# ArithmeTricks for Post Primary

**ArithmeTricks: **Is the ONLINE Section of *Scratch for Your Kids* with ideas to support young secondary students who struggle to grasp new concepts. It has 18 links to interactive projects and printable resources. It’s my hope that parents and teachers will find it useful in simplifying difficult areas of junior Secondary Maths. Topics include Arithmetic, Problem Solving, Area and Perimeter, Coordinate and Transformation Geometry, Linear and Quadratic Graphs and Trigonometry. They all operate on short, simple SCRATCH code. My favourite is #12 ‘**Discover Pythagoras**’ (which I have included in **BOOK 2**, page 151). Do you have a favourite yet? Flip through the pages or go immediately to the project you want. There are more resources in the RSC Secondary Maths Studio at https://scratch.mit.edu/studios/25892206 where there are over 40 shared projects.**The Flipbook remains a working Document in its early stages.** Opinions welcome!

## Mouse Reports Another Sprite’s x,y

**(01) **You move the apple with the arrow sprites. Meanwhile the little mouse sprite continually reports and updates the apple’s **x, y **location on the grid. The code makes use of the fabulous **attribute reporter** which is in the *Sensing* palette. It’s important for the coder to add the name of the apple (second person sprite) to the mouse sprite’s (first person sprite) drop list. Otherwise none of the apple’s attributes will appear in the mouse drop list, that includes the apple’s x and y positions. The concept of one sprite reporting the attributes of another sprite, is an essential element of graphs, where there is a dependency between a domain (x) and a range (f(x)). It is also used in the Pythagoras code and in several areas of Secondary level maths. **(More to come on this resource. The PDF has to be updated)**

## Coordinates: The 9-Dot Puzzle

**(02) **It is usual to try out solutions to this puzzle with pencil and paper. It is also possible to use your Scratch coding skills to animate your solution when you have found one. Discuss with a friend how you might arrange the 9 dots using code, to make 3 rows of 3, rather than draw the dots on the stage. You then need to instruct the Scratch pen to move and draw the path using a path through coordinates (using the 30px grid squares). You have to decide how to convey the instructions to the user. You need a pen to draw the line without using the pen up command, until the end. **(The PDF has to be updated)**

## Problem Solving: 3 Puzzles

**(03) **Another 3 PUZZLES to Solve: Here are three maths puzzles presented by the sprite boy, Danny. Press a button for a Puzzle. Read it slowly in the bottom corner. Danny’s dog might prove to be helpful as you think of your approach. Click the colour underneath to get to the solution (and the approach). Then Danny will give his solution and how he did it using Scratch code. See the other 3 Puzzles, challenges (links on the Scratch project). **(The PDF has to be updated)**

## Transformation Geometry

**(04) **A geometric TRANSFORMATION makes changes in a shape without changing its size, area or shape. A TRANSLATION (slide) changes the position of a shape. A ROTATION (turn) changes the viewing angle of a shape. A REFLECTION (flip) is a mirror image of a shape. After sliding, turning or flipping, the shape still has the same size, area, angles and shape. When one shape transforms into another shape using only slides, turns or flips, then the two shapes are Congruent. **(The PDF has to be completed)**

## the SUM of the Angles = 180°

**(05) **Drag one point of a triangle when there are 2 fixed points. This project shows how each angle in the triangle changes but always maintains a total sum of 180º in the three angles. Learn how to name a triangle by reference to its angles, or its sides or both. Take the Triangles Quiz. Try some written exercises on paper to link the Scratch projects with pencil, ruler and squared paper. **(The PDF worksheet will be ready soon)**

## Protractor and Coordinates

**(06) Draw and Measure Angles: **(Version 2) Set and connect 3 coordinates with lines to create a TRIANGLE. Bring in a Virtual Protractor to measure its angles. (a) Use the slider variables for x1: y1: and click the green Set Pt button to set a START point. (b) Use the sliders again to set x2: y2: and click Set Pt to set the second point. (c) Set the third coordinate point x3: y3: in the same way. (d) Click the Draw button to join the 3 coordinate points. (e) Click Show Protractor to show/ hide the Virtual Protractor close the triangle. (f) Drag the protractor and use RIGHT / LEFT rotate the protractor. (g) Read the size of each angle and discover that the SUM of the three angles is 180º.

## Algebra: (Graph) **Simultaneous Equations**

**(08) Simultaneous Equations: **Before hitting the start button, pause briefly to study the table. When the screen opens, you can press the graph button to activate the graph. Domain x is the small green x. Observe the action: as the value of domain x changes (from left to right), there is a corresponding change in the value of y (known as f(x)). The pen plots and draws the curved path of the change in f(x). **Note: **The PDF gives links to 3 more Quadratic Graphs. Open the PDF below.** **

## Algebra: (Graph) Quadratic Equation in x²

**(09) Graph of an expression in x²: **Before hitting the start button, pause briefly to study the table. When the screen opens, you can press the graph button to activate the graph. Domain x is the small green x. Observe the action: as the value of domain x changes (from left to right), there is a corresponding change in the value of y (known as f(x)). The pen plots and draws the curved path of the change in f(x). **Note: **The PDF gives links to 3 more Quadratic Graphs. Open the PDF below.** **

## 9-Piece Egg Tangram with PDF

**(10)** This tangram, can also provide fun as a cut-out or it can be played in SCRATCH. It is not a normal tangram, nor is it a normal egg. It can hatch a variety of birds. How many of the birds can you make using some or all the pieces of the egg. There is a link below to a **3-page **printable which explains the SCRATCH code behind the tangrams. It also contains a template of the Magic Egg Tangram. Copy the 9-piece tangram, and stick it on card and cut it into sections along the white lines. This tangram is *Mathemagic*!

## Discover Pythagoras with PDF

**(12) **Press the green flag and try it first to see what happens! Change length of the red side. Change length of the green side. As the sides change so also does the blue hypotenuse and the square on its side. The black anchor point is fixed but all three sides can change. The BLUE side is always the HYPOTENUSE (opposite 90º). At start, the right-angled triangle has sides of lengths 3, 4 and 5 (hypotenuse). Can you imagine this project without the *Ready Steady Code* grid?

NOTE 1: 3² +4² = 5² (9+16=25). Square root of Hypotenuse = length of blue side. NOTE 2: Squares get distorted at the edges of the stage. **(The 2 PDFs have to be updated)**

## Factors and Prime Numbers

**(13) **This assignment was completed as part of the first Learning Creative Learning (LCL) online course from MIT. Week 3: I see SCRATCH as a new teaching tool for parents and teachers in all areas of the primary and lower secondary school curriculum. I think it has great potential for simplifying Maths concepts and it helps to animate Maths as well as giving the learners an insight into coding. This project uses a List. You may download the sweet-jar label, Multiple Costume Number Sprite 0 to 100 designed by readysteadycode. This project is aimed at Middle/ High School (Primary/Secondary in Ireland).**(The PDF has to be updated)**

## Draw and Code a Pie Chart

**(14) **(Holding text)** **Pie charts are used in data handling and are circular charts divided up into segments which each represent a value. Pie charts are divided into sections (or ‘slices’) to represent values of different sizes. For example, in this pie chart, the circle represents a whole class. Each segment of the circle could represent different student grades. **(The PDF has to be updated)**

## Animate a Cube: Code its Volume

**(15) **(Holding text)** **Pie charts are used in data handling and are circular charts divided up into segments which each represent a value. Pie charts are divided into sections (or ‘slices’) to represent values of different sizes. For example, in this pie chart, the circle represents a whole class. Each segment of the circle could represent different student grades. **(The PDF has to be updated)**

## Animate a Cylinder: Code its Volume

**(16) **(Holding text)** **Pie charts are used in data handling and are circular charts divided up into segments which each represent a value. Pie charts are divided into sections (or ‘slices’) to represent values of different sizes. For example, in this pie chart, the circle represents a whole class. Each segment of the circle could represent different student grades. **(The PDF has to be updated)**

## Introduction to Trigonometry

**(17) **TRIGONOMETRY is about the relationship between the 6 facts of a triangle, its 3 sides and 3 angles. If the values of three facts are known, you can use trigonometry to find the other facts. The 3 main trig functions are all related to the right angled triangle. Even if a triangle is not right-angled, you can drop a PERPENDICULAR (like the chain on the crane) to create 2 right angled triangles where there was none! Vertical and horizontal lines form right angles. **Right angles** are everywhere, so it’s not surprising that trigonometry comes into real life quite a lot. The links from the image and from the button, present two different versions of the Crane project. **(A new PDF has to be created)**

## Trig: Changing Sine & Cosine

**(18) **TRIGONOMETRY is about the relationship between the 6 facts of a triangle, its 3 sides and 3 angles. If the values of three facts are known, you can use trigonometry to find the other facts. The 3 main trig functions are all related to the right angled triangle. Even if a triangle is not right-angled, you can drop a PERPENDICULAR (like the chain on the crane) to create 2 right angled triangles where there was none! Vertical and horizontal form right angles, which are all around us, so it’s not surprising that trigonometry comes into real life quite a lot. e.g. You can use trigonometry to find the height of a tree without even climbing it! **(The PDF has to be updated)**