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# Doubles and Halves are Patterns Too

Lesson 6 of 14

## Objective: SWBAT use repeated patterns to solve problems with doubles and halves.

## Big Idea: Can you double an odd number? Can you cut it in half? Patterns in doubles and halves help to answer these questions.

*45 minutes*

#### Warm Up

*15 min*

I start today by reviewing doubles. Early in the year the students wrote a doubles rhyme.Doubles Rhyme.docx I bring that rhyme back out for students to look at and read together. We review the doubles rhyme together.

Next I extend the doubles to tens, such as 20 + 20, 60 + 60. I ask students to write the answers in their math journals. I check for the responses over 100, so that 60 + 60 = 120 and not 102 or 112. These are common mistakes that I want to watch for and correct. I want students to be attend to the precision of place value as they add these larger doubles. (MP6)

Now that students are warmed up and thinking about doubles I ask them to put away journals and pencils and be ready to listen.

#### Resources

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#### What are Halves?

*15 min*

I begin this part of the lesson by asking what a half is? I take student responses and comment as necessary to clarify what a child might explain. (If they say "Well it is 2 pieces," I might ask, *What is special about these 2 pieces?* - they have to be the same and each be an equal part of the same whole.)

I hand each student a piece of construction paper. We will be modeling with manipulatives as we gain an understanding of half (MP4) I ask them to cut the paper in half.* How many pieces do they have now?* (2).* Did you just double the number of pieces or cut them in half?* (doubled the number of pieces).

Now I ask them to cut each piece in half again. *How many pieces do you have now?* (4). *What is half of 4?* (2). *Can you group your pieces to show the 2 halves?* (2 piles of 2). *Can anyone give me an addition sentence for the number of pieces we now have?* (2 + 2). A student might have said 1/2 + 1/2 here. This would also be correct for number of piles.

*Ok, this is pretty simple. Now would you cut all of your pieces in half. How many pieces do you have now?* (8). *What will happen when you cut each of these 8 pieces in half? How many pieces will there be?* (16). *Okay, cut each piece in half so you have 16 pieces. Can you display them in 2 equal piles of pieces which is the same as 2 halves of the whole pile of 16 pieces?* (students should create 2 sets of 8).

*What happens if I take my 16 pieces and cut each piece in half? Can anyone give me an addition sentence for how many pieces I will have?* (16 + 16 = 32). *Could we go on? What would the next sentence be?* (32 + 32 = 64). I display all of the number sentences we have created. *Does anyone see a pattern?* I listen to what students notice about doubling and the repeating of numbers to add.

*Doubles make a pattern. And when I cut things in half, it makes a pattern too.*

I give students a piece of paper marked into 3 even sections and ask them to cut it out. *Can I double an odd number?* (Yes). *Okay, so cut the 3 sections in half. How many pieces do you have?* (6). *We started with an odd number but what happened when we doubled it?* (became even). *Right. So I can double an odd number. But what happens if I try to break the odd number in half?* *Will it come out evenly? Try taking 3 of your pieces and putting them in 2 equal piles. Can you do it? Why or why not?*

*Okay, you can set your pieces to the side on your desk and in your journal write one thing you know about doubles and halves. *

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#### Independent Practice

*15 min*

I create a practice page that has word problems doubles word problems.docx based on doubles and halves. I ask students to work independently with these papers.

During this time I invite several students to meet with me to review place value. These students are struggling with this concept and I use this opportunity to give them extra instruction.

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##### Similar Lessons

###### Building Arrays

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*Resources(16)*

Environment: Urban

- UNIT 1: What and Where is Math?
- UNIT 2: Adding and Subtracting the Basics
- UNIT 3: Sensible Numbers
- UNIT 4: Sensible Numbers
- UNIT 5: Everything In Its Place
- UNIT 6: Everything in Its Place
- UNIT 7: Place Value
- UNIT 8: Numbers Have Patterns
- UNIT 9: Fractions
- UNIT 10: Money
- UNIT 11: The Numbers Are Getting Bigger
- UNIT 12: More Complex Numbers and Operations
- UNIT 13: Area, Perimeter and More Measurement
- UNIT 14: Length
- UNIT 15: Geometry
- UNIT 16: Getting Ready to Multiply
- UNIT 17: Getting Better at Addition and Subtraction
- UNIT 18: Strategies That Work

- LESSON 1: Using A Pattern to Solve A Problem
- LESSON 2: Skip Counting Patterns
- LESSON 3: Extending Partners of 10 and 100
- LESSON 4: Patterns in Larger Numbers
- LESSON 5: Larger Numbers: A Tie to Social Studies
- LESSON 6: Doubles and Halves are Patterns Too
- LESSON 7: Smiley Faces and Up
- LESSON 8: Put It Together and Take It Apart
- LESSON 9: Pets, Pets and More Pets
- LESSON 10: Larger Number Patterns
- LESSON 11: Let's Review
- LESSON 12: Patterns in Nature
- LESSON 13: Writing and Solving Number Stories
- LESSON 14: Trimester Assessment Day