Question 1

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

To change 315 to 295, the student would need to change the digit in the tens place from 1 to 9. Therefore, the student needs to understand the value of digits in the tens place.

Question 2

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

Accepted Answer

Option A indicates that the child counts each object individually rather than recognizing the concept of grouping by tens, which is a sign of not yet understanding the base-ten system.

Question 3

The mathematical language we use when introducing base-ten words is important to the development of the ideas.Identify the statement that consistently connects to the standard approach.

Accepted Answer

The standard approach for introducing base-ten words involves using the format of (number of tens) tens and (number of ones) ones. Therefore, option D, which reads "6 tens and 9 ones," is the best choice as it follows the standard approach. Option B is also correct as it has the same value as option D but lists the ones before the tens, which is acceptable but not the standard approach. Option A simply lists the number in word form, and option C lists the tens before the ones, which is not the standard approach for introducing base-ten words.

Question 4

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

The number of seconds in a month is not a large benchmark number.

Question 5

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

Accepted Answer

The primary reason for delaying the use of nonproportional models is that they do not physically represent 10 times larger than the one, which is a critical concept in place-value understanding.

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

The answer of As students become more confident with the...

Question 7

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

Accepted Answer

Option C is incorrect because starting at 10 and moving down diagonally does not increase the numbers by ten; instead, it increases by 11 (e.g., from 10 to 21 to 32, etc.).

Question 8

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

The number 705 would be represented on the place-value mat with 7 hundred blocks, 0 ten blocks, and 5 unit blocks. Therefore, choice D (7 hundred blocks and 5 units) is the best choice. Choices A, B, and C would all be incorrect representations of the number on a place-value mat.

Question 9

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

Accepted Answer

Base ten riddles engage students in equivalent representation because they require students to understand that a number can be represented in multiple ways using different combinations of tens and ones.

Question 10

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

Accepted Answer

Students need to have the ability to understand that certain groups (such as twos, fives, and tens) are useful and have had time to experiment with this concept before they are ready for place-value grouping activities. This demonstrates an understanding of the concept of place value and the importance of grouping by certain amounts.

Question 11

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

Accepted Answer

Relying solely on textbook examples may limit students' understanding and ability to apply the concept to real-life situations. It is important to provide hands-on experiences and use models to aid in conceptualization. Students should also be able to generalize the idea of place value to better understand numbers with 4 or more digits.

Question 12

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

Accepted Answer

The major challenge for students when learning about three-digit numbers is often understanding how to read and interpret numbers that include a zero in one of the internal positions, such as in the number 102. This can be confusing because it requires a conceptual understanding of place value and the role of zero in the number system.

Question 13

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

Accepted Answer

The multiplicative structure of a number deals with understanding the relationships between factors and multiples of a number. It may not directly help students in writing numbers greater than 100.

Question 14

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

Accepted Answer

A hundreds chart helps students identify patterns and number relationships, such as skip counting, even/odd numbers, and addition/subtraction patterns.

Question 15

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

Accepted Answer

The answer of All of the activities below would provide...

Question 16

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

Accepted Answer

The answer of What is the valuable feature of what...

Question 17

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

Accepted Answer

The relational understanding of place value requires counting by tens and ones, making the model, saying and writing the numeral. Students must be able to understand the relationship between the value of each digit in a number and how it contributes to the overall value of the number. This understanding is developed through activities that involve counting, modeling, and representing numbers in different ways. Therefore, choice D is the correct option as it includes all the necessary components for relational understanding of place value.

Question 18

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

Accepted Answer

Money is not a proportional base-ten model, as the values of the coins and bills do not represent equal units of ten. Counters and cups, cubes, strips and squares all represent equal increments of ten, making them proportional base-ten models.

Question 19

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

The answer of Place-value mats provide a method for organizing...

Question 20

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

Accepted Answer

Number sense is closely linked to a complete understanding of place-value, as it involves recognizing the value of digits based on their position within a number.

Quiz 11: Developing Whole-Number Place-Value Concepts