 'pattern.' One identical shape repeated is repetition; a pattern needs a unit of shapes repeating in a regular order; and rhythm varies the shapes' size and order, so it is neither.
Lesson 10.5Math is Boundless
Version ASupported practice
Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next.
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1Circle the letter of the best answer. Show how you know.
In geometric design, what is repetition?
- AA set of different shapes arranged randomly
- BShapes that vary in size and order of appearance
- CAny drawing that uses color
- DThe same object or shape repeated multiple times
Hint The word itself is a clue: something repeats.
Show your work -
2Circle the letter of the best answer. Show how you know.
A border shows: pink circle, purple square, blue triangle, pink circle, purple square, blue triangle. What are the next three shapes?
- ABlue triangle, purple square, pink circle
- BPink circle, purple square, blue triangle
- CPink circle, blue triangle, purple square
- DIt is impossible to predict
Hint Find the chunk that repeats.
Show your work -
3Circle the letter of the best answer. Show how you know.
In the circle-square-triangle border, how many shapes long is the pattern unit?
- A1 shape
- B2 shapes
- C3 shapes
- D6 shapes
Hint Where does the pattern start over?
Show your work -
4Circle the letter of the best answer. Show how you know.
What is rhythm in geometric design?
- AThe same objects or shapes with varying placement, size, or order of appearance
- BOne shape repeated exactly, over and over
- CShapes arranged in a strict, predictable order
- DA design with no shapes at all
Hint Rhythm uses the SAME shapes as a pattern might.
Show your work
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5Answer in complete sentences.
Where have you seen geometric patterns decorating a building, clothing, or artwork? Describe the design.
Sentence starter I have seen a geometric pattern on ___ .
Its pattern unit is ___ .Write your answer -
6Answer in complete sentences.
How would you compare the visual appeal of a design with just repetition and a design with patterns?
Sentence starter A design with only repetition feels ___ .
A design with patterns feels ___ because ___ .Write your answer
Explain your thinkingPick a card you called rhythm and your partner called repetition. What is the pattern unit, and what would have to change for it to stop being predictable?
Sentence starter The pattern unit is ___, so this is ___ rather than ___.
Lesson 10.5Math is Boundless
Version BCore practice
Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next.
-
1Circle the letter of the best answer. Show how you know.
The pattern unit circle-square-triangle repeats. What is shape number 12?
- AThe pink circle
- BThe blue triangle
- CThe purple square
- DIt cannot be determined
Show your work -
2Circle the letter of the best answer. Show how you know.
Same pattern. What is shape number 20?
- AThe purple square
- BThe pink circle
- CThe blue triangle
- DThe 20th shape starts a new pattern
Show your work -
3Circle the letter of the best answer. Show how you know.
How many COMPLETE pattern units appear in the first 18 shapes of the circle-square-triangle border?
- A3 units
- B6 units
- C9 units
- D15 units
Show your work -
4Circle the letter of the best answer. Show how you know.
How is a design with rhythm different from a pattern?
- ARhythm uses shapes and a pattern does not
- BA pattern varies its shapes and rhythm never does
- CThere is no difference between them
- DRhythm varies size, orientation, and order, so it often lacks predictability; a pattern repeats in a regular order
Show your work
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5Answer in complete sentences.
A painting shows circles whose colors, sizes, and thickness vary, along with the number of concentric circles inside each one. Describe how the painting demonstrates rhythm.
Write your answer -
6Answer in complete sentences.
If a new row of circles were added to the rhythm painting, what would they look like? Explain your thinking.
Write your answer
Explain your thinkingPick a card you called rhythm and your partner called repetition. What is the pattern unit, and what would have to change for it to stop being predictable?
Lesson 10.5Math is Boundless
ChallengeExtension
Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next.
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1Write the letter of the matching item on each line.
Match each vertex arrangement to its angle sum — and what it means for tessellation.
- 4 squares at a vertex
- 6 equilateral triangles at a vertex
- 3 regular hexagons at a vertex
- 3 regular pentagons at a vertex
- A4 × 90° = 360° — no gaps
- B6 × 60° = 360° — no gaps
- C3 × 120° = 360° — no gaps
- D3 × 108° = 324° — a gap remains
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2Circle the letter of the best answer. Show how you know.
The circle-square-triangle pattern continues. What is shape number 25?
- AThe purple square
- BThe blue triangle
- CThere is no shape 25
- DThe pink circle
Show your work -
3Circle the letter of the best answer. Show how you know.
Which element of geometric design often LACKS predictability?
- ARhythm
- BRepetition
- CPattern
- DThe pattern unit
Show your work
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4Answer in complete sentences.
Create a design that has repetition, pattern, AND rhythm. Describe (or sketch) it, and label where each element appears.
Write your answer -
5Answer in complete sentences.
Why do you think the lesson is called 'Math is Boundless'? Use repetition, pattern, and rhythm in your answer.
Write your answer