Unit of Work on Calculations with Decimal Numbers

Calculations with Decimal Numbers: A fantastic collection of lessons that incorporate all of the skills Key Stage 3 students need to work with decimal numbers. ************************************************************************* This best practice unit was created by a teacher of mathematics with over 15 years classroom experience. Classroom tested and student approved. ************************************************************************* Included: Addition with decimals Subtraction with decimals Multiplication with decimals Dividing with decimals Multiplication using the grid method Multiplication problems Rounding to a decimal place

Simplifying Expressions by Collecting Like Terms

Students learn about simplifying expressions by collecting like terms. As learning progresses they consider a mixture of unkowns and numbers. More able students also work with unknowns to a different power.At the start of the lesson they recap forming expressions using shapes. In the main they learn how to simplify expressions by identifying like terms. At the end they are challenged to complete a magic square using algebraic terms. What's Included Lesson Plan PDF Microsoft PowerPoint, Smart Notebook, Activ Inspire Flipchart presentation files. Differentiated worksheet PDF Interactive Excel File Tarsia Differentiated Learning Objectives All students should be able to simplify algebraic expressions involving a single unknown. Most students should be able to identify and collect like terms to simplify algebraic expressions. Some students should be able to simplify algebraic expressions with different powers. Visit mr-mathematics.com for hundred of mathematics lessons across 11 - 18 and structured schemes of work that are focused on pedagogy and teacher support. Become a member and download all the teaching and learning resources instantly.

Tangents Circle Theorems

This lesson guides the class through the discovery of circle theorems involving tangents. The theorems include, the angle between a tangent and radius and angles in alternate segments. Each circle theorem has an associated proof in the additional resources section. Once the theorems are discovered there is opportunity for students to consolidate their learning by calculating unknown angles. Differentiated Learning Objectives All students should be able to discover that a tangent and radius intersecting at the circumference of a circle and perpendicular. Most students should be able to discover that a tangent and radius intersecting at the circumference of a circle and perpendicular and that angles in alternate segments are equal. Some students should be able to derive both theorems relating to tangents at the circumference of a circle and apply them to solve complex problems involving multiple circle theorems. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Applying Circle Theorems Involving Tangents

Students learn about applying circle theorems involving tangents to solve complex problems. The alternate segment theorem and angle between between a radius and tangent are used as part of larger and more complicated problems. More able students are challenged to derive proofs by linking various theorems and angle properties together. The start of the lesson recaps the alternate segment theorem and angle between a radii and tangents. The plenary takes the students through a typical examination question to assess the progress made. Differentiated Learning Objectives All students should be able to solve problems involving the angle between a radius an chord. Most students should be able to apply multiple circle theorems involving tangents to solve complex problems. Some students should be able to prove multiple circle theorems involving tangents. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Addition and Subtraction with Fractions and Mixed Numbers

Students learn how to perform addition and subtraction with fractions and mixed numbers. As learning progresses students link fractions with perimeter and distances. More able students are challenged to add and subtract simple algebraic fractions and mixed numbers. The start of the lesson recaps adding fractions with different denominators. The plenary challenges students to calculate the mid-point of a line where the ends are given as mixed numbers. Differentiated Learning Objectives All students should be able to add and subtract with top heavy fractions. Most students should be able to add and subtract with top heavy fractions and mixed numbers. Some students should be able to add and subtract with algebraic fractions Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Calculating Probabilities from Two-Way Tables

Students learn how to calculate a probability from a two-way table. As learning progresses students learn how to create a a two-way table from a written description and consider how the sample size changes for specific groups. The start of the lesson recaps reading data presented in a two-way table. The end of the lesson is used to assess the progress made agains the differentiated learning objectives through an exam style questions. Differentiated Learning Objectives All students should be able to complete a two-way table. Most students should be able to use two-way tables to calculate theoretical probabilities. Some students should be able to understand the change in sample size for different criteria.

How to perform rotations about a Centre

Students learn how to rotate an object on a grid using a centre, direction and amount of turn. As learning progresses the centre is given as a coordinate pair and on a Cartesian axes. The start of the lesson is used to recap the difference between rotational and reflective symmetry. The plenary challenges students to describe two different and equivalent transformations. Differentiated Learning Objectives All students should be able to perform a rotation where the centre touches the object. Most students should be able to perform a rotation on a grid. Some students should be able to perform and describe a rotation on a Cartesian grid.

Planes of Symmetry in 3D Shapes

Students learn how to identify the planes of symmetry in 3D shapes. Learning progresses from sketching the planes of symmetry for a cube and cuboid to constructing scale drawings of prisms on isometric paper. The start of the lesson recaps the properties of 3D shapes for a composite solid. The plenary challenges students to consider shapes with an infinite number of planes of symmetry. Differentiated Learning Objectives All students should be able to identify the planes of symmetry in a cube. Most students should be able to identify the planes of symmetry in a solid shape using isometric paper. Some students should be able to identify and sketch the planes of symmetry for any solid. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Translating Shapes using Vectors

Students learn about translating shapes using vectors. As learning progresses they move from performing translations on a grid to describing translations using vector notation. The start of the lesson is used to recap describing a rotation or reflection that will map an object onto an image. The plenary is based around a jigsaw puzzle where students give their answers in the form of translation vectors. Differentiated Learning Objectives All students should be able to translate an object on a grid using vector notation. Most students should be able to perform and describe translations on a grid using vector notation. Some students should be able to perform and describe a translation on Cartesian axes using a translation vector. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Understanding Set Notation

Students learn how to find the union and intersection of elements using basic set notation. As learning progresses students consider the complement of a set while reviewing basic number properties. At the start of the lesson students recap using sample space diagrams to find the probability of cracking a code. The plenary is used to assess progress against the differentiated learning objective through a typical exam question. Differentiated Learning Objectives All students should be able to list the elements of a set. Most students should be able to enumerate sets and unions/intersections of sets systematically. Some students should be able to find the complement of a set. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Circle Theorems - Angles in the same segment, Cyclic Quadrilaterals, Angle at Centre & Circumference

Students are taken through the discovery of various circle theorems. The theorems include, angle at the centre is twice the angle at the circumference, angles in the same segment and angles in cyclic quadrilaterals. Each circle theorem has an associated proof in the additional resources section. Once the theorems are discovered there is opportunity for students to consolidate their learning by calculating unknown angles. Differentiated Learning Objectives All students should be able to discover the relationships between the angles at the centre and circumference of a circle, opposite angles in cyclic quadrilaterals and angles at the circumference in the same segment. Most students should be able to discover the three theorems and apply them individually to calculate missing angles. Some students should be able to discover and apply the three properties and apply them to calculate angles involving multiple theorems. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Problem Solving Circle Theorems - Angle at centre, Cyclic Quads, Angle in same Segment

Students learn about applying multiple circle theorems to solve complex problems. The relevant circle theorems are angle about a centre and circumference, angles in a cyclic quadrilateral and angles in the same segment. More able students combine the various theorems to derive a proof. The start of the lesson is used ot recap the individual theorems so students can combine them later in the lesson. The plenary assesses progress through a typical exam style question. Differentiated Learning Objectives All students should be able to apply a single circle theorem. Most students should be able to apply multiple circle theorems to solve complex problems Some students should be able to prove the angle at the centre, cyclic quadrilaterals and angles in the same segment circle theorems. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses.

Students learn how to solve quadratic identities by completing the square and equating terms. As learning progresses students are challenged to solve identities where the coefficient of b is odd and in the form a(x+b)^2 + c. At the start of the lesson students arrange six expressions written in the form (x + b)2 + c in order of their smallest possible value. In the plenary students are challenged to match a range of identities with their equal terms. Differentiated Learning Objectives All students should be able to solve a quadratic identity in the form (x + b)^2 + c by completing a square. Most students should be able to solve a quadratic identity in the form (x + b)^2 + c by completing a square and equating terms. Some students should be able to solve a quadratic identity in the form a(x + b^)2 + c. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Pythagoras' Theorem - Solving Complex Problems

Students learn how to use Pythagoras' Theorem to calculate unknown lengths in a range of problems involving right-angled triangles. As learning progresses this is linked to finding the area and perimeter of composite shapes. At the start of the lesson students find the perimeter of a quadrilateral plotted on Cartesian axes by calculating the hypotenuse length between the vertices. In the plenary they are challenged to calculate the perpendicular height of a triangle whose vertices form the center of three identical circles. Differentiated Learning Objectives All students should be able to calculate the length between two coordinate pairs.Most students should be able to use Pythagoras’ Theorem to solve problems involving right-angled triangles. Some students should be able to calculate the longest diagonal in a cuboid. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Scale Drawings of Bearings

Using their knowledge of triangles students learn how to construct scale drawings of bearings. As learning progresses students move from constructing scale drawings of bearings to interpreting diagrams using ratio. The start of the lesson recaps calculating angles in scalene and isosceles triangles. The plenary challenges students to apply additional construction techiniques such as bisectors to find the bearing between two towns. Differentiated Learning Objectives All students should be able to use ASA to construct and interpret bearings and scale drawings. Most students should be able use ASA and SSS to construct and interpret bearings and scale drawings. Some students should be able to construct and interpret bearings and scale drawings. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Calculating the Hypotenuse in a right-angled triangle

Students learn about calculating the hypotenuse in a right-angled triangle using Pythagoras' Theorem. Using Pythagorean Triples students calculate the area of the square attached to each edge of a triangle to discover the relationship between the sides. At the start of the lesson students recap working with order of operations, squares and square roots. The plenary challenges students to apply Pythagoras' Theorem to test whether a triangle is a right-angle or not. Differentiated Learning Objectives All students should be able to calculate the squared area of each edge of a right-angled triangle. Most students should be able to calculate the hypotenuse length of a right-angled triangle. Some students should be able to use Pythagoras’ Theorem to determine whether a triangle has a right-angle. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Finding any length of a Right-Angled Triangle

Key stage 3 mathematics for using Pythagoras' Theorem to calculate any length of a right-angled triangle. Learning progresses from working with Pythagorean Triples to calculating the area of a right-angled isosceles triangle when only the hypotenuse is given. At the start of the lesson students attempt to find the difference of two hypotenuse lengths in a composite shape. The plenary challenges students to apply Pythagoras' Theorem to a complex shape made from two triangles. Differentiated Learning Objectives All students should be able to calculate a smaller side of a Pythagorean Triple Most students should be able to calculate any side of a right-angled triangle using Pythagoras’ Theorem Some students should be able to apply Pythagoras’ Theorem to composite triangular shapes. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Fully differentiated worksheet for calculating angles in a quadrilateral. Solutions are on page two. Excellent for independent learning in the class room, homework or revision. More resources are available at mr-mathematics.com and our Facebook page.

Manipulating Sectors Formulae

Students learn how to manipulate the various formulae associated to the area of a sector and arc length to find the radius and angle theta. As learning progresses they are challenged to solve more complex problems both with and without a calculator. Differentiated Learning Objectives All students should be able to manipulate the formula for the arc length of a sector. Most students should be able to manipulate the formula for the arc length and area of sectors. Some students should be able to derive known facts for problems involving sectors through manipulating the formulae. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Area of Compound Shapes GCSE Mathematics Full Lesson

Students learn how to calculate the area of compound rectilinear shapes by splitting the shapes up into two or more rectangles and then calculating the sum. Differentiated Learning Objectives All students should be able to determine the area of a compound rectilinear shape by counting. Most students should be able to determine the area of a compound rectilinear shape by calculating. Some students should be able to determine possible perimeters when given the area of a compound rectilinear shape. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Area of Sectors

Students learn how find calculate the area of sectors using both calculator and non-calculator methods. As learning progresses they calculate the area of composite shapes involving sectors. Differentiated Learning Objectives All students should be able to calculate the area of a major and minor sector. Most students should be able to calculate the area of compound shapes involving sectors. Some students should be able to calculate the angle or radius of a sector when given the area Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Constructions – Angle, Side, Angle

Students learn how to construct triangles and polygons using a protractor and straight edge when given a length between two know angles. Differentiated Learning Objectives All students should be able to construct a triangle using a protractor and straight edge. Most students should be able to construct a quadrilateral and pentagon using a protractor and straight edge. Some students should be able to construct a regular polygon using a protractor and straight edge. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.

Perimeter of Shapes Foundation GCSE Lesson

Students learn how to measure the perimeter of 2D shapes. by counting and later by creating and using a formula. As learning progresses they area challenged to consider the perimeters of regular and composite shapes. Differentiated Learning Objectives All students should be able to measure the perimeter of a shape by counting. Most students should be able to calculate the perimeter of a shape. Some students should be able to solve problems involving the perimeter of a shape. Mr Mathematics’ annual members have instant access to all lessons across Key Stage 3 and 4. Termly GCSE assessments are also available to monitor student’s progress. Visit mr-mathematics for * Fully planned and differentiated maths lessons for the GCSE 9 - 1 and new Key Stage 3 specification * Schemes of work based on pedagogy and teacher support for Key Stage 3 and 9 – 1 GCSE courses. Follow me on twitter for updates on new lessons available at http://mr-mathematics.com @mr_mathematics.