Introductory Number Sense (new curriculum k-2)

Question 1

What is the term for the number of objects in a set; can be represented by objects, pictures, words, and numerals.

How do you determine this number of objects in a set?

Answer 1

quantity

Quantity can be determined by counting and is always counted using the same sequence of words that come in an unchanging (stable) order. E.g. 2 is always one greater than 1, and this does not change.

You can begin counting at any number, but quantity is most easily determined by new students to math by counting by ones and using the final number said. You can skip count by counting in twos for example, which is faster than counting by ones, and as you grow you will have many ways of determining quantity, including multiplication based on the pattern you see in the objects.

With money it is common to skip count in 25s, since we have a physical coin that is 25 cents. You will notice that the skip count you choose will depend on how the objects are grouped.

You can also “subitize” which means recognizing smll quantities at a glance. For example, you can immediately see 5 without having to count each object. Putting objects into small arrangements where they can be subitized can help you count larger numbers.

Question 2

A symbol or group of symbols used to represent a number

Answer 2

numeral

Question 3

How do you represent the absence of quantity?

Answer 3

0

Places that have no value within a given number use zero as a placeholder.

Question 4

the type of number that can represent an object in a set

Answer 4

natural number

“counting number”

1, 2, 3, ….

Question 5

What are the values of the places in a four-digit natural number?

Answer 5

thousands, hundreds, tens, ones

Question 6

number line

Answer 6

• you can plot points on it
• each real number has exactly one point on the number line (a given real number can only be plotted in one spot, not anymore than that)

Question 7

The 1 in this natural number represents what value?

1234

Answer 7

The 1 is in the thousands place, so there is 1 thousand, so the 1 represents one thousand.

Question 8

The 2 in this natural number represents what value?

1234

Answer 8

The 2 is in the hundreds place, so there are 2 hundreds, so the 2 represents two hundred.

Question 9

The 3 in this natural number represents what value?

1234

Answer 9

The 3 is in the tens place, so there are 3 tens, so the 3 represents thirty.

Question 10

What is the value of the 4 in the following natural number?

1234

Answer 10

The 4 is in the ones place, so there are 4 ones, so it represents four.

Question 11

whole number

Answer 11

the counting numbers (1,2,3,….) and zero

All of these can be plotted on a number line

Question 12

Count by ones up to 100

Answer 12

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
….
89
90
91
92
93
94
95
96
97
98
99
100

Question 13

skip count by 20s up to 1000

Answer 13

20
40
60
80
100
120
140
160
180
200
220
240
260
280
300
320
…
920
940
960
980
1000

Question 14

skip count by 25s up to 1000

Answer 14

25
50
75
100
125
150
175
200
225
250
…
875
900
925
950
975
1000

Question 15

skip count by 50s up to 1000

Answer 15

50
100
150
200
250
300
350
…
800
850
900
950
1000

Question 16

skip count by 2s up to 1000

Answer 16

2
4
6
8
10
12
14
16
18
20
22
…
98
100
102
104
106
108
110
112
….
888
890
892
894
896
898
900
902
…
980
982
984
986
988
990
992
994
996
998
1000

Question 17

skip count by 10s

Answer 17

10
20
30
40
50
60
70
80
100
110
120
….
820
840
860
880
900
920
940
960
980
1000

Question 18

skip count by 10s starting at 12; up to 1000 but not over 1000

Answer 18

12
22
32
42
52
62
72
82
92
102
…
902
912
922
932
942
952
962
972
982
992

Question 19

Partitioning a quantity into a certain number of groups

Answer 19

sharing

division is a specific example of sharing where the specific number groups also have an equal number within the group

Question 20

Partitioning a quantity into groups of a certain size

Answer 20

grouping

Question 21

Count backwards from 20

Answer 21

20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1

Question 22

skip count by 5s up to 100

Answer 22

5
10
15
20
25
30
35
…
80
85
90
95
100

Question 23

All natural numbers are either ______ or _________

Answer 23

even, odd

even = you can evenly make groups of two without any left over
odd = one more than even, so you will have one left over if you try to make groups of two

Question 24

comparison words of quantity

Answer 24

Relative quantities:
- more, greater than, >
- less, less than, <
- same, equal, =, equality
- different, not equal, ≠, inequality

Purpose or need:
- enough
- not enough

Question 25

equality

Answer 25

a balance between two quantities

can be modeled with a balance

when equal, the balance is level

Question 26

What are all the ways to make 5 using the natural numbers

Answer 26

1 and 4
2 and 3
1 and 1 and 1 and 1 and 1
1 and 1 and 1 and 2
1 and 1 and 3

Question 27

What are all the ways to make 10 using two natural numbers?

Answer 27

1 and 9
2 and 8
3 and 7
4 and 6
5 and 5

Question 28

Combining parts to find the whole, or increasing an existing quantity, composition

Answer 28

addition +

Question 29

comparing two quantities, taking away one quantity from another, or finding a part of a whole, decomposition of a quantity

Answer 29

subtraction -

Question 30

associative property

Answer 30

the order in which more than two numbers are added does not affect the sum, so a sum can be composed in multiple ways

For example 2, 6, and 8 can be added in these ways (where you add what is in the brackets first)

(2+6) + 8

2 + (6+8)

(2+8) + 6

One of these ways to add might be easier for you. For me, I prefer the third one since I know the ways to make ten include a 2 and 8, so I can immediately see 10 + 6, and that is easy to make 16.

Question 31

Addition and subtraction strategies

Answer 31

e.g. 2 + 8

counting on: 3,4,5,6,7,8,9,10 using 8 fingers and counting from 3

counting back: 2 + 10 is two more than 2 + 8, and 2+10 is 12, so 2 + 8 is two less than 12, or 10

decomposition: break down the numbers and fit the pieces back together to form the full picture 2 + 8 = 2 + 4 + 4 = 6 + 4 = 10

compensation: adding a number to one and subtracting it from the other later on to make sure the balance stays the same, so 2 + 8 = 3 + 7 = 4 + 6 = 5 + 5 = 10

making tens: 2 + 8 = 10 we already have this strategy embedded in the example, but if it was 2 + 9 we would know that is one more than 10 because we know 9 is one more than the number needed with 2 to make 10

Question 32

commutative property

Answer 32

the order in which two quantities are added does not affect the sum

Keep in mind that the order in which two quantities are subtracted does affect the difference!

Question 33

opposite mathematical operation to addition

Answer 33

subtraction

Question 34

whole

Answer 34

everything

so the parts 2 and 8 make a sum of 10, everything that is there is 10, so 10 is the whole

Can be a whole set of objects, or a whole object that can be partitioned into a number of equal parts

A whole can be any size and is designated by context

Question 35

part

Answer 35

a portion of the whole

Question 36

fact family

Answer 36

a group of related addition and subtraction number facts

E.g.

2 + 8 = 10

8 + 2 = 10

10 - 2 = 8

10 - 8 = 2

Question 37

one of two equal groups

one of two equal pieces

Answer 37

one half

1/2

in a quantitiy partitioned into two equal groups, each group represents one-half of the whole quantity

in a shape or object partitioned into two identical piecs, each piece represents one-half of the whole

the two halves should be the same size as each other

Question 38

unit fraction

Answer 38

one of the equal parts that compose the whole

1/2 is one part of the two equal parts that compose the whole

1/3 is one part of the three equal parts that compose the whole

one whole can be interpreted as a number of unit fractions

Question 39

fraction

Answer 39

represents a part-to-whole relationship

one whole can be interpreted as a number of unit fractions

Question 40

Which is larger assuming that the whole is the same size?

1/2

1/3

Answer 40

1/2 since this is 1 out of 2, which is half

1/3 is 1 out of 3, which means that we have divided the same object into three parts instead of the two and this means that each part must be smaller if the whole is the same for both fractions. Since we only have one of those parts, and not two or three of the parts, this will be relatively small compared to the one out of two parts.