About Course

The 2Six3 Learning Two-Week Mathematics Programme is a focused 10-hour intervention designed to address the specific gaps identified in the initial diagnostic assessment. The programme begins by strengthening core number skills, including directed numbers, fractions, decimals and percentages, before progressing into algebra, equations, ratios, proportions and percentage changes.

Across 10 one-hour lessons, Tadiswa will receive direct teaching, guided practice, homework, continuous assessment and two progress tests. The programme is supported by two tutors, allowing for both structured instruction and additional consolidation. Progress will be reviewed against the selected 2Six3 learning objectives, with approximately 80% independent accuracy used as the benchmark for an objective to be considered secure.

At the end of the two weeks, Tadiswa’s results will be reviewed to identify which objectives are secure, developing or still a priority and to recommend the next stage of her Year 8 consolidation and Year 9 preparation.

Join the lesson. Meeting ID: 896 3589 5828

Lesson	2Six3 Objective	Teaching Focus	Lesson Activities	Homework / Assessment
1	2S-N8.1	Add & subtract directed numbers	Number line, positive/negative integers, temperature and money contexts	Directed-number practice
2	2S-N8.2	Multiply & divide directed numbers	Sign rules, multiplication/division fluency, mixed operations	15–20 mixed questions
3	2S-N8.3	Add & subtract unlike fractions	LCM/common denominators, simplifying answers, mixed fractions	Fraction practice
4	2S-N8.4 & N8.5	Fractions, decimals & percentages	FDP conversions; find 10%, 5%, 25%, 50% and other percentages	Percentage word problems
5	Week 1 Review	Consolidate Number Foundations	Retrieval quiz, misconceptions, mixed problem solving	Progress Test 1 + corrections
6	2S-A8.1 & A8.2	Simplify & expand expressions	Like terms, coefficients, single brackets, checking by substitution	Algebra practice
7	2S-A8.3	Solve one-step equations	Inverse operations, balancing method, checking solutions	One-step equation set
8	2S-A8.4	Solve two-step equations	Balance method, equations involving addition/subtraction and multiplication/division	Two-step equation practice
9	2S-R8.1–R8.3	Ratio, proportion & percentage change	Simplify/share ratios, direct proportion, percentage increase/decrease	Mixed ratio & proportion problems
10	Final Review & Assessment	Apply all priority objectives	Mixed Year 8 questions, reasoning, misconceptions and corrections	Progress Test 2

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Recorded Lessons

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Lessons

Lesson 1

Directed Numbers Using Counters

Same Signs and Different Signs

2S-N8.1 • 2Six3 Learning

Know Your Counters

A positive counter represents +1.

A negative counter represents −1.

−

Zero Pair

One positive and one negative cancel each other.

+ −

= 0

Rule 1 — Same Signs

When the numbers have the same sign:

Add the numbers.
Keep the common sign.

Example 1: Positive + Positive

+3 + +2

+ + + + + +

There are 5 positive counters.

+3 + +2 = +5

Example 2: Negative + Negative

−4 + −3

− − − − + − − −

There are 7 negative counters.

−4 + −3 = −7

Rule 2 — Different Signs

When the numbers have different signs:

Make zero pairs.
Cancel each positive/negative pair.
Count the counters left.
The sign of the counters left is the sign of the answer.

Example 3: Different Signs

+5 + −3

+ + + + +
− − −

Cancel 3 zero pairs.

2 positive counters remain.

+5 + −3 = +2

Example 4

−6 + +4

− − − − − −
+ + + +

Cancel 4 zero pairs.

2 negative counters remain.

−6 + +4 = −2

Part A — Same Signs

Draw counters if needed. Then calculate.

1. +4 + +3 =

2. −3 + −5 =

3. +6 + +2 =

4. −7 + −4 =

5. −8 + −3 =

Part B — Different Signs

Make zero pairs and count what remains.

6. +6 + −4 =

7. −7 + +3 =

8. +9 + −5 =

9. −8 + +6 =

10. +4 + −9 =

Part C — Mixed Practice

11. −5 + −6 = ______

12. +8 + −3 = ______

13. −9 + +5 = ______

14. +7 + +6 = ______

15. −4 + +10 = ______

16. −12 + −3 = ______

17. +11 + −7 = ______

18. −10 + +4 = ______

19. +9 + +5 = ______

20. −6 + +6 = ______

Remember

Same signs: Add and keep the sign.

Different signs: Make zero pairs, cancel them, and use the sign of the counters remaining.

Special case: If every counter forms a zero pair, the answer is 0.

Kahoot 1: adding integers https://kahoot.it/challenge/08174506?challenge-id=a08bb442-53b7-4ca3-b02d-b1518540013a_1787133566429

Subtracting Directed Numbers

Same Signs → Different Signs → Mixed Practice

2Six3 Learning • Directed Numbers

Start by Reading the Signs

Important:

Every number has a sign.

A positive number can be written with or without its + sign.

+3 = 3

So:

+3 + +4 = 3 + 4

Example 1

+5 + +2

Rewrite: 5 + 2

Example 2

+7 − +3

Rewrite: 7 − 3

Part A — Rewrite the Signs

Rewrite these without unnecessary positive signs

Do not calculate yet. Just rewrite the expression.

1. +3 + +4

2. +7 − +2

3. +9 + +5

4. +12 − +8

5. +15 − +6

Part B — Subtracting Integers with the Same Sign

Same Signs

We will start with a positive number subtracting another positive number.

Example:

+8 − +3 = 8 − 3 = 5

Then we will move to two negative numbers.

Remember:

Subtracting a negative changes to addition.

Example:

−8 − −3 = −8 + 3 = −5

Stage 1 — Positive − Positive

1. +8 − +3 =

2. +11 − +4 =

3. +15 − +6 =

4. +18 − +7 =

5. +20 − +9 =

Stage 2 — Negative − Negative

6. −8 − −3 =

7. −12 − −5 =

8. −15 − −7 =

9. −18 − −6 =

10. −20 − −8 =

Stage 3 — Alternate Positive and Negative

11. +14 − +9 =

12. −14 − −9 =

13. +17 − +5 =

14. −17 − −5 =

15. +22 − +13 =

16. −22 − −13 =

17. +30 − +12 =

18. −30 − −12 =

19. +25 − +17 =

20. −25 − −17 =

Part C — Subtracting Integers with Different Signs

Different Signs

This time the two integers have different signs.

Positive − Negative

Subtracting a negative changes to addition.

+6 − −4 = 6 + 4 = 10

Negative − Positive

Subtracting a positive moves further into the negatives.

−6 − +4 = −6 − 4 = −10

Stage 1 — Positive − Negative

1. +5 − −3 =

2. +7 − −4 =

3. +9 − −6 =

4. +12 − −5 =

5. +15 − −8 =

Stage 2 — Negative − Positive

6. −5 − +3 =

7. −7 − +4 =

8. −9 − +6 =

9. −12 − +5 =

10. −15 − +8 =

Stage 3 — Alternate the Signs

11. +8 − −7 =

12. −8 − +7 =

13. +11 − −9 =

14. −11 − +9 =

15. +14 − −6 =

16. −14 − +6 =

17. +20 − −12 =

18. −20 − +12 =

19. +25 − −15 =

20. −25 − +15 =

2Six3 Worksheet Result

Rewrite Signs 0/5

Same Signs 0/20

Different Signs 0/20

Overall 0/45

Lesson 2 Multiplying and dividing Integers

Kahoot 2: adding and Subtracting Integers https://kahoot.it/challenge/04537317?challenge-id=a08bb442-53b7-4ca3-b02d-b1518540013a_1787133302227

activities

Activity 1:

Assessment

2Six3 Learning Progress Tracker

10 Lessons + 2 Progress Tests

Lesson Marks

Lesson 1 /10

Lesson 2 /10

Lesson 3 /10

Lesson 4 /10

Lesson 5 /10

Lesson 6 /10

Lesson 7 /10

Lesson 8 /10

Lesson 9 /10

Lesson 10 /10

Progress Tests

Test 1 /15

Test 2 /15

Programme Performance

Lesson Marks 0/100

Test Marks 0/30

Overall 0/130

Overall Percentage

Progress Status:

Enter the learner’s lesson and test marks, then select Calculate Progress.