Lesson 6

In the next activity, students are asked to look for a rule that puts together some numbers to make a target number. This warm-up activates that sort of thinking.

Arrange students in groups of 2.

Ask each student to think of a whole number. (Make this more straightforward by limiting the choices to single-digit numbers, more challenging by limiting to 0–20 or 0–100, or really challenging by placing no restrictions on the numbers.) Select four students at random to share their number, and display these four numbers for all to see.

Ask students to share their expression with a partner, so that their partner can verify that their expression is equal to 24. Then, select a few students to share their expression with the whole class and record these for all to see. How many different ways did the class find to make 24?

In this activity, students experiment with an applet in which the value displayed in some cells depend on other cells. Monitor for students who notice interesting things.

Instead of writing down responses to the questions, it would make sense for students to share their observations verbally with a partner.

Some students will probably notice that the answers are in the spreadsheet. For example if you click on cell B2, you can see the formula that was used to generate the number that appears in that cell. They should be encouraged to use the values of the other cells to verify what they notice. Ultimately, all students should be able to interpret the spreadsheet formula in the cell.

Students may be confused about how the term “related” is being used in the task statement. Explain that students should be trying to figure out what calculations take place with the numbers in column A in order to get the numbers in column B. Students may have difficulty figuring out the relationships between the numbers in column A and the numbers in column B. Suggest they try different kinds of numbers in column A, like small whole numbers, 0, multiples of 10, or decimal values. 

After students have had a chance to experiment with the applet and make conjectures about how the cells in column B are calculated, invite them to compare their conjectures with a partner.

Before selecting students to share their conclusions, select students to share their predicted value for various cells in column B based on combinations of values in column A. For example, “What would be the value in cell B4 if column A has the values 2, 4, 5, and 9?” (20)

Select students who tried or noticed interesting things to share with the whole class. 

The words “sum" and “product” appear in the formulas. Briefly ask students to recall the meaning of these words. Invite them to guess what using the : symbol in the cell formula does. For example, =Sum(A2:A5) calculates A2 + A3 + A4 + A5.

The purpose of this activity is to improve student familiarity with writing spreadsheet formulas based on references to other cells. In this activity, students have an opportunity to write their own spreadsheet formula in a cell and trade with a partner to guess their formula.

Students may have difficulty inputing a new formula in a cell. For example, students may forget to begin the formula with =. Ensure that students know how to input the symbols that represent each operation.

Ask students to report on the work they did with their partner.

• “Which formulas were interesting to guess?”
• “Which formulas were difficult to guess? What made them difficult?”
• “Which formulas were easy to guess? What made them easy?”