Unit Summary In this unit students re-visit the idea of rounding to the nearest 10, 100 and 1000 as well as to the nearest whole number, a given number of decimal places and a given number of significant figures. Building on their current knowledge the idea of bounds are explored as well as the use of rounding to a given number of significant figures to estimate and check calculations in a wide range of contexts and problems of varying difficulty. Students will also learn to estimate roots as well as use inequality notation to specify error intervals due to rounding. Big Idea – none | |
Knowledge (Curriculum content) | Rounding numbers top varying specified degrees of accuracy (nearest 10, 100, 1000, whole number, decimal places and significant figures), looking at the highest and lowest possible value a number could have taken prior to rounding (bounds) and appreciating that rounding reduces accuracy but assists with convenience, estimating calculations by rounding to one significant figure and using this to check answers accuracy, estimation of roots of numbers and specifying error intervals using inequality notation. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 1 – Rounding and error intervals
11 hours - Autumn 1
A foundation student should also be able round numbers confidently to the nearest whole number, 10, 100 and 1000. They should also be able to round a number to a specified number of decimal places and significant figures. They should be able to estimate the answer to simple problems and calculations by rounding all numbers to one significant figure and make sensible estimations of the roots of numbers.
A crossover student is also expected to be able to have a comprehensive understanding of the concept of bounds and to be able to identify the upper and lower bound of a number rounded to a specified degree of accuracy. They should also be able to specific the error interval as an inequality. In addition the will able to use rounding to one significant figure to estimate the solution to more complex and challenging calculations and problems.
Unit Summary In this unit students will re-visit the idea of finding simple percentages (10, 25, 50%) of a value and build on this to find any integer, and then non-integer, percentage of a value. The will study how to perform percentage increase and decrease calculations and solve percentage change problems in context. They will practise working between fractions, decimals and percentages. Percentage problems will be linked to every day problems such as interest repayments, compound and simple interest and ideas such as growth and decay. Students will spend time using calculators to perform efficient calculations. Big Idea – none | |
Knowledge (Curriculum content) | Finding simple percentages of an amount (10, 25, 50, 100%) of an amount, finding integer percentages of an amount, finding non integer percentages of amounts. Linking the idea of working between percentages and decimals to introduce and consolidate to concept of “the multiplier”. Finding percentage changes, increases and decreased as well as the overall percentage change after repeated percentage changes. Problem solving relating to simple interest and compound interest scenarios. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 2 – Percentages
12 hours - Autumn 1
A foundation student should also be able calculate simple percentages such as 10%, 25% 50% and 100% without a calculator as well as find integer and non integer percentages of amounts both with and without a calculator depending on the complexity of the problem. They should also be able to perform percentage increase, decrease and change problems and convert between percentages, fractions and decimals fluidly.
A crossover student is also expected to be able to work with more complex problems such as repeated percentage changes (and be able to calculate the overall percentage change) as well as apply these skills to practical problems such as simple and compound interest and best value questons.
Unit Summary In this unit students will look at ratios in a real world setting (eg catering, building) and be able identify equivalent ratios, simplest ratios and work with ratios formed from different units to be able to work out how quantities and should be shared or the total quantities involved. They will study the link between ratio and fractions as well as being able to apply the unitary method to identify the cost of a single unit of a given item. They will apply these skills to best buy problems (whilst taking into account practical considerations) as well as using their knowledge of proportion to adapt recopies and solve direct proportion problems. Big Idea – none | |
Knowledge (Curriculum content) | Writing ratios, simplifying ratios, identification of equivalent ratios, working with ratios with different units, solving ratio problems including dividing a ratio when given the share or a total. Identifying the link between fractions and ratio (and applying this to problem solving including complicated problems such as concentration, comparison and scaling), using the unitary method, solving best buy problems (including how to present solutions), using proportion to adapt recipes and solving direct proportion questions. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 3 – Ratio and proportion
11 hours – Autumn 2
A foundation student should also be able write a ratio from a real life situation as well as write equivalent ratios and find the missing number in two equivalent ratios. They should be able to reduce a ratio to its simplest form and divide into a ratio where the share or total is given. They should also be able to identify the link between fractions and ratio, apply the unitary method and solve best value problems as well as using proportion to adapt recipes.
A crossover student is also expected to be able to be able to reduce a ratio to its simplest form (even with different units), apply the links between fractions and ratios to problem solving questions and solve complex problems involving ratios such as comparisons, scaling, mixing or concentrations). They will also be able to solve a range of direct and inverse proportion questions.
Unit Summary In this unit students will focus on be able to find the perimeter (or circumference) and area of shapes based on triangles, a range of quadrilaterals and circles as well as finding missing dimensions if the area or perimeter (or circumference) is already known. Focus will be given to the correct and accurate use of units as well as applying the skills gained in the topic to practical problem solving in a variety of different settings and context. | |
Knowledge (Curriculum content) | Finding the perimeter and area of rectangles (or the length of one side if the perimeter / area is known), finding the area of compound shapes made from rectangles, solving practical problems by finding the perimeter or area of compound shapes made from rectangles, finding the area of parallelograms and trapezia (and finding a missing length if the area is known), calculating the area or circumference of circles (or the radius or diameter if the circumference / area is known). Finding the area of sectors and lengths of arcs (links to unit 3). |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 4 – Perimeter and area
11 hours – Autumn 2
A foundation student should also be able find the perimeter of rectangles, the circumference of circles and the area of rectangles, parallelograms, trapezia and circles using the correct units in their solution. They should also be able to find a missing length if the area, perimeter or circumference is already known. They should be able to find the area of compound shapes formed from rectangles, parallelograms and trapezia and solve related practical problems.
Unit Summary In this unit students will learn to find the volume and surface area of a wide range of 3D solids including cuboids, prisms, cylinders, pyramids, cones and spheres / hemispheres. There is a significant focus on linking such calculations to real world problems and situations as well as the accurate use of correct units in solutions. | |
Knowledge (Curriculum content) | Calculation of the volume of a cuboid, the surface area of cubes and cuboids, the volume of prisms (including cylinders) and the surface area of prisms (including cylinders). Applying the formula to calculate the volume and surface area of pyramids, cones, spheres and hemi-spheres. Application of these skills to real world and practical problem solving activities. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 5 – Volume and surface area
10 hours - Autumn 2
A foundation student should also be able recall (or derive) the formula and then calculate the volume and surface area of cube, cuboid, and prism as well as to solve functional and practical problems which require the application of these skills. They are also expected to be able to give a solution using the correct units.
A crossover student is also expected to be able to recall (or derive) the formula and then calculate the volume or surface area of a cylinder. They are also expected to be able to apply (but not recall) the formula to find the volume and surface area of cones, spheres, hemi-spheres and pyramids and apply all of these skills to solve functional and practical skills.
Unit Summary In this unit students will learn and use a variety of angle facts to solve problems relating to angles in triangles, quadrilaterals, straight lines or about a point. They will know about special types of triangle and be able to apply their knowledge of angle facts in these situations to solve angle problems. They will also learn about the properties of angles between parallel lines (including their application to bearing problems) and be able to find, and solve problems, relating to the interior and exterior angles of regular polygons. | |
Knowledge (Curriculum content) | Application of the sum of angles about a point, on a straight line or in a triangle, finding missing angles in a range of triangles (including special triangles) and quadrilaterals. Properties of angles between parallel lines and being able to solve problems stating the property (alternate, co-interior, corresponding) used. Using the properties of interior angles in a triangle to find the sum of the interior angles in any regular polygon (and therefore the size of one interior angle), finding unknown interior angles in any polygon, finding the size of an exterior angle in a regular polygon, finding the number of sides a regular polygon has is the interior or exterior angle is known, construction and measuring bearings on diagrams, finding the bearing of B from A when the bearing of A from B is known. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 6 – Angles and bearings
13 hours - Spring 1
A foundation student should also be able solve missing angle problems involving triangles (including special triangles such as equilateral and isosceles), angles about a point, angles on a straight line and angles in a quadrilateral. Also be able to find, and name the reason for, the size of angles between a pair or parallel lines. In addition be able to solve interior angle sum and exterior angle size problems for any regular polygon.
A crossover student is also expected to be able to be able to find the size of an interior angle for any regular polygon, find missing interior angles in any polygon as well as calculate the number of sides a regular polygon has either from the size of an interior or exterior angle. They should also be able to construct, and measure, bearings on a diagram and find the bearing of B from A when the bearing of A from B is known.
Unit Summary In this unit students will build on previous experience of transforming shapes. They will learn to translate shapes on a coordinate grid accurately using column vectors, reflecting shapes in diagonal mirror lines on a grid or lines in the form x=a or y=b on a coordinate grid as well as rotating shapes in a given direction on a grid and rotating shapes about a point on a coordinate grid. They will also be able to construct similar shapes by enlargement of a scale factor on a grid (including from a given point on a grid). Given the object and image in a transformation they will also learn to explain the transformation that has taken place. | |
Knowledge (Curriculum content) | All work is with 2D shapes. Translating shapes using column vectors, reflecting shapes using diagonal mirror lines on a grid or straight lines in the form x=a and y=b on a coordinate grid. Rotating shapes in a defined direction by a given angle, enlarging shapes by a specified scale factor on a grid or from a point on a coordinate grid. Identifying and describing basic transformations. Describing directional vectors as column vectors (and vice versa) and adding, subtracting and multiplying vectors by a scalar. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 7 – Transformations
13 hours - Spring 1
A foundation student should also be able to use the four types of transformations of a 2D shape including translating a shape using a column vector, reflecting a shape in diagonal, horizontal or vertical line, rotate a shape in a given direction by multiples of 90 degrees and enlarging a shape by a positive integer scale factor. They should also be able to identify a basic transformation that has occurred.
A crossover student is also expected to be able to describe directional vectors as column vectors (and vice versa), rotate shapes about any given angle in a specified direction, find a missing length in two shapes that are similar and enlarge shapes by any given scale factor including fractional and negative values.
Unit Summary In this unit students will re-visit accurately plotting and reading x and y coordinates in all four quadrants, solving problems on a coordinate grid, identifying the equations of horizontal and vertical lines and plotting / drawing the graph of simple linear equations either by following a rule or using a table of values. Students will also plot graphs of more complex functions such as quadratic, cubic, reciprocal or exponential functions. | |
Knowledge (Curriculum content) | Plotting and reading x and y coordinates in all four quadrants, solving problems of varying difficulty on a coordinate grid, identifying the equations of horizontal and vertical lines, plotting the coordinates from a rule to generate a straight line (F) or using a table of values to plot graphs of simple linear functions (F and C), plotting graphs of more complex functions such as quadratics (F and C), simple reciprocal functions (C), and exponential functions (C) in the form y = kn where k is positive. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 8 – Drawing graphs
8 hours – Spring 2
A foundation student should also be able to plot and read x and y coordinates in all four quadrants, solve simple problems on a coordinate grid, identify the equations of horizontal and vertical lines and plot coordinates from a rule to generate a straight line. They should also be able to use a table of values to plot graphs of simple linear functions as well as plot graphs of quadratic functions.
A crossover student is also expected to be able to solve complex problems on a coordinate grid as well as plotting graphs of more complex functions such as cubics, reciprocal functions and exponential functions.
Unit Summary In this unit units will build on unit 8 studies to work with straight lines graphs. They will learn to find the midpoint of two points and use express straight lines graphs in the general form y = mx + c. Using the equation (or by inspection) they will learn to find the y-intercept and the gradient of a given line as well as to use the general form to identify pairs of parallel lines. Students will learn how to read and interpret real life linear graphs (such as a conversion graph). Crossover students will learn more complex skills to allow the to identify the equation of a line by inspection. Big Idea – N/A | |
Knowledge (Curriculum content) | Finding the midpoint of two points (or the end point if the midpoint and one endpoint are known), use of the form y = mx+c to describe the gradient (and direction of travel) and y-intercept of a graph, using the form y = mx + c to identify parallel lines, finding the equation of a line when given the gradient (or that of a parallel line) and a point and finding the equation of a line that goes through two points. In addition reading and interpreting real life linear graphs such as conversion graphs. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 9 – Straight line graphs
11 hours – Spring 2
A foundation student should also be able to find the midpoint if two points, use the form y = mx+c to interpret a straight line graph, find the y-intercept of a linear graph from the equation of the (or inspecting the graph), interpreting the gradient of a straight line (and identifying it from the equation), use the form y = mx+c to find lines that are parallel and reading / interpreting real life linear graphs (such as conversion graphs)
A crossover student is also expected to be able to find the endpoint of a straight line when the midpoint and other end point are known and find the equation of the line when given the gradient (or that of a parallel line) and a point or, two points that lie on the line.
Unit Summary In this unit students will learn about compound measures such as speed, density and pressure (including the conversion between compound units). Students will initially focus on reading and interpreting speed-time and distance-time graphs before using distance-times to find the speed of an object or performing he required calculations to ascertain speed. Students will also learn how to categorise units into measures of length, mass or capacity and convert between metric units. Students will also learn calculate pressure/force/area and density/mass/volume problems including complex density problems involving mixing materials. | |
Knowledge (Curriculum content) | Reading speed-time graphs, distance-time (dt) graphs and using dt graphs to find the speed of an object (and by calculation). Organising units in measures of length, mass and capacity and converting between metric units and compound units. Solving problems involving speed, distance and time involving two part journeys. Calculations involving pressure/force/area and density/mass/volume (including for crossover students more complex problems where units need converting or materials and mixed). |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 10 – Compound measures
11 hours – Spr 2 / Sum 1
A foundation student should also be able to read speed-time and speed-distance graphs and calculate speed, distance and time given the other two measures. They should also be able to organise units in measures of length, mass and capacity as well as compare and order measures of length including where the units are different. They should also be able to calculate density, mass, volume and pressure, force, area.
A crossover student is also expected to be able to use a distance-time graph to find the speed of an object, convert compound units (such as m/s to km/h) and calculate speed, distance and time where units need converting. They should also be able to solve speed, distance and time problems regarding a two part journey and solve density, mass and volume problems involving the mixing of materials.
Unit Summary In this unit students will explore ideas surrounding and calculating probabilities such as placing theoretical probabilities accurately on the probability scale, finding probabilities of equally likely outcomes in simple contexts and applying the property that the probability of mutually exclusive outcomes sum to 1. They will also learn to systematically list outcomes, They will also learn to read, use and complete Venn diagrams to represent different events with crossover students also using these diagrams to help solve more complex probability questions. Some students will also complete probability trees and find probabilities of combined events or calculate expected outcomes of future experiments by applying relative frequency. Big Idea – Finance – the real cost of buying an item on finance | |
Knowledge (Curriculum content) | Using theoretical probabilities and placing them accurately on the probability scale, finding probabilities based on equally likely outcomes in simple contexts, application of the property that the probabilities of mutually exclusive outcomes sum to 1, systematically listing outcomes, completion of sample spaces for combined events with equally likely outcomes and calculation of probabilities from these, reading/completion and using Venn diagrams to solve probability problems, finding probability of A and B / A or B and applying relative frequency to find the expected outcomes of future events. |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 11 – Probability
11 hours – Sum 1
A foundation student should also be able to place theoretical probabilities accurately onto the probability scale, find probabilities based on equally likely outcomes in simple contexts, apply the property that the probability of mutually exclusive outcomes sum to 1, systematically list outcomes and read and complete a Venn diagram.
A crossover student is also expected to be able to reverse a given probability to find possible outcomes, find the probability of A and B occurring and the probability of A or B occurring and interpret the frequency of outcomes of probability experiments by applying relative frequency. Also to complete Venn diagrams (including where the intersection needs to be calculated), find probabilities from Venn diagrams and complete/use probability tree diagrams.
Unit Summary In this unit students will learn to find the mean, median, mode and range of lists of data as well as comparing these averages of two sets of data to make comparisons and draw conclusions as well identifying the appropriate average to use in a given situation. Students will also be able to adjust the mean when data is added or taken away from the set. Finally students will work with data from a discrete frequency table, grouped frequency table or continuous data to find the mode, median, mean or range (or the estimated mean / classes which the averages lie). Big Idea – Counting (start of unit), Dropping a penny from the Empire State Building (end of unit) | |
Knowledge (Curriculum content) | Finding the mean, media, mode and range from a list of data, interpretation of these averages of two sets of data (and making comparisons / interpretations). Being able to identify the appropriate average to use in a given situation. Being able to find the data based on information given on the averages and range and being able to adjust the mean when data is added or taken away from the set. Working with data from discrete frequency tables, grouped frequency tables ir continuous data to find the mean, median or mode (or any estimate / classes which the data lies in). |
Academic Literacy | We will develop mathematical academic literacy by modelling written methods and ensuring that each step is clearly explained and easy to follow. Students will also be encouraged to reason and question whether answers to calculations seem reasonable by performing appropriate estimations. Students will be introduced, repeatedly exposed to and encouraged to use appropriate terminology and vocabulary when presenting a mathematical justification, argument or explanation. |
What should learning look like at the end of a unit? | |
Assessment Activity | DAR to assess knowledge of prior key building blocks necessary for success in unit and guide teaching/re-teaching needs, retrieval starter each lesson , summative unit test, revision and review (4-6 weeks later) include a diagnostic quiz |
Year 10 (F) - Unit 12 – Averages and the range
14 hours – Summer 2
A foundation student should be able to find the mean, median, miode and range from a list of data, interpret the meaning of these averages with two sets of data and make comparisions aswell as identify the appropriate average to use in a given situation They should also be able to find them mean, median, mode and range from a discrete frequency table.
A crossover student is also expected to be able to find data based on information given on the averages and range as well as adjusting the mean when data is added or taken away from the set. They should also be able to find the modal class, class in which the median lies and estimated mean from a grouped frequency table as well comparing distributions of grouped, discrete and continuous daya using the mean, median, mode and range.