1.5 symbols and pictures w
TRANSCRIPT
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items.
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items. For example, let’s use the letter “A” to represent an apple, i.e.
is A or 1A
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items. For example, let’s use the letter “A” to represent an apple, i.e.
is 2A,
is A or 1A
then is 5A, and no apple is 0A or 0,
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items.
Addition or subtraction operation may be recorded accordingly, for example:
+
For example, let’s use the letter “A” to represent an apple, i.e.
is 2A,
is A or 1A
then is 5A, and no apple is 0A or 0,
–
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items.
Addition or subtraction operation may be recorded accordingly, for example:
is simply recorded as 3A + 2A → 5A+
For example, let’s use the letter “A” to represent an apple, i.e.
is 2A,
is A or 1A
then is 5A, and no apple is 0A or 0,
–
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items.
Addition or subtraction operation may be recorded accordingly, for example:
is simply recorded as 3A + 2A → 5A+
For example, let’s use the letter “A” to represent an apple, i.e.
is 2A,
is A or 1A
then is 5A, and no apple is 0A or 0,
–as 3A – 2A → A
Symbols and PicturesBesides numbers, we also use letters and pictures to help us to
keep track of quantities and relations. Let’s start with using letters to track different types of items.
Addition or subtraction operation may be recorded accordingly, for example:
is simply recorded as 3A + 2A → 5A+
For example, let’s use the letter “A” to represent an apple, i.e.
is 2A,
is A or 1A
then is 5A, and no apple is 0A or 0,
–as 3A – 2A → A
We may extend this notation to addition and subtraction of apple-arithmetic.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
We may record the transactions as 34A – 16A – 5A + 16A – 25A.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions:34A – 16A – 5A + 16A – 25A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions:
= 18A – 5A + 16A – 25A34A – 16A – 5A + 16A – 25A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions:
= 18A – 5A + 16A – 25A34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions:
= 18A – 5A + 16A – 25A34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
50A=
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
50A – 46A=
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
50A – 46A= = 4A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
Symbols and Pictures
I. In the order of the transactions: lI. Group it into two groups,the apples that came in vs apples that went out:= 18A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
34A – 16A – 5A + 16A – 25A
= 13A + 16A – 25A= 29A – 25A = 4A
50A – 46A= = 4A
We may record the transactions as 34A – 16A – 5A + 16A – 25A.Let’s compute the outcome in two different ways.
Example A. On the 1st day, Farmer Andy picked 34 apples. He sold 16 of them and used another 5 to bake a pie. On the 2nd day, he picked 16 more apples, then traded 25 apples for a block of cheese with his neighbor. Record these apple-transactions with addition and subtraction operations using “A” for . How many apples are left after 2 days?
So we have 4 apples left. Note that method lI tells us that Andy picked 50 apples in total and 46 apples are “spent.”
Symbols and Pictures
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as 5A + 4B:
Symbols and Pictures
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
5A + 4B:
Symbols and Pictures
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
A + B The expression means 1 apple + 1 banana.
5A + 4B:
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
5A + 4B:
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
5A + 4B:
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
.
We also use the verb “combine” for resolving an addition or subtraction problems.
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
Example B. Combine.
We also use the verb “combine” for resolving an addition or subtraction problems.
a. 2A + 3B + 5A – B
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
Example B. Combine.
We also use the verb “combine” for resolving an addition or subtraction problems.
a. 2A + 3B + 5A – B
7A=
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
Example B. Combine.
We also use the verb “combine” for resolving an addition or subtraction problems.
a. 2A + 3B + 5A – B
7A + 2B =
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
Symbols and Pictures
+
Using “A” to represent an apple and “B” to represent a banana, we may record 5 apples and 4 bananas as
5A + 4B
Note that while A + A is 2A, B + B is 2B, the expressionsA + B or B + A may not be condensed as AB or BA.
A + B The expression means 1 apple + 1 banana.
Example B. Combine.
We also use the verb “combine” for resolving an addition or subtraction problems.
a. 2A + 3B + 5A – B
7A + 2B =
5A + 4B:
We will reserve AB or BA for other purposes.
(An AppleBanana is not an Apple nor a Banana.)
(This answer may not be shorten.)
Symbols and Pictures
+
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.
––
––
––
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.
––
––
––
––
––
– 8A
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
––
––
––
––
––
– 8A
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
4. Repeat steps 1–3 for the bananas.––
––
––
––
––
– 8A
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
4. Repeat steps 1–3 for the bananas.––
––
––
––
––
––
––
––
––––
16B– 8A
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
4. Repeat steps 1–3 for the bananas.––
––
––
––
––
––
––
––
––––
– 3B16B– 8A
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
4. Repeat steps 1–3 for the bananas.––
––
––
––
––
––
––
––
––––
– 3B16B– 8A
13B
Symbols and Pictures
When combining multiple transactions of apples and bananas by hand, collect them in the following organized manner.
16A
b. 16A + 9B + 5A – B – 4A + 3A + 4B – 4A – 2B + 3B
24A
=
1. Combine all the apples that came in, the ones with a “+” signin the front.2. Combine all the apples that went out, the ones with a “–” sign in the front.3. Combine the above results to obtain the number of apples left.
4. Repeat steps 1–3 for the bananas.––
––
––
––
––
––
––
––
––––
– 3B16B– 8A
13B
16A + 13B
–– –––– ––
Symbols and Pictures
Symbols and Pictures
A
B
Suppose we have two quantities A and B represented by two line segments as shown.
Symbols and Pictures
A
B
2m
3m
Suppose we have two quantities A and B represented by two line segments as shown. Just as 5m = 2m + 3m can be view as gluing two sticks together and getting one stick of length 5 meters,
Symbols and Pictures
A
B
2m
3m2m 3m
Suppose we have two quantities A and B represented by two line segments as shown. Just as 5m = 2m + 3m can be view as gluing two sticks together and getting one stick of length 5 meters,
5m
Symbols and Pictures
A
BA B
A + B = S (Sum)
2m
3m2m 3m
Suppose we have two quantities A and B represented by two line segments as shown. Just as 5m = 2m + 3m can be view as gluing two sticks together and getting one stick of length 5 meters, we may view the sum S = A + B as the line segments formed by joining A and B into one piece.
5m
Symbols and Pictures
A
BA B
A + B = S (Sum)
2m
3m2m 3m
Suppose we have two quantities A and B represented by two line segments as shown. Just as 5m = 2m + 3m can be view as gluing two sticks together and getting one stick of length 5 meters, we may view the sum S = A + B as the line segments formed by joining A and B into one piece.
5m
Note the addition relation 2m + 3m = 5m may be phrased as subtractions: 5m – 3m = 2m or 5m – 2m = 3m.
Symbols and Pictures
A
BA B
A + B = S (Sum)
2m
3m2m 3m
Suppose we have two quantities A and B represented by two line segments as shown. Just as 5m = 2m + 3m can be view as gluing two sticks together and getting one stick of length 5 meters, we may view the sum S = A + B as the line segments formed by joining A and B into one piece.
5m
Note the addition relation 2m + 3m = 5m may be phrased as subtractions: 5m – 3m = 2m or 5m – 2m = 3m. Likewise, the sum and differences
describe the same relation between A, B and S. S – B = AS = A + B, S – A = B,
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100For example, if we have the following pictures:
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
If we know that
100
S
80
T
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
If we know that
100
S
then this = S – 100,
80
T
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
If we know that
100
S
then this = S – 100,
80
T
and this = T – 80.
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
Often in real life, we are interested in tracking a quantity that is composed of two separate parts which can be represented by pictures shown.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
If we know that
100
S
then this = S – 100,
80
T
and this = T – 80.
Symbols and PicturesSo if the total is given, we may recover the parts by
subtraction.
Often in real life, we are interested in tracking a quantity that is composed of two separate parts which can be represented by pictures shown.
A
100
then this = 100 – A,
For example, if we have the following pictures:
B
80
and this = 80 – B.
If we know that
100
S
then this = S – 100,
80
T
and this = T – 80.
The importance of the pictures is to clarify the order of subtraction visually.
Example B. With the given information, answer the following questions.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given number(s) and letters. iii. List all the addition and subtraction relations.
Symbols and Pictures
Example B. With the given information, answer the following questions.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given number(s) and letters. iii. List all the addition and subtraction relations.
Symbols and Pictures
a. Andy and Beth went to lunch, the bill came to $18 out of which Andy paid A dollars and Beth paid B dollars.
Example B. With the given information, answer the following questions.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given number(s) and letters. iii. List all the addition and subtraction relations.
Symbols and Pictures
a. Andy and Beth went to lunch, the bill came to $18 out of which Andy paid A dollars and Beth paid B dollars.Ans. i. The total is the $18 bill with A and B as the parts.
Example B. With the given information, answer the following questions.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given number(s) and letters. iii. List all the addition and subtraction relations.
Symbols and Pictures
a. Andy and Beth went to lunch, the bill came to $18 out of which Andy paid A dollars and Beth paid B dollars.Ans. i. The total is the $18 bill with A and B as the parts.
BA
18
ii. Representing them with line segments, we have
Example B. With the given information, answer the following questions.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given number(s) and letters. iii. List all the addition and subtraction relations.
Symbols and Pictures
a. Andy and Beth went to lunch, the bill came to $18 out of which Andy paid A dollars and Beth paid B dollars.Ans. i. The total is the $18 bill with A and B as the parts.
BA
18
ii. iii.
18 – B = A.
18 = A + B, 18 – A = B,
The addition and subtraction relations are:
Representing them with line segments, we have
and
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group.
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
16 (=M)F
Pii. In picture,
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
16 (=M)F
Pii. In picture, iii.
and P – 16 = F.
P = F + 16,
P – F = 16,
The addition and subtraction relations are:
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
16 (=M)F
Pii. In picture, iii.
and P – 16 = F.
P = F + 16,
P – F = 16,
The addition and subtraction relations are:
c. Let S be the number of sunny days and C be the number of cloudy (or rainy days). From previous records, on the average, LA has 263 days with sun in a year.
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
16 (=M)F
Pii. In picture, iii.
and P – 16 = F.
P = F + 16,
P – F = 16,
The addition and subtraction relations are:
c. Let S be the number of sunny days and C be the number of cloudy (or rainy days). From previous records, on the average, LA has 263 days with sun in a year.Ans. i. The total is 365 days with S and C as the parts.
Symbols and Picturesb. Let M be the number of males and F be the number
of females. After a survey, out of a group of P people, we found that there are 16 males in the group. Ans. i. The total is the P with M and F as the parts.
16 (=M)F
Pii. In picture, iii.
and P – 16 = F.
P = F + 16,
P – F = 16,
The addition and subtraction relations are:
c. Let S be the number of sunny days and C be the number of cloudy (or rainy days). From previous records, on the average, LA has 263 days with sun in a year.Ans. i. The total is 365 days with S and C as the parts.
263 (=S)C
365ii. In picture,
Symbols and PicturesExample C. A bag of 100 pieces of mixed candies contains
three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation.
Symbols and PicturesExample C. A bag of 100 pieces of mixed candies contains
three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation. Ans. i. The total is the 100 with A, B, and C as the parts.
Symbols and Pictures
A B
100
Example C. A bag of 100 pieces of mixed candies contains three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation. Ans. i. The total is the 100 with A, B, and C as the parts. ii.
26 (=C)
Symbols and Pictures
A B
100
Example C. A bag of 100 pieces of mixed candies contains three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation. Ans. i. The total is the 100 with A, B, and C as the parts. ii.
The ± relations are: 100 = A + B + 26
26 (=C)
Symbols and Pictures
A B
100
Example C. A bag of 100 pieces of mixed candies contains three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation. Ans. i. The total is the 100 with A, B, and C as the parts. ii.
100 – A = B + 26, 100 – B = A + 26, 100 – 26 = A + B,
The ± relations are: 100 = A + B + 26
26 (=C)
Symbols and Pictures
A B
100
Example C. A bag of 100 pieces of mixed candies contains three different types: Apple-drops, Butter-scotch and Chocolate. Let A be the number of apple-drops, B be the number of butter-scotches, and C be the number of chocolates. We counted that there are 26 pieces of chocolates. Answer the following.i. Which number or letter represents the total? Which numbers or letters represent the parts? ii. Draw and label a line picture with the given numbers and letters. List all the addition and subtraction relation. Ans. i. The total is the 100 with A, B, and C as the parts. ii.
100 – A = B + 26, 100 – B = A + 26, 100 – 26 = A + B,
The ± relations are: 100 = A + B + 26
26 (=C)
100 – A – B = 26, 100 – A – 26 = B, 100 – B – 26 = A
Symbols and PicturesWe note that each relation listed in part ii. may be viewed as a
physical procedure.
Symbols and PicturesWe note that each relation listed in part ii. may be viewed as a
physical procedure.
“100 – B – 26 = A” says that“take away from 100 the number of butter-scotches and the number of chocolate; we get the number of apple-drops”.
For example
Symbols and PicturesWe note that each relation listed in part ii. may be viewed as a
physical procedure.
“100 – 26 = A + B (= 74)”
“100 – B – 26 = A” says that“take away from 100 the number of butter-scotches and the number of chocolate; we get the number of apple-drops”.
“take away from 100 the 26 pieces of chocolates, the remaining 74 pieces, are butter-scotches and apple-drops,
For example
says that
or that there are 74 non-chocolates.