Question

14. State whether the numerical expression 8 x 6 - 2 - 8x (6-2) is true or false and justify
your answer

Answer 1

Answer:

In this beginning lesson, students first explore arithmetic sentences to decide whether they are true or false. The lesson then introduces students to sentences that are neither true nor false but are algebraic equations, also called open sentences, such as x + 3 = 7 or 2 x= 12. The activity appears in Maryann Wickett, Katharine Kharas, and Marilyn Burns’s new book, Lessons for Algebraic Thinking, Grades 3–5 (Math Solutions Publications, 2002).

I wrote on the board:

8 + 4 = 5 + 7

5 = 4 + 1

6 • 0 = 6

For each, I had a student read it aloud, tell if it was true or false, and explain why. Few students knew how to read the third sentence. I explained, “You can use a dot in this way instead of the times sign that you usually use for multiplication.”

“I know about the third problem now,” Tawny said. “You read it, ‘six times zero equals six,’ and that’s false.”

I then asked the students to write examples of arithmetic equations that were true and some that were false. A few minutes later I interrupted them. I drew two columns on the board, one for true mathematical sentences, and a second for false mathematical sentences. I said, “When I call on you, read one of your mathematical sentences. Don’t tell if you think it is true or false. We’ll guess and see if you agree with our guess.” I called on Rayna.

She said, “You multiply six times three and divide that by two. Then comes the equals sign. On the other side you do four plus five.”

I paused to give students time to think and then asked Rayna to come up to the board and write her equation. She wrote:

6 x 3 ÷ 2 = 4 + 5

After a few moments, most students were clear that it was correct. I wrote her equation in the True column.

After several other students shared their equations, even though more of the students wanted to do so, I moved on with the lesson. As the students watched, I wrote the following on the board:

5 +? = 13

“Is this equation true or false?” I asked. The class was quiet. Finally a few hands went up. I called on Jazmin.

“It could be either,” Jazmin said. “We don’t know what the box is, so we don’t know if it’s true or false.”

“How could we make it true?” I asked.

“Write eight in the box because five and eight equals thirteen,” Lizzie said. I did as Lizzie instructed.

5 +? = 13