Unit 8
Ratio and Graphs
Intent
The intention of this unit is to secure and build upon knowledge from Key Stage 2 and Year 7 and to introduce new concepts that lay the foundations of key concepts that will underpin units in Year 9 such as
Plotting and interpreting straight line graphs
We want all students to become keen problem solvers and agile mathematical reasoners. This unit in particular develops these skills with
The application of proportionality to real world problems
Implementation
For each strand in the unit students begin with lessons refreshing Year 7 knowledge before new concepts are introduced. At the end of each strand there are revision and mastery lessons to consolidate and ensure all students have picked up on new ideas.
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 before the test.
During this unit there will be two longer written homework tasks which include a skills check as well as problem solving questions. Students will have an opportunity to follow-up and improve their work.
Impact
The impact of this unit of work will be measured through a 45 minute written assessment. The assessment will feature questions similar to the skills check and homework tasks. 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 test.
Topics covered in this unit:
Star / Star*
Core
27n Simplifying ratios and identifying fractions from ratios
40n Share a quantity in a two part or three part ratio
41n Solve ratio problems without the original amount
42n Solve proportion problems by a unitary method
43n Comparing value for money by finding the cost of comparable amounts and work with unit prices
46n Use an exchange rate to convert between currency
59n Solving problems using a combination of percentages, fractions and ratio
59a Write or plot a linear function for a given ratio
60n Adjust a recipe or check it there are enough ingredients to make a given number
31a Take readings from conversion graph for units or currency
41a Use a conversion graph to convert larger numbers and solve extended problems
50a Use graphs of direct or inverse proportion or solve inverse proportion problems
36a Read and plot distances and times from distance-time graphs
45a Calculate speed or use speed to complete a distance-time graph
39a Plotting graphs of straight lines including horizontal and vertical lines
62a Plotting graphs of non-linear quadratic, cubic or reciprocal functions
Plus / Plus+
73n Solve hard ratio problems involving combining two or more ratios
71a Form the equation of a line through two points or through one point with a given gradient
67a Reading roots or solutions from intercepts of graphs of non-linear functions
68a Reading roots or solutions from intersections of graphs of linear or non-linear functions