Question 1

The decomposition or traditional algorithm for subtraction:

Accepted Answer

A) is too difficult for most children to learn. 
B) is the only algorithm children should learn. 
C) cannot be modeled with base-10 materials. 
D) is one of several subtraction algorithms. 
A) is too difficult for most children to learn. 
B) is the only algorithm children should learn. 
C) cannot be modeled with base-10 materials. 
D) is one of several subtraction algorithms.

Question 2

Show two different ways you could get the answer to the problem 498 - 239 using the equal-addition algorithm.

Accepted Answer

Sure! The equal-addition algorithm invol

Question 3

What is meant by compatible numbers? Give two examples to explain.

Accepted Answer

Compatible numbers are numbers that are

Question 4

Many parents were taught the traditional algorithms and are not comfortable with helping their children with the alternative algorithms. How would you reassure the parents that the alternative algorithms are an acceptable way for their children to learn to add, subtract, multiply, and divide with larger numbers?

Accepted Answer

As an educator, I understand the concern

Question 5

Students took in cookie sales of $456, $537, $245, and $329 during a four-month period at their school. The students wanted to practice the front-end estimation they had learned in their class during the semester. Which of the following is the best front-end estimate for the cookie sale?

Accepted Answer

A) $1,300 
B) $1,400 
C) $1,450 
D) $1,550 
A) $1,300 
B) $1,400 
C) $1,450 
D) $1,550

Question 6

Performance Task: Addition Algorithm Use place-value materials of your choice to represent the addition of 397 and 269. Sketch and describe manipulation of the materials as you or a child might use them to demonstrate steps in the standard addition 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: Addition Algorithm Use place-value materials...

Question 7

The ladder method for division is easier than the traditional algorithm because:

Accepted Answer

A) children can estimate the trial divisor. 
B) children use a calculator rather than estimation to find the quotient. 
C) children do fewer steps than the traditional method. 
D) children build up the quotient using several decade multiplications. 
A) children can estimate the trial divisor. 
B) children use a calculator rather than estimation to find the quotient. 
C) children do fewer steps than the traditional method. 
D) children build up the quotient using several decade multiplications.

Question 8

Suppose you wanted to teach your children about decade multiplication. Give two examples illustrating how you would go about teaching them this important concept.

Accepted Answer

One way to teach children about decade m

Question 9

Amber and Charlotte each ran a mile. It took Amber 11.79 minutes. It took Charlotte 9.08 minutes. Which number sentence can Charlotte use to best estimate the difference in their times?

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 10

Ms. Nandagopal has donated a total of $348 to a library during the past 4 years. She has donated the same amount of money each year. How much money has Ms. Nandagopal donated to the library in each of the past 4 years?

Accepted Answer

A) $82 
B) $87 
C) $352 
D) $344 
A) $82 
B) $87 
C) $352 
D) $344

Question 11

Kumail played a video game. He scored 13,567 points in the first round and 8,625 points in the second round. How many total points did Kumail score?

Accepted Answer

A) 21,192 points 
B) 22,192 points 
C) 94,717 points 
D) 99,817 points 
A) 21,192 points 
B) 22,192 points 
C) 94,717 points 
D) 99,817 points

Question 12

Ruby is given the problem below:
28 marbles are shared equally by 4 children. How many marbles will each one get?
Ruby should solve the problem by using:

Accepted Answer

A) measurement division. 
B) compensation. 
C) equal additions. 
D) partitive division. 
A) measurement division. 
B) compensation. 
C) equal additions. 
D) partitive division.

Question 13

Alternative algorithms have the following characteristics except:

Accepted Answer

A) they are based on expanded notation, which emphasizes place value of numbers. 
B) they simplify computation by allowing students to write down partial answers as they work. 
C) they build on understanding of the operations. 
D) they are based on rounding. 
A) they are based on expanded notation, which emphasizes place value of numbers. 
B) they simplify computation by allowing students to write down partial answers as they work. 
C) they build on understanding of the operations. 
D) they are based on rounding.

Question 14

Divide 2,346 by 14 using the ladder algorithm. Which of the methods for dividing is the basis for the ladder method (measurement or partitive)?

Accepted Answer

The ladder algorithm, also known as the

Question 15

Suppose Mrs. Smith has 64 pieces of candy, and she wants to give out the pieces 4 at a time. Which division definition would she be adhering to?

Accepted Answer

A) measurement division 
B) compensation 
C) equal additions 
D) partitive division 
A) measurement division 
B) compensation 
C) equal additions 
D) partitive division

Question 16

Abena needed to know about how much the sum of 19.6, 23.8, and 38.4 is. She correctly rounded each of these numbers to the nearest whole number. What three numbers did she use?

Accepted Answer

A) 19, 23, 38 
B) 19, 24, 38 
C) 20, 24, 38 
D) 20, 24, 39 
A) 19, 23, 38 
B) 19, 24, 38 
C) 20, 24, 38 
D) 20, 24, 39

Question 17

Explain the difference between front-end estimation and rounded estimation using 135 × 65.

Accepted Answer

Front-end estimation involves rounding e

Question 18

The traditional algorithm for addition is accurately labeled:

Accepted Answer

A) takeaway. 
B) regrouping and renaming. 
C) carrying. 
D) addends. 
A) takeaway. 
B) regrouping and renaming. 
C) carrying. 
D) addends.

Question 19

Procedures for front-end estimation and alternative algorithms are similar in that:

Accepted Answer

A) they both are difficult to learn. 
B) they both use expansion of digits. 
C) they both start calculation in the largest place value. 
D) they both lead to exact answers. 
A) they both are difficult to learn. 
B) they both use expansion of digits. 
C) they both start calculation in the largest place value. 
D) they both lead to exact answers.

Question 20

Using sketches of base-10 materials, show how you would teach children to add 537 + 489. Then show the traditional, expanded, and low-stress algorithms for the same problem.

Accepted Answer

To teach children to add 537 + 489 using

The decomposition or traditional algorithm for subtraction:

Show two different ways you could get the answer to the problem 498 - 239 using the equal-addition algorithm.

What is meant by compatible numbers? Give two examples to explain.

Students took in cookie sales of $456, $537, $245, and $329 during a four-month period at their school. The students wanted to practice the front-end estimation they had learned in their class during the semester. Which of the following is the best front-end estimate for the cookie sale?

The ladder method for division is easier than the traditional algorithm because:

Suppose you wanted to teach your children about decade multiplication. Give two examples illustrating how you would go about teaching them this important concept.

Amber and Charlotte each ran a mile. It took Amber 11.79 minutes. It took Charlotte 9.08 minutes. Which number sentence can Charlotte use to best estimate the difference in their times?

Ms. Nandagopal has donated a total of $348 to a library during the past 4 years. She has donated the same amount of money each year. How much money has Ms. Nandagopal donated to the library in each of the past 4 years?

Kumail played a video game. He scored 13,567 points in the first round and 8,625 points in the second round. How many total points did Kumail score?

Ruby is given the problem below: 28 marbles are shared equally by 4 children. How many marbles will each one get? Ruby should solve the problem by using:

Alternative algorithms have the following characteristics except:

Divide 2,346 by 14 using the ladder algorithm. Which of the methods for dividing is the basis for the ladder method (measurement or partitive)?

Suppose Mrs. Smith has 64 pieces of candy, and she wants to give out the pieces 4 at a time. Which division definition would she be adhering to?

Abena needed to know about how much the sum of 19.6, 23.8, and 38.4 is. She correctly rounded each of these numbers to the nearest whole number. What three numbers did she use?

Explain the difference between front-end estimation and rounded estimation using 135 × 65.

The traditional algorithm for addition is accurately labeled:

Procedures for front-end estimation and alternative algorithms are similar in that:

Using sketches of base-10 materials, show how you would teach children to add 537 + 489. Then show the traditional, expanded, and low-stress algorithms for the same problem.

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

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Exam 11: Extending Computational Fluency With Larger Numbers

The decomposition or traditional algorithm for subtraction:

Show two different ways you could get the answer to the problem 498 - 239 using the equal-addition algorithm.

What is meant by compatible numbers? Give two examples to explain.

Students took in cookie sales of $456, $537, $245, and $329 during a four-month period at their school. The students wanted to practice the front-end estimation they had learned in their class during the semester. Which of the following is the best front-end estimate for the cookie sale?

The ladder method for division is easier than the traditional algorithm because:

Suppose you wanted to teach your children about decade multiplication. Give two examples illustrating how you would go about teaching them this important concept.

Amber and Charlotte each ran a mile. It took Amber 11.79 minutes. It took Charlotte 9.08 minutes. Which number sentence can Charlotte use to best estimate the difference in their times?

Ms. Nandagopal has donated a total of $348 to a library during the past 4 years. She has donated the same amount of money each year. How much money has Ms. Nandagopal donated to the library in each of the past 4 years?

Kumail played a video game. He scored 13,567 points in the first round and 8,625 points in the second round. How many total points did Kumail score?

Ruby is given the problem below: 28 marbles are shared equally by 4 children. How many marbles will each one get? Ruby should solve the problem by using:

Alternative algorithms have the following characteristics except:

Divide 2,346 by 14 using the ladder algorithm. Which of the methods for dividing is the basis for the ladder method (measurement or partitive)?

Suppose Mrs. Smith has 64 pieces of candy, and she wants to give out the pieces 4 at a time. Which division definition would she be adhering to?

Abena needed to know about how much the sum of 19.6, 23.8, and 38.4 is. She correctly rounded each of these numbers to the nearest whole number. What three numbers did she use?

Explain the difference between front-end estimation and rounded estimation using 135 × 65.

The traditional algorithm for addition is accurately labeled:

Procedures for front-end estimation and alternative algorithms are similar in that:

Using sketches of base-10 materials, show how you would teach children to add 537 + 489. Then show the traditional, expanded, and low-stress algorithms for the same problem.

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

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