# Maths Grade 7

## Overview

The Math Syllabus at GEMS Wesgreen International Secondary School aims to support students to develop their ability to calculate fluently, to reason and solve problems through application of knowledge and transferable skills. Throughout the year we recover and extend objectives as the focus is on providing a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.

## Learning Outcomes

The aims of all subjects state what a teacher may expect to teach and what a student may expect to experience and learn. These aims suggest how the student may be changed by the learning experience.

The aims of the Math Syllabus are to encourage and enable students to:

- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

## Unit Overviews

### Term 1

**Unit 1 – Numbers **

**Approximate length: 1 week**

In this unit the children will learn to make a connection between positive and negative numbers. Also, how to work with the HCF and LCM of multiple numbers. Write numbers in the form of their prime factors and also be able to identify and explain squares and roots. Be able to use the factor tree method to calculate the prime factors or LCM and HCF using this method.

Specific National Curriculum Objectives Covered:

- To find square and cube numbers and square and cube roots.
- To use calculator to work out powers of numbers.
- To multiply and divide negative numbers.
- To find LCM of pairs of numbers.
- ·• To find the HCF of pairs of numbers.
- ·• To write a number as a product of its prime factors.

**Unit 2 – Geometry**

**Approximate length: 2 week **

- In this unit the children will be able to translate, rotate and reflect shapes in any direction. Learners will be able to identify and calculate with reason the size of an unknown angle in parallel lines. Be able to identify the properties of quadrilaterals and construct perpendicular bisectors and angle bisectors. Student will be able to identify and calculate the size of missing angles using the properties of quadrilaterals.
Specific National Curriculum Objectives Covered:

- To translate a 2D shape.
- To calculate angles in parallel lines.
- To know the geometric properties of quadrilaterals.
- To enlarge a 2D shape by a given scale factor.
- To construct perpendicular bisectors and angle bisectors.

**Unit 3 – Probability**

**Approximate length: 1 week **

- In this unit the children will be able to explain what probability means. Calculate probability using experimental data results, also be able to identify mutually exclusive events. Be able to compare the difference between sample space and random sampling. Students will also be able to represent their probability using venn diagram.

Specific National Curriculum Objectives Covered:

- To calculate probability from experimental data.
- To know what mutually exclusive outcomes are.
- To use the probability of an outcome to calculate the probability that the outcome does not happen.
- To use sample spaces and Venn diagrams to calculate probabilities.
- To understand relative frequency as an estimate of probability.

**Unit 4 – Percentages**

**Approximate length: 5 lessons **

- In this unit the children will be able to calculate percentage of one unit into another. Students will be able to calculate percentage using a calculator and also using the multiplier method. Learners will learn to work out the percentage increase or change as well as working backward to find the percentage if the new and original amount had been given. Learners will also be taught to calculate with percentages over 100%

Specific National Curriculum Objectives Covered:

- To write one value as a percentage of another value.
- To use multiplier to calculate percentage changes.
- To write a change of value as a percentage increase or decrease.
- To calculate or identify an increase of more than 100%.

**Unit 5 – Congruent triangles**

**Approximate length: 3-4 lessons **

- In this unit the children will be taught to reason and recognise what congruent shapes are, and how they can be identified with reasons. Learners will also be able to divide a shape into 2 or more congruent shapes using a ruler and pen/pencil. Learners will learn to use the AAS, RHS, SSS and SAS as reasons for triangles to be congruent. And prove that two triangles are congruent because of their ratio and ASS, RHS, SSS and SAS.

Specific National Curriculum Objectives Covered:

- To recognise congruent shapes.
- To divide a shape into congruent shapes.
- To recognise congruent triangles.
- To prove that two triangles are congruent.

**Unit 6 – Volume of Prisms (conversion of units)**

**Approximate length: 1 week **

- In this unit the children will be taught to convert units of area, volume and capacity. They will learn how to calculate SA of 3D shapes using the formula for each face individually. As well as know that you can add all the surfaces together to get the area of the 3D shape. Learners will also be able to identify the difference in formula for SA and for volume for 3D shapes.

Specific National Curriculum Objectives Covered:

- To convert the units of area, volume and capacity.
- To calculate the surface area of prisms.
- To calculate the volume of prisms.

**Unit 7 – Graphs**

**Approximate length: 1-2 weeks **

- In this unit the children will be able to complete tables using linear Equation and using the coordinates to draw a graph for his equation. They will also be able to identify and read our coordinates on a straight line if asked for specific points. Learners will be taught to work out the gradient of and straight line. Learners will be able to use and calculate with the formula y = mx + c. Draw graphs and identify graphs that fit with certain linear equations. And also solve for quadratic equations.
- Specific National Curriculum Objectives Covered:
- To complete a table of values for a linear equation and use this to draw a graph of the equation.
- To calculate the gradient of a straight line drawn on a coordinate grid.
- To work out an equation of the form y = mx + c from its graph
- To draw and interpret real life graphs
- ·To complete a table of values for a quadratic equation and use this to draw a graph of the equation.
- To solve a quadratic equation using a graph.

**Unit 8 – Numbers **

**Approximate length: 1 Week **

In this unit the children will be able to multiply and divide by 10 and larger numbers up to 1000 000. They will be taught to round using Significant Figure values and be able to identify how many SF figures a number has been rounded to. They will write numbers in standard form and be able to use standard from to multiply numbers out. Learners will be able to reason as to why the exponent is positive or negative and whether the final answer is in the correct standard form or not.

Specific National Curriculum Objectives Covered:

- Learner can successfully multiply and divide with negative power of 10
- Learner can round to specific significant figures
- Write large numbers in standard form
- Multiply with numbers in standard form.

**Unit 9 – interpreting graphs**

**Approximate length: 1 week **

In this unit the children will demonstrate the correct method of drawing pie charts, with emphasis on starting the measurement of each angle at the end of the previous sector. The sum of the angles of the sectors of any pie chart must always be 360°, so pupils should check that the angles add up to 360. We will ensure that learners know the difference between different types of correlation. Make sure pupils understand that scatter diagrams are different to line graphs. Also how to draw the line of best fit and what the outlier is.

Specific National Curriculum Objectives Covered:

- To be able to Interpret graphs and diagrams
- To draw pie charts relative to total frequency
- To read scatter graphs
- To understand correlation
- To create scatter graphs and use a line of best fit

### Term 2

**Unit 10 – Algebra **

**Approximate length: 2 weeks**

In this unit, the pupils will have plenty of opportunity to reflect on the use of algebra as generalised number, and to make clear links to the rules they have learnt for number. Discuss the power of algebra or generalisation. Pupils will learn how to multiply all the terms in brackets. Pupils will interpret negative signs in brackets accurately. Pupils will make links to grid multiplication, which may be useful to help pupils make links and visualise what is happening.

Pupils will identify what constitutes ‘like’ when powers are included. Provide plenty of opportunity for pupils to compare and discuss what are and what are not like terms.

Specific National Curriculum Objectives Covered:

- To simplify algebraic expressions involving the four basic operations
- To simplify algebraic expressions by combining like terms
- To remove brackets from an expression (simplifying)
- To manipulate algebraic expressions and identify algebraic expressions
- To write algebraic expressions involving powers

**Unit 11a**- **Chapter 7 Ratio **(Collins Maths Frameworking Pupil Book 1.3)

**Approximate length: 1 week**

In this unit, the pupils will convert units in questions involving ratio. They will understand that the units must be the same before they form a relationship-involving ratio.

Pupils will use a point/coordinate as the centre of enlargement and they will enlarge the shape without reference to the given point. Pupils will enlarge various shapes by a given scale factor. Remind pupils that the shape produced after an enlargement will look similar to the original; it will just be a bigger or smaller version.

Pupils will use the correct units when working with map scales. Make sure pupils understand that units must be the same before writing a ratio.

Specific National Curriculum Objectives Covered:

- To simplify ratios
- To simplify ratios in different units
- To solve ratio and proportion problems

**Unit 11b – Ratio and Proportion **

**Approximate length: 1 week**

Specific National Curriculum Objectives Covered:

- To compare lengths, areas and volumes of 2D and 3D shapes (ratio)
- To enlarge a 2D shape by a fractional scale factor
- To understand how to use map scales

**Unit 12 – Fractions and Decimals**

**Approximate length: 2 weeks **

- In this unit, the pupils will apply the rules in different contexts and the rules for adding and subtracting fractions with those for multiplying and dividing fractions. Pupils will add or subtract the denominators as well as the numerators when adding and subtracting fractions.
- Pupils will work with decimals and understand place value. Pupils will understand that each column to the left of another is 10 times greater. Build on this so that pupils are aware that each column to the right is 10 times smaller.

Specific National Curriculum Objectives Covered:

- To add or subtract fractions including mixed numbers
- Multiply a fraction or a mixed number and an integer
- To divide a fraction or a mixed number by an integer and divide an integer or a mixed number by a fraction
- To multiply with combinations of large and small numbers mentally
- To divide combinations of large or small numbers mentally

**Unit 13 – Proportion**

**Approximate length: 2 weeks **

- In this unit, pupils will understand the difference between direct and inverse proportion, usually by using direct proportion to answer inverse proportion questions. Pupils will learn to use the correct multiplier. Pupils will draw correctly scaled axes for questions. Pupils will be able to explain the reasoning behind the chosen values. Make sure pupils can point out key words in a question that indicate inverse proportion. Also, make sure that pupils write the variables the correct way around in their formula.

Specific National Curriculum Objectives Covered:

- To understand the meaning of direct proportion
- To find missing values in problems involving proportion
- To understand inverse proportion
- To represent direct proportion and indirect proportion graphically and algebraically
- To recognise direct and inverse proportion and work out missing values

### Term 3

**Unit 14 – Circles **

**Approximate length: 2 weeks**

In this unit, pupils will understand the difference between radius and diameter. Give them plenty of opportunity to use both. Provide pupils with collective memory activities, which will be useful to help pupils remember which is which. Pupils will make the link between the work they have done previously on perimeter and area, and the work on the circumference and area of a circle.

Specific National Curriculum Objectives Covered:

- To knows the definition of a circle and the names of its parts
- Works out the relationship between the circumference and diameter of a circle
- To calculate the circumference of a circle
- To calculate the area of a circle
- To solve problems involving circles

**Unit 15 – Equations and Formulae**

**Approximate length: 2 weeks **

- In this unit, pupils will expand brackets and understand you have to multiply the first term by the number outside the bracket and just write down the second term. Pupils will understand the difference with adding or subtracting from each side when dealing with equations with unknowns on both sides.
- Pupils will learn to remove the smallest
*x*value by adding or subtracting from both sides (explain, for example, that –5*x*is smaller than 2*x*). Pupils will also remove the number on the same side as the remaining*x*value by adding or subtracting from both sides. Finally, divide both sides by the number in front of the*x*to obtain the answer.

Specific National Curriculum Objectives Covered:

- To solve equations involving brackets
- To solve equations where the answers are fractions or negative numbers
- To solve equations with the variable on both sides
- To solve equations with brackets and fractional coefficients
- To solve simple equations involving squares
- To change the subject of a simple formula
- To change the subject of a formula involving squares

**Unit 16 – Interpreting Data**

**Approximate length: 2 weeks **

- In this unit, the pupils will identify appropriate groups. They will make links between the data and the question provided. They will appreciate how this should inform their decisions. Give them many real life examples to discuss. This will help them see there is not necessarily a correct answer but that some grouping is more efficient/informative than others.
- Give pupils a range of examples, some good and some less good, from real-life contexts. Ask pupils to discuss how useful the representations are in terms of assessing the evidence and/or delivering a clear message. Provide many opportunities for pupils to compare different representations. Encourage pupils to generate their own questions about the data and to assess the advantages and disadvantages of different representations and statistical measures.

Specific National Curriculum Objectives Covered:

- To create a grouped frequency table from raw data
- To interpret frequency diagrams
- To draw a frequency diagram from a grouped frequency table
- To be able to compare data from two sources
- To recognise when a statistical chart may be misleading

## Blended Learning

Throughout this year there will be blended learning and we are using multiple teaching methods in order to help our students learn more effectively. All students whether face to face or learning from home will have the opportunity access all the lessons and resources. This will include a combination of traditional classroom instruction and digital learning, such as:

- Using wifi microphone to enable remote student to hear more clearly during lessons
- Using different types of instructional materials
- Incorporate different means of technology (zoom, teams, phoenix classroom, screencastify)
- Using their newly acquired knowledge, by applying it in breakout rooms/ or in groups in classroom.

## Assessment

**Formative: **Throughout the units, the children will complete graded work, quizzes and problem solving activities which allows the teacher to assess the students’ attainment and inform their planning.

**Summative: **At the end of each term we complete internal tests – Unit based and combined Units. Students complete standardized tests such as mid-term tests as well as end of term tests. This allows us to measure the students’ progress throughout the term and year. At the end of the academic year, the students sit for the end of year exams.