##
* *Reflection: Connection to Prior Knowledge
Writing Expressions the Right Way! - Section 1: DO NOW

I was expecting the students to solve the problem by multipyling by 2, 28 times over and some students did just that. I was pleasantly surprised when I saw some different ways of solving this problem. First of all, students exhibited MP 1 by finding an entry point and not giving up on the problem. Second, some students used MP 6 by utilizing a table to keep track of their work. Finally, a handful of students made some generalizations about the math to make their math easier.

I gave students the opportunity to discuss their strategy with a partner. Any unique situations were brought to the board to show the whole group.

Using a table: This student used a table to help organize their work. The table helped them use smaller steps (multiplying by 2) and be able to see when the coins went over 50,000

Using base 4: This student said to me "I know that 1/2 of 28 is 14 so if I double up the amount daily, I can put 4 x 4 x 4 x 4 x 4... (14 times) in the calculator." This student then proceeded to multiply in groups of 2 to simplify it even more. This way was more difficult to find the day the coins went over 50,000.

Using smaller steps: This student started out by multiplying by 2, 28 times. She realized this got very difficult to keep track of her days. She then erased and started over. She broke the 2, 28 times into groups of 7. She had 4 groups. She then could find the value of 2 to the 7th power and continued the pattern. Genius!

Finally, I showed the students how to use their expressions 2 to the 28th power on the calculator. They were so mad. "Why didn't I show them this to begin with?" I told them they wouldn't have come up with so many ways to solve this problem if I did that!

*Connection to Prior Knowledge: All sorts of ways to solve this problem.....*

# Writing Expressions the Right Way!

Lesson 6 of 14

## Objective: SWBAT write numeric and algebraic expressions using words, numbers, and variables

*85 minutes*

#### DO NOW

*15 min*

The DO NOW is an **illustrative math** problem that sets them up for the learning for the day. Even though the students have not written formal expressions, they have dealt with expressions and they have worked with tables.

The problem is looking for them to write an expression using numbers. First they have to decide which option they would choose. Have students write this down. It will be interesting to see who chose they correct option. Next, students should be able to write the expression 2³ to represent the answer to the first question. If students do have difficulty with this, ask them if there is a simplified way of writing 2x2x2 or what do they notice about the numbers**?(SMP 7)** What happens when a factor repeats itself**?(SMP 6)** This will help with recall of exponents. The final question is going to require them to use a calculator and make a table. Students should be able make this decision on their own, but may need some prompting. For students that are having difficulty recognizing that this will be 2 to the 28^{th} power, have them start by making a table and looking for the pattern **(SMP 5 and 7).**

Students can work in pairs for this activity, but all students must show work. If students finish early, you can ask them on what day did they have more than 50,000 coins? **(SMP8)**

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I’ve set up this part of the lesson so that students can make connections between where they are going to see it and how they are suppose to learn it. Before discussing the words used to indicate an addition, subtraction, multiplication, or division problem, I will be having the students look at simple word problems and discussing how they know what operation should be used. I will be using the **think-pair-share** strategy for each problem. **(SMP 3 and 6)**. I don’t want students to solve the problems. The idea here is to get them thinking about how they know what operation to use for each problem. **(SMP 2)**

Once the students have done the think-pair-share, I’m going to show them the chart of words that belong to each operation. The charts are set up numerically and algebraically. They will be filling in the chart as I speak about each expression. A common misconception when writing addition and subtraction expressions is the word “than”. In order to address this, I’m going to point out the expressions that have the word “than” in them and ask them what they notice about that expression? Students should be able to say that the expression is turned around. I’m going to make sure students write this in their notes and bold or highlight the word to express its importance. I will do this for both addition and subtraction.

When discussing multiplication, it will be important to show students the many different ways to write this type of expression. The most difficult part for students to understand is that 3y means 3 times y. We will prove this in a later lesson, so for now, I tell the students when they see a number and a variable mushed together it means to multiply. You can also ask students what the 3 means to the variable. They should remember that 3 is the coefficient to y and their relationship is to multiply **(SMP 6).**

When discussing division, it will be important to show students that order matters. I always tell them that the way they read it is the way they write it. Also, remind students that the line between the two numbers means to divide. Ask students where they have seen this before to make a connection to past learning. **(SMP 8)**

**Tools: writing expressions power point and notes, words in math (math-aid.com)**

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#### Mix-Freeze-Group

*20 min*

The students have been sitting for a while so it’s time to get them up and moving around. mixfreezegroup is a nice way to get the students to do just that. This activity requires no calculations so they don’t need paper and pencil. Some student may find comfort in using their notes. This activity requires some classroom management. If students are not participating appropriately, start over and model exactly how you want it done. As students are doing each part of the mix-freeze-group, I tell them what I’m expecting to see.

Mix – students moving around room giving high 5’s or fist pumps as they pass each other

Freeze- quiet, thinking in our heads, no signaling or hand motions.

Group – Find your group, move to perimeter of the room.

Mix-Freeze-Group supports:

**SMP 2:** What does the information tell me?

**SMP 3:** Did you convince me?

**SMP6:** Am I saying exactly what I mean?

**Tools: Mix-Freeze-Group power point**

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#### Independent Practice

*10 min*

As students return to their seats, have them work independently on writing expressions. I’ve chosen several different formats for them to practice. First section has them taking the algebraic expression and writing it in words. Students should write at least two expressions for each. The next section has them answer multiply choice problems to determine the “solution” words. For example, the solution to a multiplication problem is called the product. The last independent practice section has them matching the algebraic expression to the correct word phrase.

This is pretty straight forward and I’m not anticipating any misunderstandings as students can use their notes to assist with their learning.

Go over these problems as a whole group so students have correct answers in their notes. I will be randomly calling on students to explain why they chose the answer they did.

This section supports **mathematical practice 2** by figuring out what the numbers and other information mean?

Tools: Independent Practice questions from power point

#### Resources

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#### Closure

*10 min*

The students will be filling out a **comprehension menu** so I can get a clear understanding of where they are. Students should fill out all four sections, but place a mark in the section that was most comfortable for them to solve.

The comprehension menu supports mathematical practices:

SMP1: Sense making. Students make sense of problems by looking for entry points

SMP2: Reasoning. Students make sense of mathematical relationships

SMP3: Arguing. Students create justifications for their responses

SMP5: Tools. Students use the tool strategically.

Tools: Comprehension menu

#### Resources

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- LESSON 1: Exploring Exponents
- LESSON 2: Learning About the Orders of Operations
- LESSON 3: Orders of Operations - Stations
- LESSON 4: What is Algebra?
- LESSON 5: Evaluating Expressions and Not the Emotional Kind!
- LESSON 6: Writing Expressions the Right Way!
- LESSON 7: Working with the Properties!
- LESSON 8: Area and Expressions
- LESSON 9: Exploring the Distributive Property
- LESSON 10: Are We Alike?
- LESSON 11: Expressions in the Real World
- LESSON 12: Review 6.EE.1, 6.EE.2, 6.EE.3, and 6.EE.4
- LESSON 13: Assessment Day!
- LESSON 14: Deepening our understanding