# Lesson 7

## 7.1: Dust Off Those Cobwebs (5 minutes)

### Warm-up

The purpose of this warm-up is to remind students of some familiar mathematical contexts, to prepare them for engaging with some word problems later in the lesson.

### Student Facing

1. A person walks 4 miles per hour for 2.5 hours. How far do they walk?
2. A rectangle has an area of 24 square centimeters. What could be its length and width?
3. What is the area of this triangle?

### Student Response

For access, consult one of our IM Certified Partners.

## 7.2: A Spreadsheet Is a Calculator (10 minutes)

### Optional activity

The purpose of this activity is for students to learn and practice how to use a spreadsheet to do calculations using some common operations, including some illustrations of how parentheses can be used to indicate order of operations.

### Launch

Ensure that each student has access to a spreadsheet. If using the digital version of the materials, there is a spreadsheet in the Math Tools.

Display the same type of spreadsheet students are using (or the student task) on your projector, and demonstrate how to use it as a calculator. Be sure to communicate:

• The = symbol often must be typed as the very first thing in the cell. (Demonstrate what happens if the = symbol is not included.)
• How to "submit" the formula so the computation takes place. If student devices have a keyboard, it's likely the enter key. On a tablet, they may have to tap a check mark.
• Symbols to use for various operations, and how students can find them on their keyboards. Be sure to include:
• - for subtract or for a negative number (this symbol does double duty in most spreadsheets)
• * for multiply
• / for divide or for a fraction
• ^ for exponent
• . for a decimal point
• ( ) to tell it what to compute first. (often needed around fractions)

Consider displaying these commands for all to see and leaving them visible while students work on the activity.

Representation: Develop Language and Symbols. Display or provide charts with symbols and meanings. The chart should include all the symbols to use for various operations in a spreadsheet. Be sure to demonstrate using the commands in the spreadsheet as a calculator.
Supports accessibility for: Conceptual processing; Memory

### Student Facing

Use a spreadsheet to compute each of the following. Type each computation in a new cell, instead of erasing a previous computation.

• $$2+7$$
• $$2−7$$
• $$7 \boldcdot 2$$
• $$7^2$$
• $$7 \div 2$$
• $$\frac17$$ of 91
• $$0.1 \boldcdot 2+3$$
• $$0.1(2+3)$$
• $$13 \div \frac17$$
• The average of 2, 7, 8, and 11

### Student Response

For access, consult one of our IM Certified Partners.

### Anticipated Misconceptions

If students want to modify their formula, they should try to double click on the cell. If students forget which symbol to use for an operation or how to use the keyboard to type it, draw their attention to the display from the launch.

### Activity Synthesis

Ask students to compare their answers with a partner and resolve any discrepancies. Help students understand how to use parentheses to get the spreadsheet to perform the desired calculation. For example, to compute $$7 \div \frac12$$, you may have to type = 7 / ( 1 / 2 ).

Note that the average of 2, 7, 8, and 11 can be calculated by typing =(2+7+8+11)/4 but also by typing =MEAN(2,7,8,11) or =Average(2,7,8,11) depending on the spreadsheet software.

Representing, Speaking, Listening: MLR 7 Compare and Connect. Invite students to share with a partner what they typed to do each computation. As students investigate each others’ work, ask them to consider what is the same and what is different about the formatting of computations in cells. Ask students how these observations help them determine whether there is a difference in their answers. Listen for and amplify the language students use to describe how to use parentheses in spreadsheets. This will help students make sense of different ways to express the same computation in a spreadsheet using a variety of examples. Design Principle(s): Optimize output (for representation); Maximize meta-awareness

## 7.3: Use the Contents of a Cell in a Calculation (5 minutes)

### Optional activity

The purpose of this activity is for students to understand how to use references to cells to calculate values. In later lessons, students may wish to use spreadsheets to perform similar calculations on different numbers and using references can save time so that students do not need to retype all the calculations.

### Launch

Display a blank spreadsheet. In cell B3, type a 2 and press enter. Point to that cell and ask students how to reference that cell. Tell students that people often call B3 the "address" of the cell, and 2 the "contents" of the cell.

### Student Facing

1. Type any number in cell A1, and another number in cell A2. Then in cell A3, type =A1+A2. What happens?
2. In cell A4, compute the product of the numbers in A1 and A2.
3. In cell A5, compute the number in A1 raised to the power of the number in A2.
4. Now, type a new number in cell A1. What happens?
5. Type a new number in cell A2. What happens?
6. Use nearby cells to label the contents of each cell. For example in cell B3, type "the sum of A1 and A2." (This is a good habit to get into. It will remind you and anyone else using the spreadsheet what each cell means.)

### Student Response

For access, consult one of our IM Certified Partners.

## 7.4: Solve Some Problems (15 minutes)

### Optional activity

The purpose of this activity is to demonstrate that spreadsheets can be efficient when repeating similar calculations with different values. A single spreadsheet formula can refer to the contents of cells and the calculation will automatically update when the values change.

If time is short, the first two questions can be skipped or you can tell students to choose only one of them. It's important that all students complete the last two questions to illustrate why a spreadsheet can be more useful than a handheld calculator when you need to repeat the same calculation for different values.

### Launch

Representation: Access for Perception. Read all situations aloud. Students who both listen to and read the information will benefit from extra processing time.
Supports accessibility for: Language

### Student Facing

For each problem:

• Estimate the answer before calculating anything.
• Write down the answer and the formula you used in the spreadsheet to calculate it.
1. The speed limit on a highway is 110 kilometers per hour. How much time does it take a car to travel 132 kilometers at this speed?
2. In a right triangle, the lengths of the sides that make a right angle are 98.7 cm and 24.6 cm. What is the area of the triangle?
3. A recipe for fruit punch uses 2 cups of seltzer water, $$\frac14$$ cup of pineapple juice, and $$\frac23$$ cup of cranberry juice. How many cups of fruit punch are in 5 batches of this recipe?
4. Check in with a partner and resolve any discrepancies with your answer to the last question. Next, type 2, $$\frac14$$, $$\frac23$$, and 5 in separate cells. (You may find it helpful to label cells next to them with the meaning of each number.) In a blank cell, type a formula for the total amount of fruit punch that uses the values in the other four cells. Now you should be able to easily figure out:
1. How much in 7.25 batches?
2. How much in 5 batches if you change the recipe to 1.5 cups of seltzer water per batch?
3. Change the ratio of the ingredients in the fruit punch so that you would like the flavor. How many total cups are in $$\frac12$$ batch?

### Student Response

For access, consult one of our IM Certified Partners.

## 7.5: Cool-down - Good Old Raisins and Peanuts (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Lesson Summary

### Student Facing

A spreadsheet can be thought of as a type of calculator. For example, in a cell, you could type $$=2+3$$, and then the sum of 5 is displayed in the cell. You can also perform operations on the values in other cells. For example, if you type a number in A1 and a number in A2, and then in A3 type $$=A1+A2$$, then A3 will display the sum of the values in cells A1 and A2.

• $$a$$ / $$b$$ for the fraction $$\frac{a}{b}$$