Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.7

Lesson 10.510.5 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
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: circle, square, triangle. How many squares are in the first 20 shapes?

  1. Find the complete units in 20 shapes: 6 × 3 = 18; 20 − 18 = 2
  2. Count the squares in the complete units: 6 units → 6 squares
  3. Check the 2 leftover shapes: shape 19: circle · shape 20: square
  4. Add the squares: 6 + 1 = 7
  5. There are 7 squares in the first 20 shapes.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

The border repeats: pink circle, purple square, blue triangle. What is shape number 20? Then explain how the remainder tells you.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

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.

Grade 6 Mathematics · Unit 10: Math Is...Standard MPP.7

Lesson 10.510.5 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can create and describe geometric designs using repetition, patterns, and rhythm, and use a pattern unit to predict what comes next, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    03691215182124? units?
    How many complete units fit in 25?

    A border repeats: circle, square, triangle. How many triangles are in the first 25 shapes?

    1. 1How many complete units are in 25 shapes?
    2. 2Is the 1 leftover shape a triangle?
    3. 3How many triangles are in the first 25 shapes?
    Final answer:
  2. 2Complete each step, then write the final answer.
    0369121518212427? units???
    Count the units. Then check the leftover shapes.

    A new unit has 4 shapes: circle, circle, square, triangle. It repeats. How many circles are in the first 27 shapes?

    1. 1How many complete units are there? How many shapes are left?
    2. 2How many circles are in the 6 complete units?
    3. 3Add the circles in the 3 leftover shapes. How many circles in all?
    4. 4Why must you check the leftover shapes on their own?
    Final answer:
  3. 3Complete each step, then write the final answer.

    A bracelet repeats 5 beads: red, red, blue, white, white. What color is bead number 43?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.

    A border repeats: star, moon, moon. How many moons are in the first 40 shapes?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.

    A hallway floor repeats tiles: white, black, white, gray. The hallway has 50 tiles. How many tiles are white?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.

    Circle, square, triangle repeat. Jon says shape 60 is a square, because 60 is even. What is shape 60?

    Show your work
    Final answer:

Explain your thinkingTo find shape 3,000, would you draw the border or divide? Explain what the quotient and the remainder each tell you.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help