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Listed under:  Equations

### Graphing functions

This collection contains five digital curriculum resources (all interactive learning objects) that introduce students to graphing linear, parabolic, cubic and trigonometric functions. Through exercises, students investigate how the constants in each function equation influence relevant aspects of graphing, such as dilations ...

### Applications of differentiation

This is a teacher resource for applications of differentiation consisting of a website and a PDF with identical content. It contains a discussion of graph sketching, related rates of change and the solution of maxima and minima questions.

### The take-away bar: generate hard subtractions

Solve subtractions such as 87-29. Use a linear partitioning tool to help solve randomly generated subtractions. Learn strategies to do complex arithmetic in your head. Split a subtraction into parts that are easy to work with, work out each part and then solve the original calculation. This learning object is one in a series ...

### EagleCat: cubic-G

Explore the graphs of cubic equations in two forms: (a) the general form, y = a(x – h)³ + k, and (b) the intercept form, y = (x – a)(x – b)(x – c). Observe changes to the point of inflexion and the shape of cubic graphs through various transformations. Alternately, change the equation and observe changes in the x-intercepts ...

### EagleCat: trig-G

Explore the graphs of trigonometric equations in the form: (a) y = a sin[n(x - h)] + k, (b) y = a cos[n(x - h)] + k and (c) y = a tan[n(x - h)] + k. Use sliders or enter values to dilate, reflect and translate the basic trigonometric equations y = sin(x), y = cos(x) and y = tan(x), and observe the changes in the amplitude, ...

### The take-away bar: go figure

This tutorial is suitable for use with a screen reader. It explains strategies for solving subtractions in your head such as 87-39. Work through sample questions and instructions explaining how to use linear partitioning techniques. Solve subtractions by breaking them up into parts that are easy to work with, work out each ...

### Filling glasses: find the right graph

Look closely at some line graphs. Examine the relationship between the shape of a glass and the time taken to fill it with juice. Notice that the fluid level rises more quickly in a narrow glass than in a wide glass. Choose both sections of a line graph representing the filling rate for a glass shape. This learning object ...

### Maths and the car: loan calculator

Use a calculator to estimate loan repayments needed to buy a car. Look at variables such as price, compound interest rate, term of loan and payment frequency. Work out the total interest to be paid by the borrower.

### Compound shapes

Select from three levels of complexity for working with polygons. Estimate the area of a randomly-generated polygon. Try counting squares on a grid to help your estimate. Cut the shape into rectangles and triangles. Use a formula to calculate the exact area for each of the simple shapes. Then find the total area for the ...

### Working it out!

See how small a cubic centimetre looks when compared with a cubic metre (100 cm x 100 cm x 100 cm). Then estimate the volume of cuboids, such as a packet of food and a tool box. Rotate a 3D grid to help you work out dimensions in centimetres. First work out the area of the base. Then multiply your answer by the height to ...

### Bridge builder: complex squares

Build bridges by adding regular sections (each made up of three beams plus a shared beam). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build a wider span. Describe the number pattern. This learning object is the fourth in a series of five ...

### Bridge builder: complex pentagons

Build bridges by adding pentagonal sections (each made up of four beams plus a shared beam). Examine a table and graph of the total number of beams used in bridges of different sizes. Predict the number of beams needed to build a wider span. Describe the number pattern. This learning object is the last in a series of five ...

### Squirt: two containers

Examine the relationships between capacities of various containers. Look at two containers that may have different diameters, heights and shapes. Fill a container and squirt liquids between the containers to establish the proportional relationship. Express relationships using mathematical notation such as a=6xb. This learning ...

### Squirt: two containers: level 1

Examine the relationships between capacities of containers of the same shape, but different size. Squirt liquids between two containers to establish the proportional relationship. Express relationships using mathematical notation such as a=6xb. This learning object is the first in a series of five objects that progressively ...

### Squirt: two containers: level 2

Examine the relationships between capacities of containers of different shapes and sizes. Squirt liquids between two containers to establish the proportional relationship. Express relationships using mathematical notation such as a=6xb. This learning object is the second in a series of five objects that progressively increase ...

### Finding the area of rectangles

Find the area of rectangles on a grid. Explore how the formula works. First, estimate the area of a rectangle on a grid. Second, work out the correct formula for finding area by placing rows and columns of squares inside the rectangle. Then, compare the actual area of the original shape with your first estimate. Practise ...

### Balance the cups

Put blocks (or balls) into the cups on the scales to make them balance, using the number rules A = B + C and A + B = C + D. Use your knowledge of addition and multiplication to help you work out how many blocks you need in each cup. Finish the number sentence to show an equal number of blocks on each side. This learning ...

### Balance the cups: use the rule 1

Put blocks into the cups on the scales to make them balance, using the number rule A = B + C. Use your knowledge of addition to help you work out how many blocks you need in each cup. Finish the number sentence to show an equal number of blocks on each side. This learning object is the first in a series of three learning objects.

### Balance the cups: use the rule 2

Put balls into the cups on the scales to make them balance, using the number rule A = B + C. Use your knowledge of addition and multiplication to help you work out how many balls you need in each cup. Finish the number sentence to show an equal number of balls on each side. This learning object is the second in a series ...

### Balance the cups: use the rule 3

Put blocks into the cups on the scales to make them balance, using the number rule A + B = C + D. Use your knowledge of addition to help you work out how many blocks you need in each cup. Write the number sentence to show an equal number of blocks on each side. Look for patterns to help you think of another solution. This ...