INforM – Interactive Notebooks for Mathematics
Book 14 – Ratio
Ratio
The activities are related to work in Ma2. Solve simple problems involving ratio and proportion and use ratio notation, including reduction to its simplest form.
Organisation of the materials
The Smart Notebook file is saved as ‘Book 14 Ratio.notebook’
It consists of 7 pages of which the first is the title page, shown above.
There are 4pages to support the activity. Page 6 is a blank page. Page 7 contains teacher notes which are amplified here.
The first activity
Pupils can explore simplifying ratios by dragging stars and ‘smileys’ and arranging them in rows.
The main activity
The purpose of the main activity is to explore ratio and similarity. Page 3 simply presents a range of pictures of the same subject, some of which are similar shapes.
Ask pupils which pictures they think are essentially the same shape but made larger.
Pupils can use the dragging facility in Smart Notebook to enlarge the pictures they think are similar to test if they will fit exactly on top of each other.
Use page 4 to explore the numerical relationship between the height and width of similar rectangles. On the attachments tab there is a ruler and a calculator which can be dragged onto the main page as necessary. Ask pupils to measure the initial rectangle and record its height and width on the table. The size of the rectangle can then be altered and re-measured.
You might choose to write the ratio using notation and simplifying the ratios to show that they are the same. Alternatively, or as a further stage, you could ask pupils to divide the height by the width to show that it is constant.
After a few rectangles have been measured, simply take one measurement and ask pupils to predict the second measurement.
Page 5 then requires pupils to solve a problem using this skill. One of the pictures on the page can be enlarged to exactly fill the space on the article. Pupils will need to measure the space and each of the pictures and then work out which one is the correct one to use. The chosen picture will need to be unlocked before it can be moved and enlarged.
The extension task
Pupils can explore the connectionbetween the diameter and circumference of a circle using one of the attached ‘circumference’ files or practically.
Once pupils have discovered a relationship, they can use the ‘wheel’ file to predict the length of the circumference having measured the diameter.
SMART specific issues
The Smart Notebook Gallery has an education area within which there is a Mathematics area. This contains some useful Notebook resources, including Flash resources such as the calculator and the stopwatch which is used in this activity.
Additional resources can be downloaded from the EdCompass website. ( Follow the links to Notebook collections and Mathematics. If you are in an open Notebook page, Select Import and Import Online Contentand, providing you have an internet connection, the relevant web page will open automatically.
When using the ruler on page 4 you need to make sure that it remains the same size, even when rotating it, to measure the height.
To do this, use the drop down menu located in the top right-hand corner of the ruler, select locking and then allow move and rotate.
The attachments tab makes opening files and locating resources within the lesson very convenient. Simply drag a picture file on to the page to open it or double click on a file that requires other software – such as the dynamic geometry files.
Ideas for follow up work
Pupilscould investigate standard paper sizes, such as A3 and A4, exploring the connection between the length and width of the page.
The Golden Ratio in classical artwork gives scope for classroom work. Pupils could be asked to find the dimensions of a rectangle such that when a square (whose side length = the width of the rectangle) is cut off, the remaining rectangle is a mathematically similar shape to the initial one. i.e is the white rectangle a similar shape to the whole rectangle?