# Math Grade 6

## 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 – Using numbers **

**Approximate length: 7 Lessons**

In this unit the children will read, write, order and compare numbers up to 10,000,000 and determine the value of each digit. Round any, whole number to a required degree of accuracy and use negative numbers in context. Solve number and practical problems that involve all of the above.

Specific National Curriculum Objectives Covered:

- To read and use calendars
- To read and use 12-hour and 24 hour clock
- To convert between the 12 hour and 24 hour systems
- To work out everyday money problems
- To use a number line to order positive and negative numbers, including decimals
- To understand and use the symbols < (less than) and > (greater than)
- To carry out addition involving negative numbers
- To carry out subtractions involving negative numbers

**Unit 4 – Decimal Numbers **

**Approximate length: 7 lessons **

In this unit the children will understand and use place value for decimals. Order decimals use the symbols =, <, >. Recognise and use relationships between operations including inverse operations.

Specific National Curriculum Objectives Covered:

- Multiplying and dividing by 10,100 and 1000
- Ordering decimals
- Estimates
- Adding and subtracting decimals
- Multiplying and dividing decimals

**Unit 5 – Working with numbers Approximate length: 7 lessons **

In this unit the children will multiply multi-digit numbers, divide numbers using the formal written method of long division, and interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context. Use their knowledge of the order of operations to carry out calculations involving the 4 operations.

Specific National Curriculum Objectives Covered:

- Square numbers
- Rounding
- Order of operations
- Long and short multiplication
- Long and short division
- Calculations with measurements

**Unit 12 – Probability **

**Approximate length: 7 lessons **

In this unit the children will record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale. Generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Specific National Curriculum Objectives Covered:

- Probability with words
- Probability scales
- Experimental Probability

**Unit 11 – Percentages **

**Approximate length: 7 lessons **

In this unit the children will define percentage as ‘number of parts per hundred’, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express 1 quantity as a percentage of another, compare 2 quantities using percentages, and work with percentages greater than 100%.

Specific National Curriculum Objectives Covered:

- Fractions and percentages
- Fractions of a quantity
- Percentages of a quantity
- Percentages with a calculator
- Percentages increase and decrease

**Unit 16 – Shapes **

**Approximate length: 7 lessons **

In this unit the children will use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D.

Specific National Curriculum Objectives Covered:

- 3D shapes and nets
- Using nets to construct 3D shapes
- 3D shape investigations
- Surface area and volume

**Unit 10 – Coordinates and Graphs **

**Approximate length: 7 Lessons **

In this unit the children will describe positions on the full coordinate grid (all 4 quadrants). Draw and translate simple shapes on the coordinate plane, and reflect them in the axes.

Specific National Curriculum Objectives Covered:

- Coordinates
- Naming graphs
- Graphs in the real world
- From mappings to graphs. Work out coordinates from rules
- To draw a graph from a simple rules

### Term 2

**7 – Algebra **

**Approximate length: 7 Lessons **

In this unit the children will substitute numerical values into formulae and expressions, understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors. Simplify and manipulate algebraic expressions to maintain equivalence. Understand and use standard mathematical formulae.

Specific National Curriculum Objectives Covered:

- Expressions and substitution
- Simplifying expressions
- Using formulae
- Writing formulae

**Unit 17 – Ratio **

**Approximate length: 7 Lessons **

In this unit the children will express 1 quantity as a fraction of another, where the fraction is less than 1 and greater than 1. Use ratio notation, including reduction to simplest form. Understand that a multiplicative relationship between 2 quantities can be expressed as a ratio or a fraction.

Specific National Curriculum Objectives Covered:

- …Simplifying ratios
- …Ratios and sharing
- …Ratios and fractions

**Unit 8 – Fractions **

**Approximate length: 7 Lesson **

In this unit the children will use common factors to simplify fractions; use common multiples to express fractions in the same denomination. Compare and order fractions. Add and subtract fractions with different denominators and mixed numbers, using the concept of equivalent fractions.

Specific National Curriculum Objectives Covered:

- Equivalent fractions
- Comparing fractions
- Adding and subtracting fractions
- Mixed number and improper fractions
- Calculations with mixed numbers

**Unit 3 – Perimeter and Area **

**Approximate length: 7 Lessons **

In this unit the children will derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders) calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes.

Specific National Curriculum Objectives Covered:

- Length and perimeter
- Area
- Perimeter and area of triangles

### Term 3

**Unit 15 – Interpreting data / statistics **

**Approximate length: 7 Lessons **

In this unit the children will describe, interpret and compare continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range). Construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Specific National Curriculum Objectives Covered:

- Pie charts
- Comparing data - mean, median, mode and range
- Statistical surveys
- Data collection
- Grouped data
- Recording data from tables and tally charts

**Unit 2 – Sequences **

**Approximate length: 7 Lessons **

- In this unit the children will generate terms of a sequence from either a term-to-term or a position-to-term rule. Recognise arithmetic sequences and find the nth term. Recognise geometric sequences and appreciate other sequences that arise.

Specific National Curriculum Objectives Covered:

- …Function machines
- Sequences and rules
- …Finding terms in patterns
- …Square numbers
- Triangular numbers

**Unit 14 – Equations **

**Approximate length: 7 Lesson **

In this unit the children will understand and use the concepts and vocabulary of equations, find pairs of numbers that satisfy an equation with 2 unknowns.

Specific National Curriculum Objectives Covered:

- Finding unknown numbers
- Solving equations
- Solving complex equations
- Setting up and solving equations

**Unit 13 – Symmetry **

**Approximate length: 7 Lessons **

In this unit the children will identify properties of, and describe the results of, translations, rotations, tessellation and reflections applied to given figures.

Specific National Curriculum Objectives Covered:

- Line symmetry
- Rotational symmetry
- Reflections
- Tessellations

**Unit 9 - Angles **

- In this unit the children will draw and measure line segments and angles in geometric figures, including interpreting scale drawings. Derive and use the standard ruler and compass constructions. Interpret mathematical relationships geometrically.

Specific National Curriculum Objectives Covered:

- Using compass to give directions
- Measuring angles
- Drawing angles
- Calculating Angles
- Properties of triangles and quadrilaterals

**Textbooks**

• **Collins Maths Frameworking Pupil Book 1.1**

## 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 to access all the lessons and resources. The objectives for Term 1 will be delivered through both face to face and remote learning. In addition to the textbooks, worksheets and class discussions we will be utilizing online platforms such as, Microsoft teams/Phoenix, Powerpoints, my imaths, Kahoot and Microsoft Forms. Interaction between students will be encouraged and integrated into lessons using the discussions and chat options available on online platforms.

## Assessment

**Formative: **Throughout the units, the children will complete graded work, quizzes and problem solving activities which will allow 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 PUMA. 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 covering topics from the whole year.