##
* *Reflection: Staircase of Complexity
Doubles and Halves are Patterns Too - Section 2: What are Halves?

In math it is important to get students to explain their thinking. Young children do not think in mathematical terms (MP2) without some help in understanding those terms. As students were looking at patterns, I wanted them to understand how doubling is not the same as counting by twos. I could tell them that, but it was important for me to step back and let students discover this on their own. My goal is for students to be able to verbalize about what doubling is, but I wanted them to make that discovery.

When I had them cut the paper in half, one piece doubled to two. Most students were really clear that if they cut those in half they would have four pieces, but when I asked them to cut the four pieces in half to double the amount, some students predicted that there would be 6 pieces and some predicted 8. Students are exploring halvesI listened to why students thought that there might be 6 or 8 and could see that some were using a skip count pattern instead of a doubling pattern. With a few more cuts, the students were grasping what the term of doubling meant so that they could explain it.

*Staircase of Complexity: Predicting from Patterns*

# 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

*Favorites(12)*

*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