Measuring Mass

Est. Class Sessions: 2–3

Developing the Lesson

Part 3. Writing Number Sentences

For Question 1 on the Number Sentences pages, Pan 1 should be on the students' left and Pan 2 should be on the students' right. They can place labels in the pans using small pieces of paper that are the same size.

Using two-pan balances to complete number sentences allows students to translate between concrete representations and symbols. They use the balances to complete three types of number sentences on the Number Sentences pages in the Student Activity Book. See Content Note. Direct students' attention to these pages. To complete Questions 1–4, each student group will need a two-pan balance and a set of standard masses. Review the directions on the page with the students before assigning the questions. Discuss the example given in Question 1 with the prompts that follow.

Using Parentheses or Ovals in Number Sentences. The agreed-upon rules for the order in which to perform operations say:

Do all the operations in parentheses first.
Then do all the multiplications and divisions from left to right.
Then do all the additions and subtractions from left to right.

In this lesson, we use ovals instead of parentheses to emphasize the order of operations. Using ovals helps students make the transition to using parentheses. In the expression 5 × 3 and 2 × 3, the ovals are not needed, since the multiplication of 5 × 3 and 2 × 3 would be completed first whether or not they are written, but we include them to help students make sense of the number sentence. The ovals highlight to students which operations need to be performed first.

Question 1 asks students to place given numbers of masses into Pan 1 and then to find the number and type of masses to place into Pan 2 in order to balance the pans. Pan 1 is on the students' left. Pan 2 is on the students' right. The given masses are represented in a number sentence on the table and students must complete it to make it a true sentence.

After reading the directions, display the number sentence 1 × 10 + 4 × 5 = 3 × 10 as shown on the table and ask:

How can I show what is in this number sentence in the pans? (Put one 10-gram mass and four 5-gram masses in Pan 1 and three 10-gram masses in Pan 2.)
What does 1 × 10 represent on the left side of the equal sign? (the 10-gram mass in Pan 1)
What does the 4 × 5 represent? (the four 5-gram masses in Pan 1)
Why are the pairs of numbers circled? (They show that the numbers go together and need to be multiplied together.)
Find the total on the left side of the equal sign. (Multiply the first pair of numbers that are circled, 1 × 10, and then multiply the second pair of numbers that are circled, 4 × 5. Add the two products 10 + 20 together to get 30.)
What does 3 × 10 represent on the right side of the equal sign? (the three 10-gram masses in Pan 2)
What does the equal sign tell us in this multiplication sentence? (It tells us that both sides of the equation equal the same amount, 30.)
Is this a true number sentence? How do you know? (Yes, because both sides of the equal sign amount to 30.)
Will the pans be balanced? (Yes. Each side has a mass of 30 grams.)
How can you use the two-pan balance to check your number sentence? (I could put the number and type of masses represented in the number sentence in the pans, and if they balance I will know that my number sentence is correct.)
Is the number sentence on the table the only possible answer? What are some other ways to make 30 grams in Pan 2? (Possible responses: one 20-gram mass and one 10-gram mass; six 5-gram masses; two 10-gram masses and ten 1-gram masses)
Use your balance to show that your number sentence is true.

Questions 2–3 ask students to complete open number sentences and then show that they are true using their two-pan balances. Students can use their balances to help them solve the problem using a guess-and-check method. Or they can solve the problems using their number skills and then show that their solutions are correct using the balances.

Question 4 asks students to mass several small items. Suggest that one be the item they brought from home and that the others come from their desks or the classroom. Tell students to pick items that are small enough to fit into their hands, and ones they have not yet massed. Suggested school items might include scissors, erasers, connecting cubes, packs of self-adhesive notes, paperback books, glue, staplers, a box of crayons, and markers. First they predict whether the item's mass is greater than, less than, or equal to 20 grams. Then they measure and record the item's mass. Finally, they write a number sentence using the symbols for greater than (>), less than (<), or equal to (=). They mark correct predictions with a star on the table.

After explaining the directions, review the three symbols >, <, and =. Display the following number sentences and ask students to place the correct symbol within the sentence:

25 15

5 20

10 10

6 16

32 30