## Tuesday, August 17, 2010

### Question About 4 x 4 = ___ + 7

Second grade students have some difficulties with tasks such as 4 x 4 = ____ + 7. They are students in billingual school and use Spanish and English.

A teacher in Chile

It is expected that students who do not understand the meaning of the equal sign (=) to give 16 as the answer to 4 x 4 = ____ + 7. The teacher can ask students: "What is the value on the right hand side?" (16 + 7) which is 23 and "What is the value on the left hand side?" which is 16. They should realize that these are not equal.

You could read the number sentence this way: 4 x 4 is equal to 16 which is what plus 7.

The task requires a two-step process and students need some metacogntion to complete the task. Use drawing and concrete materials to help the students.

## Sunday, August 1, 2010

### Two Times More Than

There were some yellow balls and red balls in a box.
The yellow balls were 2 times more than the red balls.
The box had 9 red balls.
How many balls were there in the box?

Should the answer be 36 or 27?

Wendy

This task is poorly phrased. I hope this is not a test item.
Firstly, the quatity to be compared is not clear. Is it the mass, volume, number or some other quantity that is being compared? In this case i believe it is the number. Thus, it should be written as: The number of yellow balls was 2 times as that of red balls. Alternatively, it can be written as : There were twice as many yellow balls as there were red balls.

I believe MOE has addressed this point some years back. At the NIE, this issue should have come up during discussions on test item writing component of the course.

There were some yellow balls and red balls in a box.
There were twice as many yellow balls as there were red balls
There were 9 red balls in the box.
How many balls were there in the box?

In this case, the answer is 27 balls.

We say x is twice as much as y. We say x is 2 more than y. We do not say x is twice more than y. We might say x is 20% more than y.