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a. \(4 \times 5 + 5 \times 2 \times 6 + 4 = (4 + 5) + (5 \times 2) \times (6 + 2)\)

b. \(1 + 3 + 6 \times 2 + 3 \times 5 = 10 \times 2 + 3 \times 5\)

c. \(4 \times 3 + 5 \times 2 \times 6 = 12 + 10 + 12\)

In each expression, the learners incorrectly apply the distributive property. The distributive property states that for any numbers \(a\), \(b\), and \(c\), \(a \times (b + c) = a \times b + a \times c\). However, the learners misapply this property by incorrectly distributing the multiplication across addition in some parts of the expression.

For example:

a. In the expression \(4 \times 5 + 5 \times 2 \times 6 + 4\), the learner incorrectly tries to distribute the multiplication across addition as if it were \(5 \times (2 \times 6)\). This leads to a misunderstanding of the correct order of operations.

b. In the expression \(1 + 3 + 6 \times 2 + 3 \times 5\), the learner incorrectly tries to distribute the multiplication across addition, resulting in \(10 \times 2 + 3 \times 5\). This disregards the correct precedence of operations.

c. In the expression \(4 \times 3 + 5 \times 2 \times 6\), the learner incorrectly distributes the multiplication as if it were \(5 \times (2 \times 6)\), which is not applicable in this context.

Overall, the learners incorrectly apply the distributive property, leading to incorrect simplifications of the expressions.

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GROUP A

They multiplied twice with the number 2:

5 x 2 and 2 x 6

They should have only multiplied 5 x 2 x 6

GROUP B

They first added 1 + 3 + 6 and then multiplied the sum of it with 6.

They should have multiply ( 6 x 2 ) and ( 3 x 5) first before they added 1 + 3 .

GROUP C

The grouping of the numbers to do the calculations are wrong.

They should have multiply 5 x 2 x 6 first before they added the other numbers.

The answer should be 73

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Learners do not apply BODMAS.

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Group 1

The learner insert brackets around 4 x 3 and 5 x 2 x6 to show that they will be multiplying first and then adding. There is an error in calculation as well where the learner has multiplied the number 2 twice.

Group 2

The learners should multiply 6x 2 and 3x5 first before adding. The learner has made a mistake by adding 1 + 3+6 which gave 10 and then continued to multiply the 10 by 2.

Group 3

The learner could of inserted brackets with 5 x 2 x 6 and then continued to add the rest of the sum. The learners should understand that by inserting brackets it indicates the first step of the order of operations.

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They inserted bracketsandnthey multiplied 2 by 6  

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They inserted bracketsandnthey multiplied 2 by 6  

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Group 1

They used ×2 twice (5×2) and (2×6)

Group 2

They added 1,3 and 6 together i stead of multiplying first.

Group 3

They used brackets in correctly instead of multiplying first 5×2×6 and then add

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Group 1: Instead of multiplying the answer of 5×2, by 6. The learner multiplied 2 by 6, which is wrong.

Group 2: These learners added 1,3 and 6 together, where they were only supposed to add 1 and 3. 6 was supposed to be multiplied by 2.

Group 3: 5×2×6 was supposed to be in one bracket.

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Group 1: Uses x2 twice (5x2 and 6x2 instead of 5x2x6 =60)

Group 2: Adding 1,3 and 6 before multiplying.

Group 3: Adding before multiplying and splitting 5x2x6 into to separate parts.

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They need to follow BODMAS or BOMDAS

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Group 1- (4x3) +(5x2)x6=

2- 1+3+( 6x2)+(3x5)=

3- Total wrong usage of brackets.

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Group 1 multiplied the 6 with 2 and the 5 with 2 instead of multiplying them all together. . Group 2 added the 6 meant to be multiplied by the 2. Group 3 added the 6 with 4 instead of multiplying it with the 5 and 2.

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Group 1 : They used 2 to multiply it with 5 and used 2 again to multiply it with 6.

Group 2 : They added the first 3 digits together and then mulitply it.

Group 3 : Places brackets incorrectly.

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Group 1 do not know how to use BODMAS which say that there understanding is lacking the rule (4x3) + (5x2) x6 = 132

Group 2 applies to the same rule 1+3 +(6x2) + (3x5)=31

Group 3 is 4+5+(5x2x6)+4=190 . The rule is to always solve the bracket first

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Group 1: They used 2 to multiply it by 5 and then 6, instead they should have multiplied each number by each other.

Group 2: They added first by adding the first 3 digits together and then multiplied

Group 3: The grouping is incorrect

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Group 1: The learner calculated incorrectly. He said (5x2 = 10 and again used 2x6= 12) instead of 5x2=10x6=60) S0, 12 + 60 = 72 compared to 34 as seen in Group1.

Group 2: The learner added 1+3+ 6 together but in this case "6" is not meant to be added, therefore the learner reaches the incorrect answer compared to 1+3=4+12+15= 16+15= 31

Group 3: The learner grouped them in the wrong manner. It was suppose to be: 4+5= 9+

(5x2x6= 10x6= 60)

+4

9+ 60 +4 =73

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Group 1: The correct way to do this calculation is to firstly recognise the multiplication which has to be done.

(4 x 3) + (5x 2 x 6)

The answer will be 72 since 4 x 3 is 12 and 5 x2 x6 is 60. Therefore 12 + 60 is 72

What this group has done is that they had multiplied the 2 with both 5 and 6 separately.

Group 2: This group went to add 1+3+6 which gave them 10 and then they multiplied is by 2, but the 6 is not an addend. So they had to multiplied 6 x2 first which will give them 12 then 5x3 = 15

And lastly add 1+3 which is 4

Therefore the answer will be 4 + 12 + 15 = 31

Group 3: They also made the mistake to say that the 6 is an addend, but it is part of the multiplication. Therefore the had to multiply the 5x2x6 which is 60 adn then add all the other numbers which will be 5+4+60+4 = 73

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Group 1:

The learners multiply 5 by 2 and 2 by 6 instead of multiplying 5x2x6 THEN adding 12.

Group 2:

Performs addition before multiplication.

Group 3:

Places brackets incorrectly, thus failing to perform all multiplication before addition.

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Group 1:

Learners added 10 to 12, where they should have multiplied the two numbers.

Group 2:

Learners first proceeded to add (1+3+6), instead of first multiplying (6x2)+(3x5).

Group 3:

Learners mistakenly put (6+4) at the end of operation in brackets, which means that it must be calculated first.

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In group 1:

Learners calculated in such a manner that they used the number 2 twice. The number sentence should read as : 5 x 2 x 6 = 60

Not 5 x 2 = 10 + 2 x 6 = 12

Group 2:

The number sentence should read as 12 + 3 + 1 + 15

Group 3:

9 + 60 + 10 =

Learners did not calculate in the correct order, which is why they ended up with the wrong number sentences

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Group 1:

When multiplying with more than one number, you need to work from left to right.

Correct - 4 x 3 = 12

Incorrect - 5 x 2 x 6 = 10 + 12 (this was split into two where it should have remained one sum reading from left to right).

Corrected - 12 + 10 x 6 = 12 + 60 = 72

Group 2:

Addition was completed with a part of a multiplicative expression, not a whole one.

Corrected - 1 + 3 + 6 x 2 + 3 x 5 = 4 + 12 + 15 = 31

Group 3:

Addition was once again completed with a part of a multiplicative expression, not a whole one.

Correct - in grouping the (4 + 5)

Incorrect - separating (5 x 2) x (6 + 4)

Corrected - (4 + 5) + (5 x 2 x 6) + 4 = 9 + 60 + 4 = 73

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Group 1 used addition instead of multiplication.

12 + 10 x 6

12 + 60

72

Group 2

Added then multiplied.

Answer should be 31

Group 3

Grouped wrong

Answer should be 73

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Group 1

4x3+5x2x6

= 12 + 10 x6

= 12 + 60

=72

Group 1 wrongly used the 2 twice. They multiplied it with the 5 and the 6.

Group 2

1+3+6x2+3x5

=1+3+(6x2)+(3x5)

= 4 + 12 + 15

=31

The rules of BODMAS applies here. As I have shown with brackets.

Group 3

4+5+5x2x6+4

=4+5+(5x2)x6+4

=4+5+(10x6)+4

=4+5+ 60 +4

=73

All multiplications must be done first. Group 3 put the brackets in the wrong place when they grouped the 6 and 4 together.

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Group 1

4x3+5x2x6

5x2x6 is not 10+12 it is 60

Group 2

they did addition first

Group 3

4+5+5x2x6+4

=(4+5) + (5x2) x (6+4) they should have done (4+5) + (5x2x6) + 4= 73

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Group 1

The learners calculated 5 x 2 x 6 as:

(5x2) + (2x6) instead of (5x2) x 6 or 5 x (6x2)

Learners viewed the multiplicative expression as two expressions instead of one.

Group 2

The learners solved the additive expression first.

Group 3

The learners are perhaps showing confusion with regards to identifying "terms" as referred to in algebra. similar to group 1 not aware that 5 x 6 x 2 is one term and needs to be solved together, but simply separating terms by pairing them together with an operation sign.

A. Waterboer

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GROUP 1

4x3+5x2x6

: 5x2x6 is 60 not [10+12]

therefore 12+60=72

GROUP 2

1+3+6x2+3x5

[1+3+6x2 is not 10x2] you need to start with multiplication first then do the addition after ]NB : BODMAS

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Group 1

The learner is multiplying the 5x2x6 incorrectly. 5x2 = 10 and 10x6=60.

Group 2

The learner is working from left to right.

Group 3

The numbers are paired off incorrectly.

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Learner error- Understanding the importance of number signs

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Learner error- Understanding the importance of number signs

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Based on the images displayed it is clear to see that learners are not following the rules of bodmas.

InGroup 1:

4x3+5x2x6

=12+10+12

=34

The error occured at 5x2x6

Tearners multliplied 5x2 and 2x6

Instead of

4x3+5x2x6

=12+5x12 or 12 +10x6

=12+60 12+60

=72 72

In Group 2: 1+3+6x2+3x5

=10x2+3x5

The error is in 1+3+6x2

Learners cannot add 1+3+6 as the 6 must be multiplied by 2

Therefore it should be 1+3+6x2+3x5

= 4+ 6x2+3x5

= 4+12+ 15

= 16+15

=31

In Group 3

4+5+5x2x6+4

=(4+5)+ (5x2)x (6+4) - learner grouped incorrectly

it should read

= 4+5+ (5x2x6)+4

= 9+ (10x6) +4

= 9+60+4

=73

Ms. F. Arendse