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Intent
Intent
The intention of this unit is build on and increase the level of rigour in students' mathematical understanding from Key Stage 3, whilst introducing new Key Stage 4 concepts.
Students extend their numerical reasoning to algebraically prove results about odd, even and consecutive numbers.
Students extend their understanding of formulae to function notation and composite and inverse functions. As well as how an iterative formula can produce approximate solutions to equations
Students extend their graphical understanding to calculate and interpret the gradient and and area under curved graphs.
Students develop an understanding of column vectors and diagrammatic and algebraic manipulation of vectors.
Students look at the full range of area and volume formulae and solve geometric problems that lead to linear or quadratic equations.
Students extend their knowledge of charts and measures of location and spread to cumulative, frequency, box-plots and histograms.
Students extend their probabilistic reasoning to look at combinations of independent and conditional events.
Implementation
Implementation
To develop students as independent learners this unit of work covers three terms with a period of revision before a substantial assessment in term 6. This requires students to take ownership of their mathematical understanding and engage in a process of identifying gaps and improving ahead of the tests.
From the 3rd week of the unit students will complete a weekly knowledge check so they can measure how their knowledge and expertise is building. The content of the knowledge checks updates as more concepts are covered, to provide a rolling check of what students can recall.
During this unit there will also be several longer written homework tasks which include a knowledge check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work on these homework tasks.
Impact
Impact
The impact of this unit of work will be measured through a Two 90 minute written assessments in term 6
The assessment will cover every aspect of the unit of work and using the knowledge organiser together with this website is a great way to prepare for the tests.
Topics covered in this unit:
Core
Core
32n Use a written method to multiply decimals
30n Estimate answers by rounding including word problems
43n Comparing value for money by finding the cost of comparable amounts and work with unit prices
60n Adjust a recipe or check it there are enough ingredients to make a given number
24n Put decimals in order and round to decimal places
44n Using a calculator correctly with powers, roots and division
58n Rounding to significant figures
34a Using BIDMAS to evaluate numerical expressions (without powers and roots)
47n Using the three index laws with whole numbers
72n Evaluate negative powers or reciprocal of whole numbers
47a Using the three index laws to simplify expressions
66a Simplifying expressions by applying index laws more than once or to several terms
31a Take readings from conversion graph for units or currency
41a Use a conversion graph to convert larger numbers and solve extended problems
44s Solve speed-distance-time problems (including converting minutes to hours when necessary)
36a Read and plot distances and times from distance-time graphs
45a Calculate speed or use speed to complete a distance-time graph
28a Using a two-step formula written in words both forwards and backwards
38a Using an algebraic formula both forwards and backwards
49a Write algebraic formulae from a written description
43a Listing integers that satisfy inequalities and representing inequalities on a number line
48a Solve equations with x on both sides and solving inequalities by algebraic manipulation
73a Addition, subtraction and resultants of 2D column vectors
74a Writing a vector in terms of the free vectors on a diagram
34s Converting between metric units (and to imperial given the conversion factor)
67s Solve density-mass-volume or pressure-force-area problems
27s Calculate the area and perimeter of a rectangle
35s Calculate the area of a parallelogram or a triangle
42s Calculate the area of a trapezium or a compound shape involving trapeziums
39s Calculate the area of a compound shape
54a Forming and solving equations arising from shape, measure or word problems
50s Calculating the area or circumference of a circle giving answers approximately or in terms of π
64s Calculating the arc length or area of a sector
49s Calculate the volume of a prism or the surface area of a cuboid
57s Calculate the volume of a cylinder giving answers approximately or in terms of π
72s Use the volume or surface area formulae for cones and spheres
65s Calculate lengths in similar 2D shapes
35d Draw and read from combined bar charts
47d Draw and read from stacked bar charts
36d Draw and read from a vertical line chart for discrete data
28d Recognise the mode from a list of data or a bar chart
30d Calculate the range from a list of data or a bar chart
31d Calculate the median from an odd or even list of data
42d Calculate the mean from a list of data and compare which is the best average to use
64d Compare distributions of data by referring to averages and spread
52d Identify possible outliers from a list of data and omit them in calculating range
60d Use averages to work out the values of missing data
38d Draw a stem and leaf diagram and use it to find mode, median or range
29d List the possible outcomes of an experiment
39d Calculate probability based on equally likely outcomes
45d List possible combinations and use your list to calculate probabilities
44d Use the fact that probabilities sum to 1
50d Define mutually exclusive and calculate the probability of either event happening
53d Calculate probability based on relative frequency
54d Work out the expected number of successes given the probability and number of trials
57d Understand that by increasing sample size outcomes will tend towards theoretical probabilities
46d Sort sets of numbers into a Venn diagram
61d Use set notation including {},A´, Ø, ∩ and U to refer to Venn diagrams
67d Define independent and calculate the probability of independent events both happening
68d Complete a tree diagram with independent probabilities and use it to calculate probabilities
Plus / Plus+
Plus / Plus+
78n Use the product rule for counting combinations
90n Provide algebraic proof for statements about divisibility
91n Provide algebraic proof for statements about odd, even, consecutive numbers
77n Evaluate 1/n fractional powers of whole numbers
79n Evaluate positive or negative fractional powers of whole numbers
84n Evaluate fractional negative powers of fractions or mixed numbers
94n Solve an index equation by first making the bases match
85a Use function notation and substitute values and expressions into functions
97a Obtain an inverse function by rearranging formulae and express this in the form f¯¹(x) =
98a Obtain a composite function by substituting the output expression of one function into another
43a Listing integers that satisfy inequalities and representing inequalities on a number line
77a Shade a region or mark integer coordinates satisfied by 2D Inequalities
96a Find approximate solutions to equations using an iterative formula
99a Form an iterative scheme for a given equation and understand that it may converge or diverge
100a Solve quadratic inequalities giving solutions in set notation
88a Recognise or form the equation for a circle around (0,0)
89a Recognise and form equations for exponential growth or decay
87s Calculate and interpret the gradient of a distance-time or velocity-time graph
88s Calculate and interpret the area under a distance-time or velocity-time graph
96s Know that the gradient at a point on a curve describes an instantaneous rate of change
97s Use a chord to estimate the average rate of change of a non-linear graph
98s Use a tangent to estimate the instantaneous rate of change of a non-linear graph
99s Find the equation of a tangent to a circle at a given point
100s Estimate the area under a non-linear graph eg using trapezium rule
87a Prove that two vectors are parallel
92a Prove that three points are colinear using vectors
44s Solve speed-distance-time problems (including converting minutes to hours when necessary)
76a Solve quadratic equations that require rearranging first or arise from geometry problems
77s Determine and use area or volume scale factors for similar 2D and 3D shapes
68s Convert between compound measures and units of area and volume
78d Find the quartiles from a list of data and calculate and compare inter-quartile range
79d Plot a cumulative frequency graph
80d Read median and frequency above or below a given value from a cumulative frequency graph
81d Read quartiles from a cumulative frequency graph and calculate and compare inter-quartile range
82d Draw a box plot from summary statistics or a list of data
83d Compare distribution of data shown in box plots
84d Read bivariate data from a scatter graph and use it to draw and compare box plots
86d Calculate frequency density and draw a histogram
87d Read and use frequencies from a histogram
91d Use a partial frequency table and partial histogram to complete both
72d Use a Venn diagram to calculate probabilities of combined events
73d Solve a two-event probability problem by drawing up a tree diagram
74d Know and use the addition rule for probability
88d Know and use the multiplication rule for conditional probability
77d Calculate conditional probabilities from Two-way tables
75d Complete a tree diagram with conditional probabilities and use it to calculate probabilities
85d Use a tree diagram or binomial reasoning to find probabilities of three or more events
92d Solve algebraic conditional probability problems
90d Draw up and populate a Venn diagram for 3 events and use it to calculate probabilities
93d Calculate conditional probabilities of combined events from a Venn diagram
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