Basic operations – Using the four digits 2, 0, 1 and 6 and the four operations (addition, subtraction, multiplication and division) can you make equations that equal all the numbers from zero to 20?
- Which multiplication tables do you know best?
- What do all the multiples of 2 and 4 and 8 have in common?
- How do you know if a number is divisible by 5 or 10?
- Write down all the multiples of 3 in order and see if you can determine something that they all have in common (clue – add the digits together).
This recipe serves 4 people, 2 pancakes each
- 2 cups self raising flour, sifted (250g at 0.32c per gram)
- 2 large eggs, separated (40 cents each)
- 2 cups milk (500ml at 0.25c per ml)
- 2 tsp sugar (8 grams at 0.024c per gram)
- 50g butter, melted plus extra butter or oil for cooking (at 0.88c per gram)
How much do you think it costs to make pancakes at home? How much do you pay at a cafe or McDonalds? When restaurant owners and chefs calculate the cost of their menu they need to take into account the cost of ingredients as well as staff costs, overheads (rent, power, telephone, gas etc) and also make a profit.
There are many skills to learn to master Algebra, but we have already made a great start – You :
1. Can recognise and continue a pattern
2. Understand that a pro-numeral (a letter) represents a variable (changing number)
3. Understand that it is mathematical convention to leave out the multiplication sign in expressions and equations involving pro-numerals.
4. Can substitute positive and negative numbers into an equation
5. Can plot points on a cartesian plane
6. Can determine the equation from a table of values
7. Can solve an equation using backtracking
The next step is to be able to solve an equation by doing the same operation to both sides. Try these online activities:
Algebra Balance Scales (a virtual manipulative from Utah State University)
Algebra Balance Scales with negatives (same as above, but with negative numbers)
Equation Buster – from MathsNet
This last week of Term 2 we will be doing some transformations and tessellations. Our learning intention is to understand and describe translations, reflections in an axis, and rotations of multiples of 90° on the Cartesian plane using coordinates and to identify line and rotational symmetries.
Your first task is to use the letters of your name, on a poster, to demonstrate your understanding of translation (slide), rotation (turn), reflection (flip) and dilation (increase in size).
Your second task is to use a shape that tessellates (fits together with no gaps or spaces) to create an artwork, similar to the ones in these YouTube videos:
These links will help you to plan, design and construct your own:
Learning Intention: To distinguish between prisms and other three-dimensional shapes and to work out the relationship between vertices, edges and faces (Euler’s Formula).
These two Year 7 students are making three-dimensional models with jubes and toothpicks (or satay sticks) to record vertices, edges and faces. Start with simple shapes, such as triangular pyramids, cubes and square pyramids, distinguishing between shapes that are prisms and those that are not. When students have made at least six or more shapes ask them to see if they can find a relationship between V (vertices); E (edges) and F (faces). I usually give a clue that they only need to use addition and subtraction (not multiplication or division).
To calculate the area of a triangle use the formula:
Area = One half multiplied by the base multiplied by the height (A=1/2 x bh)
National Curriculum Standard: “Students use formulas for the area and perimeter of rectangles.”
The perimeter of a rectangle is calculated by adding the four sides. The area of a rectangle is calculated by multiplying the length by the width.
Perimeter =2 x (L+W) = 2L + 2W
Area = Length x Width = LW
Find at least three rectangles around the classroom and measure the length and width. Draw a sketch showing the object and the measurements, including the units (millimetres, centimetres or metres). Calculate the perimeter and the area of the object using the formulae above.
For example; your laptop, the table top, your maths book, a window pane, the door, the whiteboard, the front of the heater, the noticeboard etc.
The perimeter of the locker door will be:
(2 x 35) + (2 x 59) = 70 + 118 = 188 cm
The area of the locker door will be:
35 x 59 = 2065 cm^2 (square centimetres)
Over the next few weeks we are working with Scratch to create projects that demonstrate maths concepts using simple drag-and-drop programming. Please make sure you have completed the following steps:
1. Join Scratch with your school Username (eg gow0054) and Password. Being a registered member allows you to save and share your work. Make sure Mrs Gow has recorded your Scratch username.
2. Join the Hawkesdale P12 College Studio and the Victorian Coding Challenge (1, 2 and 3) Studios on Scratch, so you can share your work and see what other students have created.
3. Challenge #1: Create a character that draws a shape and upload to the Hawkesdale P12 College page.
4. Draw your initials, like these students in 5/6 Clark/Smith. Can you translate and reflect your initials so they appear in all four quadrats?
5. Challenge #2: Create a project that explains a maths concept. For example:
- Draw your initials in block letters and calculate their perimeter and the area they cover. Use the Cartesian Co-ordinate grid as a background.
- Explain how to calculate the perimeter of a polygon or circle.
- Name the parts of a circle (radius, diameter, circumference, sector, arc)
- Describe different triangles (equilateral, isoceles, scalene, right-angled, acute-angled or obtuse-angled)
- Explain how the sum of angles in a triangle always equals 180 degrees.
- Explain how the sum of angles in a quadrilateral always equals 360 degrees
- Explain how to calculate the area of a polygon (triangle, rectangle, parallelogram, trapezium, kite) or circle
- Describe right angles, straight angles and complementary (adds to 90 degrees), supplementary (adds to 180 degrees) and equal angles.
- Describe ‘pi’ and how it can be used to calculate the circumference and area of circles.
- Describe Euler’s Rule about the faces, vertices and edges of a polyhedron (Faces + Vertices – Edges = 2)
Make sure you add your project to the Hawkesdale P12 College Studio page.
6. Challenge #3: Create a simple game that uses maths concepts. It could be something like this Hungry Fish game. Someone even created a Scratch project for Co-ordinate Grid Battleships.
This term we will be studying Measurement and Geometry.
Year 7 Maths (JacPlus Chapter 9 – Measurement and Chapter 5 – Geometry)
By the end of this term I hope you will be able to:
- Use appropriate units of measurement
- Calculate the perimeter of 2D shapes
- Calculate the area of triangles, quadrilaterals and composite shapes.
- Identify types of polygons (different triangles and quadrilaterals)
- Estimate, measure and draw angles between 0 and 360 degrees.
- Identify the properties of parallel and perpendicular lines and the angles that form between them.
- Calculate the missing angles in polygons, knowing that the internal angles of a triangle add to 180 degrees.
- Recognise various transformations (translations, reflections, rotations and dilations)
Year 8 Maths (JacPlus Chapter 7 – Congruence and Chapter 10 – Measurement)
By the end of this term I hope you will be able to:
- Use and convert units of measurement for perimeter, area and volume
- Calculate the area of various quadrilaterals.
- Calculate the area and perimeter of circles.
- Calculate the volume of various prisms using formulae.
- Identify congruent shapes
- Transform various shapes (translate, dilate, rotate and reflect).
- Solve geometric problems using congruence.
- Work out problems around different time zones using the 24 hour clock.
Learning Intention: Students will understand that there are many different ways to express the concept of ‘part of a whole’.
Success criteria: Each student will produce a poster that demonstrates eight different ways to express a certain fraction, chosen by the distribution of individual fraction cards. We will use these cards and our ‘Fraction Walls’ to demonstrate adding, subtracting, multiplying and dividing fractions.
Each student will recieve a card with a fraction and create a poster that shows this fraction eight different ways (as above for one half). When you have finished, place your poster on the number line in the room.