Deck 11: Extending Computational Fluency With Larger Numbers

Question 1

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?

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

Answer 1

$1,400

Question 2

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:

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

Answer 2

decade multiplication.

Question 3

Lattice multiplication may be helpful to some children because:

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.

Answer 3

all the multiplication is done first, then addition.

Question 4

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

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 5

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

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.

Question 6

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?

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

Question 7

Which statement best describes the computational skills children need to learn?

A)Students should learn to use a calculator to do their computations as soon as an operation is introduced.
B)Students need good estimation skills because exact answers are seldom needed in everyday life.
C)Students should learn a variety of computational processes including paper-pencil algorithms, estimation and mental arithmetic strategies, and technological applications.
D)Students should become proficient with the algorithms involving large multi-digit numbers.

Question 8

Alternative algorithms for multiplication use:

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

Question 9

Alternative algorithms have the following characteristics except:

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 10

Compensation is an alternative algorithm that:

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.

Question 11

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

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 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:

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

Question 13

The decomposition or traditional algorithm for subtraction:

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 14

The traditional algorithm for addition is accurately labeled:

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

Question 15

Addition and subtraction algorithms used with larger numbers:

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 16

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

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 17

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?

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

Question 18

The equal-additions algorithm:

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 19

Instruction with algorithms should stress all of the following except:

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

Question 20

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

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 21

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

Question 22

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?

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

Question 23

Decade multiplication is an important skill to develop because:

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 24

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?

Question 25

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

Question 26

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?

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

Question 27

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

Question 28

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

Question 29

Extensive practice time on number operations:

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 30

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

Question 31

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

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

Question 32

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?

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

Question 33

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)?

Question 34

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

Question 35

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.

Question 36

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

Question 37

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?

A)
B)
C)
D)

Question 38

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.

Question 39

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

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

Question 40

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?

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

Question 41

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.