Ch 11 & 12 Quiz

List two examples of the benefits associated with reasoning strategies.

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Answer explanation

Students make fewer errors because they pick their own method for problem-solving.

Students develop number sense, which helps them gain a better understanding.

Frequently more efficient than standard algorithms.

Supports students when it comes to standardized tests.

Develops positive math identities and understanding.

*There are a ton, these are just a few!

Select the answer that has an incorrect attached definition regarding addition and subtraction strategies.

• Jump Strategies: Known as counting on, frequently uses an open number line to reference.

• Decomposition: Breaking apart numbers into place value parts.

• Compensation: flexible adjustment of numbers and equalization of change.

• Count Back: Counting to the nearest ten in a multidigit addition problem.

Answer explanation

Counting back is used for subtraction.

is a higher level thinking skill that involves determining an efficient way to estimate a sum or difference.

Select all correct explanations of various computational estimation strategies.

• Front End: Adding only the largest place value to work towards an accurate estimate.

• Rounding: Only applies to tens and hundreds place values.

• Compatible Numbers: Looking for numbers that can be grouped to equal benchmark values.

• Rounding: Can be up or down depending on the question at hand. Can round up and down within the same problem.

Answer explanation

Although rounding is typically for tens and hundreds place values, it is not exclusive to them.

When a student struggles to see what part is taken from an added using the decomposition strategy, how would you help to breakdown the problem?

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Answer explanation

Have students model the value of the addends using base-ten materials. When making the move from one place value to another, the student can see where the remainder goes.

Discuss how you would draw an open array model for 22 times 17.

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Answer explanation

You would start with four boxes, two per column and two per row all connected. On one side, you would put 20 and 2, as a breakdown of 22. On the other side, 10 and 7, as a breakdown of 17. you would multiply per box, and 20x10=200, 20x7= 140, 2x10=20, and 2x7=14. Then you add the final numbers to get 374.

What is the most efficient way to solve 625 divided by 5?

• Repeated subtraction

• Rounding

• Missing Factor

• Decomposition

Answer explanation

Decomposition would be the easiest because you can do 600 divided by 5, and then 25 divided by 5, give you 120, and 5 respectively. Which leaves your final answer as 125.

Using the repeated subtraction method, solve 300 divided by 14. Explain your answer.

Answer explanation

300 divided by 14:

300-280 (20 14's)

280-14 (1 14)

20+1=

21 R. 6

You subtract continuously until you've reached your remainder that can no longer fit the divisor in it. The number of times you fit the divisor in is your answer, with the remainder.

True or False: Estimation strategies are not meant to be flexible in giving an idea of a product.

• True

• False

Answer explanation

They are meant to be flexible! Estimates are not exact, and can be done a number of ways.

Discuss a common error with zeroes.

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Answer explanation

Zeroes are frequently called place-holders. By doing this, the value they hold is negated and they are overlooked. It is important to understand that zeroes are there and represent a value regardless of their position.