Friday, November 6, 2009

Math problem of the week: 5th Grade Trailblazers vs. Singapore Math

I. The first place value/multiplication problems in Math Trailblazers Student Guide 5, pp. 48-49:

Reach for the Stars

Mr Moreno's class is about to begin a unit on the solar system. Irma, Alexis, and Nila thought it would be fun to decorate the classroom. Mr. Moreno allowed them to stay after school to work on this project.

[Illustration of three girls in front of a blackboard and the following cartoon-bubble dialog]

Irma: Let's make a banner of stars.

Alexis: Great idea. We can make a banner with 2 rows of 30 stars.

Nila: Then how many stars do we need to cut out?

Irma: Since 2 × 3 is 6, I know 2 × 30 is 60.

1. A. Explain in your own words how Irma solved 2 × 30 = 60.
B. How would you solve 2 × 30 = 60? Explain your method to a friend.

[Illustration of the three girls in front of a blackboard that now has two long rows of stars on it, and the following cartoon-bubble dialog]

Nila: How about putting stars on the ceiling? Maybe we could get a parent to help us put them up?

Irma: First we need to know how many stars we need. Let's put a star on each ceiling tile. I counted 20 tiles wide and 30 tiles across. How many tiles is that?

Alexis: Looks like we have to multiply by numbers ending with zeros again!

2. Irma learned to look for patterns when multiplying numbers that end in zeros. Find the following products. Use a calculator if needed. Describe the patterns you see.

A. 2 × 3 =
B. 2 × 30 =
C. 20 × 3 =
D. 20 × 30 =
E. 20 × 300 =
F. 200 × 30 =
G. 200 × 300 =

II. The first place value/multiplication problems in Singapore Math Primary Mathematics 5B, p. 16:

Multiply.

(a) 254 × 10 =

(b) 692 × 100 =

(c) 93 × 40 =

(d) 57 × 1000 =

(e) 43 × 600 =

(f) 392 × 800 =

(g) 728 × 5000 =

(h) 8056 × 3000 =

III. Extra Credit:

1. Which activity leads to deeper mathematical understanding: calculator-facilitated pattern recognition, or pen and paper calculation? Which of these is a more important 21st century skill?

2. Estimate the reading comprehension skills necessary to identify the numerical typo in the second Trailblazers problem.

3. Enumerate the math skills necessary to do the Trailblazers vs. the Singapore problem sets.

4. Which problem set is more accessible to:
-Children with autism and/or language delays
-Children learning English as a second language
-Children with attentional delays/disorders

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