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# Topic 10 Year 9 Mathematics

 Mathematics Topic Similarity and enlargement No of lessons 8 When is it happening Term 2 What will students learn Understand angles do not change and proportions remain constant in similar shapes.  Be able to find scale factors and constants of proportionality and use them to find missing side lengths. Experience recognising and visualising congruent and similar shapes.  Understand the constant of proportionality is a relationship within a shape and the scale factor is a relationship between shapes. Understand the centre of enlargement (CoE) determines the position of an enlarged shape.  Be able to enlarge a shape from a given CoE and on a coordinate grid and find the CoE. Understand the relationship between the area of an enlarged shape and the scale factor. Key Knowledge that students should know at the end of 'Topic' This is the knowledge that students will meet for the first time in this topic Congruence is revisited with polygons. Students are challenged to identify corresponding angles and sides under different transformations to determine if shapes are congruent. Similarity is introduced in the context of enlargement. The scale factor is used to find missing side lengths in the enlarged shape and the original shape. The constant ratio of corresponding side lengths in similar shapes is focussed on today. Students use this ratio to calculate scale factors and use the scale factor to determine similarity. Constant proportions within similar shapes are considered today and the concept ‘constant of proportionality’ is revisited. Students examine the numerical relationships within shapes and between shapes to clarify their understanding of the differences and similarities between the two. The centre of enlargement is introduced. Students learn that the centre of enlargement determines where an enlarged shape will be and in this lesson focus on the scale factor between the original shape and the enlarged shape. The constant of proportionality is focussed on again, this time in the context of similar triangles to draw attention to the relationships between side lengths in preparation for trigonometry. Students end the week looking at the effect of enlargement on area. This is knowledge that students may have met before but will need to deepen their understanding Congruence is revisited with polygons. Students are challenged to identify corresponding angles and sides under different transformations to determine if shapes are congruent. Key Skills that students should be able to demonstrate at the end of 'Topic' This is the skills  that students will meet for the first time in this topic Use of scale factor This is skills that students may have met before but will need to develop Rules of similar shapes Key vocabulary that students should know and understand The Big Question Can you use scale factors to find missing side lengths? Key questions that students should be able to answer at the end of the 'Topic' Can you identify congruent shapes? Can you use the scale factor to find missing side lengths of similar shapes? Can you identify whether shapes are similar? Can you find constants of proportionality? Can you find the scale factor between two similar shapes? Can you find the scale factor from corresponding distances? Can you enlarge a shape on a coordinate grid? Can you calculate the area of a shape enlarged on a coordinate grid?