Question 1

What mathematical representation would help students identify patterns and number relationships?

Accepted Answer

A) Blank number line. 
B) Hundreds chart. 
C) Place value chart. 
D) 10 x 10 Multiplication Array. 
A) Blank number line. 
B) Hundreds chart. 
C) Place value chart. 
D) 10 x 10 Multiplication Array. B

Question 2

All of the activities below would provide opportunities for students to connect the base-ten concepts with the oral number names EXCEPT:

Accepted Answer

A) Using arrays to cover up rows and columns and ask students to identify the number name. 
B) Lie out base-ten models and ask students to tell you how many tens and ones. 
C) A chain of paper links is shown and students are asked to estimate how many tens and ones. 
D) Students need to show with fingers how to construct a named number. 
A) Using arrays to cover up rows and columns and ask students to identify the number name. 
B) Lie out base-ten models and ask students to tell you how many tens and ones. 
C) A chain of paper links is shown and students are asked to estimate how many tens and ones. 
D) Students need to show with fingers how to construct a named number. C

Question 3

A calculator activity that is good assessment to see whether students really understand the value of digits is titled "Digit Change".Students must change one number without putting in the new number.What place value would a student need to know in order to change 315 to 295?

Accepted Answer

A) Ones. 
B) Tens. 
C) Hundreds. 
D) Tens and ones. 
A) Ones. 
B) Tens. 
C) Hundreds. 
D) Tens and ones. B

Question 4

What does the relational understanding of place value needs to begin with?

Accepted Answer

A) Counting by ones and saying and writing the numeral. 
B) Counting by ones,making a model and saying and writing the numeral. 
C) Counting by tens and ones and saying and writing the numeral. 
D) Counting by tens and ones,making the model,saying and writing the numeral. 
A) Counting by ones and saying and writing the numeral. 
B) Counting by ones,making a model and saying and writing the numeral. 
C) Counting by tens and ones and saying and writing the numeral. 
D) Counting by tens and ones,making the model,saying and writing the numeral.

Question 5

Complete this statement,"Number sense is linked to a complete understanding of..".

Accepted Answer

A) Problem solving. 
B) Place-value. 
C) Base-ten models. 
D) Basic Facts. 
A) Problem solving. 
B) Place-value. 
C) Base-ten models. 
D) Basic Facts.

Question 6

As students become more confident with the use of place value models they can represent them with a semi-concrete notations like square-line-dot.What number would be represented by 16 lines,11 dots and 5 squares?

Accepted Answer

A) 16115 
B) 5,171 
C) 671 
D) 32 
A) 16115 
B) 5,171 
C) 671 
D) 32

Question 7

All the examples below are examples of proportional base-ten models EXCEPT:

Accepted Answer

A) Counters and cups. 
B) Cubes. 
C) Strips and squares. 
D) Money. 
A) Counters and cups. 
B) Cubes. 
C) Strips and squares. 
D) Money.

Question 8

The ideas below would give students opportunities to see and make connections to numbers in the real world.The statements below identify examples that would engage students with large benchmark numbers EXCEPT:

Accepted Answer

A) Measurements and numbers discovered on a field trip. 
B) Number of milk cartons sold in a week at an elementary school. 
C) Number of seconds in a month. 
D) Measurement of students' height in second grade. 
A) Measurements and numbers discovered on a field trip. 
B) Number of milk cartons sold in a week at an elementary school. 
C) Number of seconds in a month. 
D) Measurement of students' height in second grade.

Question 9

The statement below are all helpful when guiding students to conceptualize numbers with 4 or more digits EXCEPT;

Accepted Answer

A) Students should be able to generalize the idea that 10 in any one position of the number result in one single thing in the next bigger place. 
B) Because these numbers are so large,teachers should just use the examples provided in the mathematics textbook. 
C) Models of the unit cubes can still be used. 
D) Students should be given the opportunity to work with hands-on,real-life examples of them. 
A) Students should be able to generalize the idea that 10 in any one position of the number result in one single thing in the next bigger place. 
B) Because these numbers are so large,teachers should just use the examples provided in the mathematics textbook. 
C) Models of the unit cubes can still be used. 
D) Students should be given the opportunity to work with hands-on,real-life examples of them.

Question 10

What statement below would represent a child that has yet grasped the knowledge of recognizing groups of ten?

Accepted Answer

A) Counts out sixteen objects and can tell you how many by counting each piece. 
B) Counts out sixteen and puts the 10 in one pile and 6 in another and tells you there are sixteen. 
C) Counts out sixteen and makes two piles of eight and tells you there are sixteen. 
D) Counts out sixteen and places 6 aside and tells you 10 and 6 are sixteen. 
A) Counts out sixteen objects and can tell you how many by counting each piece. 
B) Counts out sixteen and puts the 10 in one pile and 6 in another and tells you there are sixteen. 
C) Counts out sixteen and makes two piles of eight and tells you there are sixteen. 
D) Counts out sixteen and places 6 aside and tells you 10 and 6 are sixteen.

Question 11

What is the major challenge for students when learning about three-digit numbers?

Accepted Answer

A) Students are not clear on reading a number with an internal zero in place. 
B) A different process is used than how students learned with two-digit numbers. 
C) Students are not competent with two-digit number names. 
D) An instructional process that values quick recall and response. 
A) Students are not clear on reading a number with an internal zero in place. 
B) A different process is used than how students learned with two-digit numbers. 
C) Students are not competent with two-digit number names. 
D) An instructional process that values quick recall and response.

Question 12

What is the valuable feature of what hundred charts and ten-frame cards demonstrate?

Accepted Answer

A) The meaning behind the individual digits. 
B) The identity of the digit in the ones place and in the tens place. 
C) The distance to the next multiple of ten. 
D) The importance of place-value. 
A) The meaning behind the individual digits. 
B) The identity of the digit in the ones place and in the tens place. 
C) The distance to the next multiple of ten. 
D) The importance of place-value.

Question 13

Describe an activity that would help students to better conceptualize very large numbers.How would this activity build conceptualization?

Accepted Answer

Better conceptualiza

Question 14

Three section place-value mats can help students see the left to right order of the pieces.What statement below would correctly depict 705?

Accepted Answer

A) 7 hundred blocks and 5 tens. 
B) 7 hundred blocks and 0 tens. 
C) 7 hundred blocks and 0 units. 
D) 7 hundred blocks and 5 units. 
A) 7 hundred blocks and 5 tens. 
B) 7 hundred blocks and 0 tens. 
C) 7 hundred blocks and 0 units. 
D) 7 hundred blocks and 5 units.

Question 15

What would be a strong indication that students are ready to begin place-value grouping activities?

Accepted Answer

A) Students understand counting by ones. 
B) Students have had time to experiment with showing amounts in groups of twos,fives and agree that ten is a useful-sized group to use. 
C) Students have only worked with small items that can easily be bundled together. 
D) Students are able to verbalize the amounts they are grouping. 
A) Students understand counting by ones. 
B) Students have had time to experiment with showing amounts in groups of twos,fives and agree that ten is a useful-sized group to use. 
C) Students have only worked with small items that can easily be bundled together. 
D) Students are able to verbalize the amounts they are grouping.

Question 16

Place-value mats provide a method for organizing base-ten materials.What would be the purpose of using two ten-frames in the ones place?

Accepted Answer

A) Show the left-to-right order of numbers. 
B) Show how numbers are built. 
C) Show that there is no need for regrouping. 
D) Show that there is no need for repeated counting. 
A) Show the left-to-right order of numbers. 
B) Show how numbers are built. 
C) Show that there is no need for regrouping. 
D) Show that there is no need for repeated counting.

Question 17

Base ten riddles engage students in what type of mathematical demonstration?

Accepted Answer

A) Part-part-whole representation. 
B) Commutative representation. 
C) Equivalent representation. 
D) Nonproportional representation. 
A) Part-part-whole representation. 
B) Commutative representation. 
C) Equivalent representation. 
D) Nonproportional representation.

Question 18

The statements below are true of patterns and relationships on a hundreds chart EXCEPT:

Accepted Answer

A) Count by tens going down the far-right hand column. 
B) Starting at 11 and moving down diagonally you can find the same number in the ones and tens place. 
C) Starting at the 10 and moving down diagonally the numbers increase by ten. 
D) In a column the first number (tens digit)counts or goes up by ones as you move down. 
A) Count by tens going down the far-right hand column. 
B) Starting at 11 and moving down diagonally you can find the same number in the ones and tens place. 
C) Starting at the 10 and moving down diagonally the numbers increase by ten. 
D) In a column the first number (tens digit)counts or goes up by ones as you move down.

Question 19

The multiplicative structure of a number would help students in acquiring skill in all of the following EXCEPT:

Accepted Answer

A) Writing numbers greater than 100. 
B) Reading large numbers. 
C) Knowing ten in any position means a single thing. 
D) Generalizing structure of number system. 
A) Writing numbers greater than 100. 
B) Reading large numbers. 
C) Knowing ten in any position means a single thing. 
D) Generalizing structure of number system.

Question 20

What is the primary reason for delaying the use of nonproportional models when introducing place-value concepts?

Accepted Answer

A) Models do not physically represent 10 times larger than the one. 
B) Models like abacus are hard to learn how to use. 
C) Models like money provide more conceptual than procedural knowledge. 
D) Models do not engage the students as much as the proportional models. 
A) Models do not physically represent 10 times larger than the one. 
B) Models like abacus are hard to learn how to use. 
C) Models like money provide more conceptual than procedural knowledge. 
D) Models do not engage the students as much as the proportional models.

Exam 11: Developing Whole-Number Place-Value Concepts

What mathematical representation would help students identify patterns and number relationships?

All of the activities below would provide opportunities for students to connect the base-ten concepts with the oral number names EXCEPT:

A calculator activity that is good assessment to see whether students really understand the value of digits is titled "Digit Change".Students must change one number without putting in the new number.What place value would a student need to know in order to change 315 to 295?

What does the relational understanding of place value needs to begin with?

Complete this statement,"Number sense is linked to a complete understanding of..".

As students become more confident with the use of place value models they can represent them with a semi-concrete notations like square-line-dot.What number would be represented by 16 lines,11 dots and 5 squares?

All the examples below are examples of proportional base-ten models EXCEPT:

The ideas below would give students opportunities to see and make connections to numbers in the real world.The statements below identify examples that would engage students with large benchmark numbers EXCEPT:

The statement below are all helpful when guiding students to conceptualize numbers with 4 or more digits EXCEPT;

What statement below would represent a child that has yet grasped the knowledge of recognizing groups of ten?

What is the major challenge for students when learning about three-digit numbers?

What is the valuable feature of what hundred charts and ten-frame cards demonstrate?

Describe an activity that would help students to better conceptualize very large numbers.How would this activity build conceptualization?

Three section place-value mats can help students see the left to right order of the pieces.What statement below would correctly depict 705?

What would be a strong indication that students are ready to begin place-value grouping activities?

Place-value mats provide a method for organizing base-ten materials.What would be the purpose of using two ten-frames in the ones place?

Base ten riddles engage students in what type of mathematical demonstration?

The statements below are true of patterns and relationships on a hundreds chart EXCEPT:

The multiplicative structure of a number would help students in acquiring skill in all of the following EXCEPT:

What is the primary reason for delaying the use of nonproportional models when introducing place-value concepts?

Teaching Mathematics in the 21st Century

Exploring What It Means to Know and Do Mathematics

Teaching Through Problem Solving

Planning in the Problem-Based Classroom

Building Assessment Into Instruction

Teaching Mathematics Equitably to All Children

Using Technology Tools to Teach Mathematics

Developing Early Number Concepts and Number Sense

Developing Meanings for the Operations

Helping Students Master the Basic Facts

Developing Strategies for Addition and Subtraction Computation

Developing Strategies for Multiplication and Division Computation

Algebraic Thinking, equations, and Functions

Developing Fraction Concepts

Developing Strategies for Fraction Computation

Developing Concepts of Fractions and Decimals

Proportional Reasoning

Developing Measurement Concepts

Geometric Thinking and Geometric Concepts

Developing Concepts of Data Analysis

Exploring Concepts of Probability

Developing Concepts of Exponents, integers, and Real Numbers

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