Question 1

Compensation is an alternative algorithm that:

Accepted Answer

A) is used to subtract larger numbers. 
B) involves adjusting numbers higher or lower to ease computation. 
C) is the same thing as equal additions. 
D) involves multiplication and division. 
A) is used to subtract larger numbers. 
B) involves adjusting numbers higher or lower to ease computation. 
C) is the same thing as equal additions. 
D) involves multiplication and division. B

Question 2

The main difference between mental computation and estimation or rounding is:

Accepted Answer

A) mental computation is done before estimation or rounding is applied. 
B) mental computation is easier to understand than estimation or rounding. 
C) mental computation gives exact answers while estimation or rounding only gives approximate answers. 
D) mental computation is preferred by teachers over estimation or rounding because it is easier to grade since there is only one right answer. 
A) mental computation is done before estimation or rounding is applied. 
B) mental computation is easier to understand than estimation or rounding. 
C) mental computation gives exact answers while estimation or rounding only gives approximate answers. 
D) mental computation is preferred by teachers over estimation or rounding because it is easier to grade since there is only one right answer. C

Question 3

A runner ran 3,000 meters in exactly 8 minutes. What was his average speed in meters per second?

Accepted Answer

A) 3.75 m/s 
B) 6.25 m/s 
C) 16.0 m/s 
D) 37.5 m/s 
A) 3.75 m/s 
B) 6.25 m/s 
C) 16.0 m/s 
D) 37.5 m/s B

Question 4

Multiply 37 × 24 using the transitional, alternative, and traditional algorithms. Explain the progression from the first through the third algorithms.

Accepted Answer

To multiply 37 by 24 using the transitio

Question 5

Alex collected 22 pounds of aluminum cans. How many ounces of aluminum cans did he collect?

Accepted Answer

A) 6 oz. 
B) 38 oz. 
C) 352 oz. 
D) 220 oz. 
A) 6 oz. 
B) 38 oz. 
C) 352 oz. 
D) 220 oz.

Question 6

Extensive practice time on number operations:

Accepted Answer

A) is recommended so students can perform rapidly. 
B) is recommended so students understand the steps. 
C) is not recommended because students need to learn several computational strategies and when to use them. 
D) is not recommended because students should just use calculators. 
A) is recommended so students can perform rapidly. 
B) is recommended so students understand the steps. 
C) is not recommended because students need to learn several computational strategies and when to use them. 
D) is not recommended because students should just use calculators.

Question 7

Instruction with algorithms should stress all of the following except:

Accepted Answer

A) number sense. 
B) estimation. 
C) extensive calculator usage. 
D) selecting the most appropriate process for each calculation. 
A) number sense. 
B) estimation. 
C) extensive calculator usage. 
D) selecting the most appropriate process for each calculation.

Question 8

Addition and subtraction algorithms used with larger numbers:

Accepted Answer

A) are much harder to understand because the numbers are bigger. 
B) cannot be modeled with base-10 materials. 
C) parallel the situations, stories, and rules as smaller numbers. 
D) should be introduced when children can count to 100. 
A) are much harder to understand because the numbers are bigger. 
B) cannot be modeled with base-10 materials. 
C) parallel the situations, stories, and rules as smaller numbers. 
D) should be introduced when children can count to 100.

Question 9

The average number of passengers who use a certain airport each year is 350,000. A newspaper reported the number as 350 million. The number reported in the newspaper was how many times the actual number?

Accepted Answer

A) 10 
B) 100 
C) 1,000 
D) 10,000 
A) 10 
B) 100 
C) 1,000 
D) 10,000

Question 10

Since the answer for both 23 − 17 and 26 − 20 is 6, the logic behind equal addition subtraction algorithm is:

Accepted Answer

A) adding the same number to both the subtrahend and minuend changes the answer. 
B) increasing the subtrahend and decreasing the minuend does not change the answer. 
C) subtracting any two numbers will give the same answer. 
D) adding or subtracting the same number to both subtrahend and minuend keeps the difference between two numbers the same. 
A) adding the same number to both the subtrahend and minuend changes the answer. 
B) increasing the subtrahend and decreasing the minuend does not change the answer. 
C) subtracting any two numbers will give the same answer. 
D) adding or subtracting the same number to both subtrahend and minuend keeps the difference between two numbers the same.

Question 11

Decade multiplication is an important skill to develop because:

Accepted Answer

A) multiplication and division of larger numbers depend on accuracy and speed with the skill. 
B) it simplifies computation 
C) it uses place value. 
D) it uses rounding. 
A) multiplication and division of larger numbers depend on accuracy and speed with the skill. 
B) it simplifies computation 
C) it uses place value. 
D) it uses rounding.

Question 12

Alternative algorithms for multiplication use:

Accepted Answer

A) the commutative property. 
B) the multiplicative property. 
C) the inverse property. 
D) the distributive property. 
A) the commutative property. 
B) the multiplicative property. 
C) the inverse property. 
D) the distributive property.

Question 13

An advantage of using an alternative or low-stress algorithm is because:

Accepted Answer

A) they often better preserve the meaning of the number and place value. 
B) they are quicker to use. 
C) they don't require as much thinking. 
D) they are always accepted and encouraged by teachers and parents. 
A) they often better preserve the meaning of the number and place value. 
B) they are quicker to use. 
C) they don't require as much thinking. 
D) they are always accepted and encouraged by teachers and parents.

Question 14

Performance Task: Subtraction Algorithm Use place-value materials to represent steps in the decomposition algorithm for the subtraction of 288 from 467. Sketch and describe manipulation of the materials as you or a child might use them to represent steps in the algorithm. Show a progression of steps in the algorithm alongside your sketches to show the relationships between the model and the algorithm as each step is completed. This rubric will be used to evaluate your work on this task. Credit will be awarded on a four-point scale.

Accepted Answer

The answer of Performance Task: Subtraction Algorithm Use place-value materials...

Question 15

Lattice multiplication may be helpful to some children because:

Accepted Answer

A) all the multiplication is done first, then addition. 
B) all the addition is done first, then multiplication. 
C) it keeps the numbers lined up vertically. 
D) they can switch back and forth between addition and multiplication operations. 
A) all the multiplication is done first, then addition. 
B) all the addition is done first, then multiplication. 
C) it keeps the numbers lined up vertically. 
D) they can switch back and forth between addition and multiplication operations.

Question 16

Multiply 345 × 67 using lattice multiplication. Explain why you add numbers in the diagonals to get your final answer.

Accepted Answer

To multiply 345 by 67 using lattice mult

Question 17

Explain what is meant by decomposition as it applies to subtraction.

Accepted Answer

Decomposition in subtraction refers to b

Question 18

Mia wants to subtract 57 - 29, but thinks of it as (57 + 1)- (29 + 1)in order to yield 58 - 30 and arrives at the answer 28. Mia is using which of the following algorithms?

Accepted Answer

A) compensation 
B) regrouping and renaming 
C) equal additions 
D) decomposition 
A) compensation 
B) regrouping and renaming 
C) equal additions 
D) decomposition

Question 19

The equal-additions algorithm:

Accepted Answer

A) is too difficult for most children to understand. 
B) introduces multiplication. 
C) is often taught in Europe as the standard subtraction algorithm. 
D) is another name for decomposition. 
A) is too difficult for most children to understand. 
B) introduces multiplication. 
C) is often taught in Europe as the standard subtraction algorithm. 
D) is another name for decomposition.

Question 20

A child needs to multiply 1300 × 40. She begins to multiply using the traditional algorithm but gets confused with the placement of the zeros. An alternative strategy that would make this problem easier would be to use:

Accepted Answer

A) compensation. 
B) equal additions. 
C) decade multiplication. 
D) regrouping and renaming. 
A) compensation. 
B) equal additions. 
C) decade multiplication. 
D) regrouping and renaming.

Compensation is an alternative algorithm that:

The main difference between mental computation and estimation or rounding is:

A runner ran 3,000 meters in exactly 8 minutes. What was his average speed in meters per second?

Multiply 37 × 24 using the transitional, alternative, and traditional algorithms. Explain the progression from the first through the third algorithms.

Alex collected 22 pounds of aluminum cans. How many ounces of aluminum cans did he collect?

Extensive practice time on number operations:

Instruction with algorithms should stress all of the following except:

Addition and subtraction algorithms used with larger numbers:

The average number of passengers who use a certain airport each year is 350,000. A newspaper reported the number as 350 million. The number reported in the newspaper was how many times the actual number?

Since the answer for both 23 − 17 and 26 − 20 is 6, the logic behind equal addition subtraction algorithm is:

Decade multiplication is an important skill to develop because:

Alternative algorithms for multiplication use:

An advantage of using an alternative or low-stress algorithm is because:

Lattice multiplication may be helpful to some children because:

Multiply 345 × 67 using lattice multiplication. Explain why you add numbers in the diagonals to get your final answer.

Explain what is meant by decomposition as it applies to subtraction.

Mia wants to subtract 57 - 29, but thinks of it as (57 + 1)- (29 + 1)in order to yield 58 - 30 and arrives at the answer 28. Mia is using which of the following algorithms?

The equal-additions algorithm:

A child needs to multiply 1300 × 40. She begins to multiply using the traditional algorithm but gets confused with the placement of the zeros. An alternative strategy that would make this problem easier would be to use:

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Problem-Solving Strategies

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters

Exam 11: Extending Computational Fluency With Larger Numbers

Compensation is an alternative algorithm that:

The main difference between mental computation and estimation or rounding is:

A runner ran 3,000 meters in exactly 8 minutes. What was his average speed in meters per second?

Multiply 37 × 24 using the transitional, alternative, and traditional algorithms. Explain the progression from the first through the third algorithms.

Alex collected 22 pounds of aluminum cans. How many ounces of aluminum cans did he collect?

Extensive practice time on number operations:

Instruction with algorithms should stress all of the following except:

Addition and subtraction algorithms used with larger numbers:

The average number of passengers who use a certain airport each year is 350,000. A newspaper reported the number as 350 million. The number reported in the newspaper was how many times the actual number?

Since the answer for both 23 − 17 and 26 − 20 is 6, the logic behind equal addition subtraction algorithm is:

Decade multiplication is an important skill to develop because:

Alternative algorithms for multiplication use:

An advantage of using an alternative or low-stress algorithm is because:

Lattice multiplication may be helpful to some children because:

Multiply 345 × 67 using lattice multiplication. Explain why you add numbers in the diagonals to get your final answer.

Explain what is meant by decomposition as it applies to subtraction.

Mia wants to subtract 57 - 29, but thinks of it as (57 + 1)- (29 + 1)in order to yield 58 - 30 and arrives at the answer 28. Mia is using which of the following algorithms?

The equal-additions algorithm:

A child needs to multiply 1300 × 40. She begins to multiply using the traditional algorithm but gets confused with the placement of the zeros. An alternative strategy that would make this problem easier would be to use:

Elementary Mathematics for the 21st Century

Defining a Comprehensive Mathematics Program

Mathematics for Every Child

Learning Mathematics

Organizing Effective Instruction

Integrating Assessment

Developing Problem-Solving Strategies

Developing Concepts of Number

Extending Number Concepts and Number Systems

Developing Number Operations With Whole Numbers

Developing Understanding of Common and Decimal Fractions

Extending Understanding of Common and Decimal Fractions

Developing Aspects of Proportional Reasoning: Ratio, Proportion, and Percent

Thinking Algebraically

Developing and Extending Geometric Concepts and Systems

Developing and Extending Measurement Concepts

Understanding and Representing Concepts of Data

Investigating Probability

Filters