These PowerPoint slides contain teaching materials for Primary 5. It is designed to aid teachers in the delivery of Matrix Math lessons. The slides contain solutions to Matrix Math questions in detailed steps enhanced with Powerpoint animation to help students better understand and grasp complex concepts.

# Primary 5 Online Materials

### Who are the slides for?

The slides are specially designed for Matrix Math teachers to deliver lessons effectively and consistently.

### Holiday Programmes

Going to Primary 5

- Fractions operations problem sums
- Fractions comparison model (Quantity and units)
- Equivalent proportions
- Advance supposition concepts applications
- Before change after
- Advance part and whole applications
- Remainder theory concepts
- Advance stacking model applications
- Advance Equivalent proportion applications
- Internal quantity transfer
- Before change after, advance applications
- Simultaneous concept applications

### Lesson 1 to 10

This week (Lesson 1), we will begin our 1st lesson for the new academic year.

This will be a challenging year. Similar concepts the children learned in P4 will be designed to be more challenging and indirect. Also, new heavy topics will be introduced to the children this year, namely Ratio and Percentage. Given the upcoming challenges, we will be "pushing" the students harder and a little earlier than at other levels. We seek your support and understanding.

This week's lesson will only focus on 2 concepts instead of the usual 4 concepts per lesson.

- Grouping given total
- Grouping given the difference

These two concepts are the most commonly tested in P5 and P6. It can be tested on many topics and incorporated with other concepts. Thus we would like our students to have a strong grasp of these two concepts early in the year.

**Calculators:**

Please purchase a scientific calculator for your children and allow them to bring it to class next week.

This week (Lesson 2), we will continue with Whole Numbers and Decimals.

In this lesson, we will cover the concepts

- Age
- Factors and multiples
- Shortage and Surplus

"These three concepts were taught in P4 but will undoubtedly be tested again in P5 WA and SA.

"Shortage and surplus" - Schools teach with either the listing method** or the model method. We will introduce the model method to solve "Shortage and surplus" questions. Whilst the model method is more difficult to grasp, it involves fewer steps, minimising the risk of careless computational mistakes.

**The listing method had been taught in Primary 4.

This week (Lesson 3), we will continue with Whole Numbers and Decimals 3.

In this lesson, we will cover Difference concepts and Simultaneous concepts.

The "Difference concept "for P5 will be slightly more complicated than in P4.

"Simultaneous concept" is arithmetic math. It is solving 2 unknowns with 2 number statements. This is a useful skill to acquire early in the year as it can be applied to solve subsequent problem sums.

This week (Lesson 4), we will continue with Whole Numbers and Decimals 4.

This lesson will cover Quantity **Internal** transfer and Quantity** External **Transfer. This lesson's important takeaway is knowing how to use models to visualise quantity transfer.

These two concepts are commonly tested heuristic questions in P5 and P6.

This week is the last lesson for 2022. We will like to take this opportunity to wish all parents and students a Merry Christmas and a Happy New Year!

This week (Lesson 5), we will continue with Fraction 1.

This lesson will focus on the multiplication and division of fractions.

The problem sum concepts we will cover this week will be

- Fractions as values. E.g. John gave 3/4 kg of his cake to Peter.
- Fractions as units. E.g. John gave 3/4 of his cake to Peter.

Mistakenly applying the concept of fractions as units or values is a common error among P5 students.

This week's lesson (Lesson 6) will be focused on Fraction 2. Specifically, we will introduce the concept of The Remainder Theory and how to apply it through model drawing. While these problems can also be solved using the Branching Methods, we have chosen to teach the Model Methods as they are more consistent with the methods typically used in schools and what your children learned in Primary 4.

Next week, in Lesson 8, we will focus on the topic of Fractions, specifically delving deeper into the concept of Remainder Theory. Next week's lesson involves solving problem sums where the remainder is unknown. We have observed that these types of questions are frequently tested in school exams. In order to master this concept, it is crucial that students become proficient in using model drawing techniques related to Remainder Theory.

To support their learning, we recommend that students practice by redoing the worksheets from Lessons 7 and 8.

This week (lesson 9) and the next, we will revise all the taught concepts. In this revision lesson, we will focus on

- Difference concept
- Shortage and surplus
- Quantity external/internal transfer
- Fractions
- Remainder theory

*CALCULATORS*:

1. Please remind your children to bring their calculators. Many of the questions involve huge numbers that make solving the questions unnecessarily stressful without a calculator.

2. Do not substitute the calculator with a phone.

This week (Lesson 10), we will continue to revise the concepts taught in previous lessons. The concepts we will cover are as follows:

> How to use differences to solve problem sums

> Grouping concept

> Problem sums involving intervals

> Area and perimeter

> Equivalent proportion

> Whole numbers

### Lesson 11 to 20

This week, students will be introduced to the topic of Triangles.

While some schools may cover this topic later in the year, based on previous experience, most schools will cover it in the first half of the academic year.

From our observation, most students can easily find the area of triangles, even for complex problems. However, they sometimes need help identifying the correct height and base. To help improve this, we will provide additional exposure and practice through triangle-related questions.

*All students must attend this lesson at the centre*.

We will continue our exploration of the Area of Triangles, focusing on four common ways these types of questions can be tested. These include

- Finding the area involving folding,
- Finding the area given the value of units, base or height,
- Finding the area given the value of units in the perimeter, and
- Finding the area of triangles inside a grid.

To do well in this topic, it is essential to have broad exposure to different forms of Area of Triangles questions. In subsequent lessons, we will expose the children to more questions to help them develop a deeper understanding of the concept.

This week (Lesson 14), we will be continuing with Ratio Lesson 2

In this lesson, we will focus on identifying Common Bases in Ratios. Identifying a common base is central to solving Ratio questions.

This week (Lesson 15), we will be introducing Ratio Lesson 3

The students will be learning to solve Fraction problem sums using Ratio methods.

Using Ratio methods to solve fractions problem sums will minimise the need to draw complex models. It is beneficial for children who dislike drawing models.

This week (Lesson 16), we will continue with Ratio lesson 4

In this lesson, we will cover three basic ratio heuristic concepts. These three concepts will form the basic building blocks of more complex ratio problem sums.

They are:

1. Group unchanged.

2. Total unchanged.

3. Difference unchanged.

### Lesson 21 to 30

This week (Lesson 26), we will be covering a new topic - “Rate”.

“Rate” is a commonly tested concept under “Volume”. We will also cover Rate questions that do not involve volume in this lesson.

This week (Lesson 27), we will be going back to Ratio, lesson 5.

This lesson is relatively more challenging and we expect most of the students to struggle a little. Instead of the regular 4 concepts, we will focus on only 3 concepts this week. The concepts we will be covering will also involve solving units and parts.

- Unchanged total with a presumption
- All changed without presumption
- Quantity and value with Difference Concept

This week (Lesson 28), we will return to Ratio, lesson 6.

This lesson will be our last lesson on Ratio. In this lesson, we will cover higher-order Ratio concepts that is not so commonly tested in P5. We expect this lesson to be challenging for most students.

This week (Lesson 29), we will begin a new Topic, "Percentage."

In this lesson, we will cover the basics of Percentages.

> Express part of a whole as a percentage.

> Convert between fractions, decimals and percentages.

> Finding the percentage of a quantity.

> Using the unitary method

> Finding percentage increase/decrease

Next week, we will be covering discount/GST/interest. This is where parents can help. Parents can take this opportunity to explain the discounts they receive. How do merchants use discounts to attract customers? (e.g 50% discount = buy 1 get 1 free) What is GST? How does fixed deposit work?

This week (Lesson 30), we will continue with “Percentage 2”

We will also cover

- Concept of discounts.
- Concept of profit and loss.
- Concept of GST.
- Concept of interest.

### Lesson 31 to 40

This week (Lesson 31), we will continue with “Percentage 3”

In this lesson, we will cover heuristics problem sums involving percentages.

1. Identifying a common base.

2. Equivalent proportions.

3. Branching out.

In this lesson (Lesson 32) and the following two lessons, we will revise all the concepts we have taught since June. In this revision lesson, we will focus on:

- Area and perimeter.
- Concepts relating to Triangles.
- Percentage problem sums involving discounts.
- Heuristic problem sums involving both ratios and fractions.
- Whole number applying "Quality and value" concepts.
- Pattern.

This week (Lesson 33), we will continue to revise previously taught concepts. In this revision lesson, we will focus on:

- Higher-order application of Area of triangles concepts.
- Common base in ratios
- Branching concepts involving percentage.
- Equivalent proportion
- Difference concepts.

This week (Lesson 34), we will continue to revise previously taught concepts. In this revision lesson, we will focus on:

- Geometry
- Percentage
- Comparison concepts
- Supposition concepts

This week (Lesson 35), we will begin a new topic, Average. In this lesson, we will be covering basic and introductory concepts:

- Application of Basic Average formula
- Average involving part and whole

This week (Lesson 36), we will continue with Average 2. In this lesson, we will cover:

1. Using Average to find the largest and smallest possible values

2. Average involving difference concept. This is one of the more challenging concepts tested under the topic of Average. We will be revising this concept with the students again in subsequent lessons.

This week (Lesson 37), we will continue with Average 3.

In this lesson, we will cover the following commonly tested problem sum concepts:

1. Involving comparison of quantity.

2. Involving comparison of quantity and units.

3. Involving simultaneous equations.

4. Involving finding change.

This week (Lesson 38), we will begin with a new topic - Geometry.

In this lesson, we will cover finding basic angles:

1. Angles at a point.

2. Angles on a straight line.

3. Vertically opposite angles.

4. Angles properties in a triangle.

5. Properties of equilateral triangles.

6. Properties of isosceles triangles.

7. Properties of a rhombus.

8. Properties of a parallelogram.

This week (Lesson 39), we will begin with a new topic - Geometry 2.

In this lesson, we will cover the following concepts:

1. Properties of trapezium.

2. Finding unknown angles.

3. Finding combined angles.

4. Angles involving angles.

This week (Lesson 40), we will begin revising previously taught topics and concepts.

In this lesson, we will be revising the following topics and concepts:

1. Area and perimeter.

2. Area of triangles.

3. Average.

4. Angles.

5. Volume.

6. Quantity value involving money.

7. Percentage

6. Whole numbers.

### Lesson 41 to 50

This week (Lesson 41), we will continue preparing for SA2 with Select 12.

This week (Lesson 42), we will continue with the revision of previously taught topics and concepts.

The topics and concepts we will cover are:

- Area and perimeter.
- Area of triangles.
- Angles.
- Average with percentage
- Money - quantity value
- Ratio with percentage change
- Fractions
- Volume

This week (Lesson 43), we will continue preparing for SA2 with Select 14. It is also essential that the children attempt the prescribed homework. The questions in the additional practice papers are integral to the preparation system. The primary and additional practice papers are designed to prepare the children for the final year exams.

This week (Lesson 44), we will continue preparing for SA2 with Select 15. It is also essential that the children attempt the prescribed homework. The questions in the Additional Practice papers are integral to the preparation system. The main and Additional Practice papers are designed to prepare the children for the final year exams.

This week (Lesson 45), we will continue preparing for SA2 with Select 16. It is also essential that the children attempt the prescribed homework. The questions in the Additional Practice papers are integral to the preparation system. The Main and Additional Practice papers are designed to prepare the children for the final year exams.

This week (Lesson 46), will be the last Select Paper for the academic year 2022.

In the next 3 weeks, we will summarise the learnings of 2022 with the students.

This week (Lesson 47), we will begin the first three lessons on “summary of concepts”.

As shared in the previous message, these three lessons will summarise the key problem sums concepts that will bridge the student to the next academic year.

This week (Lesson 48), we will continue with the second of three lessons on “summary of concepts”.

As shared in the previous message, these three lessons will cover all the key must-know concepts that will bridge the student to the next academic year.

This lesson (Lesson 49), will be the final lesson for 2022 academic year. Next week we will begin with Primary 6 syllabus.

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