Deck 10: Developing Number Operations With Whole Numbers

Question 1

Modeling the inverse nature of multiplication and divisions might be done by:

A)putting five beans into each of 6 cups and separating 30 beans into 6 cups.
B)showing that 3 × 5 is 15 and 5 × 3 is 15.
C)showing 273 as 2 hundred, 7 tens, and 3 ones with base-10 blocks.
D)giving 4 children 3 cookies each.

Answer 1

putting five beans into each of 6 cups and separating 30 beans into 6 cups.

Question 2

The problem below is an example of what?
Huang has 3 shirts, 4 pairs of shorts, 2 pairs of socks, and a pair of shoes. How many different outfits can he make with these items of clothing?

A)repeated addition model for multiplication
B)geometric interpretation or array model for multiplication
C)Cartesian cross-product or combinations model for multiplication
D)partitive or sharing model for division

Answer 2

Cartesian cross-product or combinations model for multiplication

Question 3

The problem below is an example of which type of subtraction situation?Tamar found 18 ballpoint pens in a desk at her house. Eleven were out of ink. How many usable pens did she find?

A)takeaway
B)comparison
C)completion
D)whole-part-part

Answer 3

takeaway

Question 4

Subtraction is represented by which four different stories or situations?

A)takeaway, whole-part-part, comparison, and completion
B)commutative, inverse, associative, and identity
C)fluency, algorithms, estimation, and mental computation
D)difference, remainder, subtrahend, and minuend

Question 5

The most difficult multiplication and division facts for most children to learn are:

A)multiplication by 0, 1, and 2.
B)multiplication by 5 and 10.
C)facts for the square numbers.
D)multiplication facts with 7, 8, and 9 as factors.

Question 6

Which question is associated with the completion situation of subtraction?

A)"How many are left?"
B)"How many can you see?"
C)"What is the difference?"
D)"How many more are needed?"

Question 7

The problem below is an example of what?
Hannah had 37 cookies and decided to give each friend 3 cookies. How many friends could she give 3 cookies to?

A)repeated addition model for multiplication.
B)geometric interpretation or array model for multiplication.
C)partitive or sharing model for division.
D)  measurement or repeated subtraction model for subtraction.

Question 8

The problem below is an example of what?
A bag of ready-to-pop popcorn costs 59 cents. How much do 15 bags cost?

A)repeated addition model for multiplication.
B)geometric interpretation or array model for multiplication
C)Cartesian cross-products or combinations model for multiplication
D)measurement or repeated subtraction model for division

Question 9

The commutative property may be modeled by:

A)moving back and forth on a number line.
B)rotating a domino by 180 degrees.
C)plus one and plus zero facts.
D)showing combinations of 10 using Unifix cubes.

Question 10

The problem below is an example of what?
Eric has 23 cookies. He has 4 friends coming to his party. How many cookies does each friend get?

A)repeated addition model for multiplication
B)geometric interpretation or array model for multiplication
C)partitive or sharing model for division
D)measurement or repeated subtraction model for subtraction

Question 11

When learning the meanings for multiplication and division, students:

A)concentrate on learning the facts.
B)model situations with stories, objects, and pictures.
C)are too mature to need manipulatives.
D)must wait until they understand place value.

Question 12

Skip counting by 3s, 4s and 5s:

A)is not helpful to students learning multiplication.
B)may help children learn the multiplication facts.
C)is best done with a special calculator.
D)relates to the associative property of multiplication.

Question 13

Which is the least effective way for children to learn the 100 multiplication facts?

A)Children discover relationships and make generalizations about fact combinations.
B)Children show how an 8 by 4 array is the same as (4 × 4)+ (4 × 4).
C)Children complete speed practices every day for 30 minutes.
D)Children see the relationship between 9 × 8 = 72 and 8 × 9 = 72.

Question 14

When children are learning basic addition facts, they can reduce the learning demands by:

A)concentrating on the 20 to 30 hard facts.
B)learning strategies that apply to many facts.
C)memorizing only 2 or 3 facts each day.
D)writing each fact 20 times.

Question 15

Addition is represented in stories, action, and drawings as:

A)the union of sets.
B)the decomposition of sets.
C)the elaboration of sets.
D)the common elements of sets.

Question 16

The problem below is an example of what?Penelope's 40-page stamp book has spaces for 35 stamps on each page. How many stamps can she put in the book?

A)repeated addition model for multiplication
B)geometric interpretation or array model for multiplication
C)Cartesian cross-product or combination model for multiplication
D)measurement model for division

Question 17

For which situation would the remainder 12, remainder 4 be interpreted as 13?

A)How many cars are needed for 64 children when 5 can ride in each car?
B)How many dollars per person when $64 is divided fairly among 5 people?
C)How many miles per gallon when a truck goes 64 miles on 5 gallons?
D)How many marbles per person when 64 marbles are shared fairly by 5 people?

Question 18

The problem below is an example of which type of subtraction situation?Shafi has 21 rookie baseball cards, and Bandar has 12 cards. How many more cards does Shafi have than Bandar?

A)takeaway
B)comparison
C)completion
D)whole-part-part

Question 19

The equations 7 + 2 = 9 and 9 - 2 = 7 demonstrate:

A)commutative property.
B)associative property.
C)identity element for addition and subtraction.
D)inverse operations.

Question 20

Assessment shows that many primary children interpret the equal sign as:

A)meaning "3 + 4 write the answer now 7."
B)meaning "3 + 4 is the same as 7."
C)meaning "3 + 4 is the opposite of 4 + 3."
D)meaningless.

Question 21

What is the role of drill and practice in learning basic number facts? What are cautions you would take with drill and practice?

Question 22

Which number makes the following number sentence true?

A)4
B)7
C)9
D)17

Question 23

Match the number operations with examples related to that operation.
Santino can run to the fence in 55 seconds. Estela can run the distance in 52 seconds. Who is faster?

A)addition
B)subtraction
C)multiplication
D)division

Question 24

Mr. Horowitz wants to buy 48 cans of dog food to give to the animal shelter. There are 6 cans of dog food in a package. How many packages of dog food should Mr. Horowitz buy?

A)7 packages
B)8 packages
C)42 packages
D)54 packages

Question 25

Match the number operations with examples related to that operation.
John has 3 pets and Sally has 4 pets. Who has more pets?

A)addition
B)subtraction
C)multiplication
D)division

Question 26

In primary grades, the emphasis is on the first three phases of number operations, which are:

A)concepts, memorization of number facts, and practice.
B)learning strategies, practice, and maintenance.
C)integration of number with language arts, social studies, and science.
D)concepts, strategies for number combinations, and accuracy with speed.

Question 27

Kayla has 15 strawberries. She gives 4 strawberries to each of her 3 friends. How many strawberries are left for Kayla?

A)1
B)2
C)3
D)4

Question 28

Use of compatible numbers makes computation easier because children:

A)work with numbers less than 100.
B)look for numbers with sums such as 10, 100, or 1,000.
C)the sum of compatible numbers is always even.
D)the product of compatible numbers ends in 5 or 0.

Question 29

Emma wants to give 8 stickers to 4 friends. She wrote this number sentence to find out how many stickers she needs.

Write a multiplication number sentence that Emma could use to find out how many stickers she needs. Be sure to show your work.

Question 30

Match the number operations with examples related to that operation.
Huang has 3 pants and 4 shirts. How many days can he wear a different outfit before repeating?

A)addition
B)subtraction
C)multiplication
D)division

Question 31

Sample Test Items
What is the greatest number of 40-cent apples that can be purchased with $5.00?

A)6
B)12
C)15
D)20

Question 32

How should 3 children share 12 cookies equally?

A)3 portions of 4 cookies each
B)4 portions of 3 cookies each
C)1 portion of 5 cookies, 1 portion of 4 cookies, and 1 portion of 3 cookies
D)2 portions of 6 cookies each

Question 33

Drew entered four numbers less than 10 on his calculator. He forgot what his second and fourth numbers were. This is what he remembered doing.

List a pair of numbers that could have been the second and fourth numbers. (You may use number tiles to help you.)

Question 34

Match the number operations with examples related to that operation.
A bag of ready-to-pop popcorn costs 59 cents. How much do 15 bags cost?

A)addition
B)subtraction
C)multiplication
D)division

Question 35

Match the number operations with examples related to that operation.
Counting by 2s, 3s, 4s, or 7s

A)addition
B)subtraction
C)multiplication
D)division

Question 36

What is computational fluency? What must children know and be able to do to achieve computational fluency?

Question 37

Describe two activities you could use to build children's understanding of addition or subtraction.

Question 38

Match the number operations with examples related to that operation.
John has 3 pets and Sally has 4 pets. How many pets do they have?

A)addition
B)subtraction
C)multiplication
D)division

Question 39

Match the number operations with examples related to that operation.
The bag of cookies has 28 cookies. How many children can be served if they each get 3?

A)addition
B)subtraction
C)multiplication
D)division

Question 40

Match the number operations with examples related to that operation.
Eight children get 3 cookies each.

A)addition
B)subtraction
C)multiplication
D)division

Question 41

Explain why division by zero is undefined.

Question 42

Define and give examples for the two types of division.

Question 43

What roles do the commutative and associative properties play in learning the basic facts?

Question 44

What is the value of teaching strategies rather than memorization for learning basic facts?

Question 45

John multiplied  and obtained the product (2)(10). Explain his error in terms of properties or in terms of the concept of multiplication being a binary operation.

Question 46

Define and give examples for the three types of multiplication.

Question 47

Sketch all possible rectangular areas for rectangles of area 6 and 5 square units, respectively. Explain how the areas relate to prime and composite numbers.

Question 48

The owner of the bookstore gave the school 17 books. The principal is going to divide the books equally among 5 classes and give the rest to the school library. Draw a picture that shows how many books each class will get and how many the library will receive. Show your work, then explain in words how you got your answer.