##
* *Reflection: Diverse Entry Points
Variables - Section 2: Variable Puzzle

I was surprised that one of my students began at the bottom of this puzzle by thinking that the only multiplication problem with a product of 5 is 1x5. He then worked his way up the symbols, rather than beginning with the division problem at the top. This was a wonderful discussion about how you would have to test the values for the variables in different locations.

*Surprise*

*Diverse Entry Points: Surprise*

# Variables

Lesson 3 of 15

## Objective: Students will be able to use multiplication or division to solve for a variable.

## Big Idea: Children will learn the term variable and then work to "attack" a problem using what they know about the relationship between multiplication and division to solve for an unknown.

*55 minutes*

#### Warm Up

*10 min*

It is a good teaching move to review a problem done in a previous lesson as a class at the beginning of some lessons. I find this a good way to introduce a concept with some familiar work. This way the students don't have to work their understandings of more than one or two concepts. Today, I chose to use a word problem from yesterday to review and then model today's concept.

*Boys and girls, let's look at a problem from yesterday. I would like to discuss our thinking around it and then offer some tips. *

The problem,* "There are 10 baseball cards in each trading card pack. Joe bought 9 packs. How many cards did he buy altogether? * An equation to best represent this word problem is already on the board. The students completed this problem yesterday.

The goal today is to focus on the reasoning used to solve. I pay particular attention to those students who realize they have both factors. The equation should read 9 x 10 = 90, as the 10 is the group size and 9 is the multiplier. However, this is a heavy duty concept and it may take time for this structure to be realized.

*Excellent thinking mathematicians. It is important to know what a word problem tells you and to understand what you are solving for. In today's lesson, we are going to look at an idea called variables. A variable, in math, is a lower case letter that represents a number we don't know yet. Let's take a look.*

*expand content*

#### Variable Puzzle

*20 min*

At this point, I have a puzzle prepared for students to copy into their Math Reflection Journals. You may also consider creating it as a label that the children can just place in their journals.

The object of this puzzle is that the children will "comfortably struggle" with finding the value of each symbol. When I give the students the task, I expect some confusion, but the excitement of solving for the symbol carries them through. Prior to understanding the rich tasks coupled with perseverance described in Common Core standards, I would not have tried this. I was pleasantly surprised by my students' response to this work.

*Boys and girls, after you copy this puzzle into your reflection journals, use what you know about multiplication, division, and patterns to figure out what number each symbol represents. Remember, the value of each symbol remains the same in each equation. You may work alone or with your table group.*

After some time, allow children to approach the board and present what they think each symbol represents and why they think so. Encourage the rest of the class to comment using the talking moves.

*Wow! What fantastic thinking and problem solving. You are all working hard to test ideas without worrying about mistakes and you are really finding interesting patterns. Great Job! Now let's look at some other math equations just like they are puzzles.*

#### Resources

*expand content*

You may want to use word problems that you make up, or a page in your resource workbook of a program you use in your school. I have decided to use a page of word problems in the workbook supplied by my district, but instead of only solving, I am asking the students to write an appropriate equation with a variable. They should then solve for the variable.

This is good practice and in both solving word problems, and choosing the correct equation to represent the story using a variable.

#### Resources

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#### Home Practice

*5 min*

The assignment I have chosen for homework is pretty difficult, but it will give me a lot of insight on what students understand about multiplication, division, and variables. For children that I know will have a hard time off the bat, I work with them on sentence starters with blanks for their numbers and variables. For example:

**There are ____trees. Each tree has ________apples on it. How many apples are there altogether? Use "a" to represent______________.**

*Mathematicians, for homework tonight, I would like you to write 3 word problems. Your partner will write an equation with a variable in them tomorrow and solve for that variable. Please make sure you have an answer key on another sheet of paper. You may write word problems that focus on multiplication or division. Have fun!*

*expand content*

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- UNIT 1: Developing Mathematical Practices
- UNIT 2: Understanding Multiplication
- UNIT 3: Using Multiplication to Find Area
- UNIT 4: Understanding Division
- UNIT 5: Introduction To Fractions
- UNIT 6: Unit Fractions
- UNIT 7: Fractions: More Than A Whole
- UNIT 8: Comparing Fractions
- UNIT 9: Place Value
- UNIT 10: Fluency to Automoticity
- UNIT 11: Going Batty Over Measurement and Geometry
- UNIT 12: Review Activities

- LESSON 1: It's As Basic As That
- LESSON 2: Naming Arrays
- LESSON 3: Variables
- LESSON 4: X Represents Groups Of
- LESSON 5: Each Orange Had 8 Slices
- LESSON 6: Creating a Word Problem Book
- LESSON 7: Equal Groups on a Number Line
- LESSON 8: Collections of Equal Groups
- LESSON 9: Explaining Multiplication
- LESSON 10: The Story Of Multiplication Day 1
- LESSON 11: The Story of Multiplication Day 2
- LESSON 12: Making Equal Groups Part 1
- LESSON 13: Making Equal Groups Part 2
- LESSON 14: Associative Property
- LESSON 15: Associative Property With Manipulatives