There are 366 different Starters of The Day, many to choose from. You will find in the left column below some starters on the topic of Simultaneous Equations. In the right column below are links to related online activities, videos and teacher resources.

A lesson starter does not have to be on the same topic as the main part of the lesson or the topic of the previous lesson. It is often very useful to revise or explore other concepts by using a starter based on a totally different area of Mathematics.

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### Simultaneous Equations Starters:

Boxing Day: Work out the contents and the cost of the Christmas boxes from the given clues.

Light Shopping: A lamp and a bulb together cost 32 pounds. The lamp costs 30 pounds more than the bulb. How much does the bulb cost?

Oblongs: Find the dimensions of a rectangle given the perimeter and area.

Pentadd: Five numbers are added together in pairs and the sums shown. What might the five numbers be?

Planet Numpair: The sum and product are given, can you find the two numbers?

Rabbits and Chickens: There are some rabbits and chickens in a field. Calculate how many of each given the number of heads and feet.

Rail Weigh: Use the weights of the trains to work out the weight of a locomotive and a coach. A real situation which produces simultaneous equations.

Refreshing Revision: It is called Refreshing Revision because every time you refresh the page you get different revision questions.

Same Same: A problem involving two people's ages which can be solved using algebra.

Santa's Sleigh: Work out the number of clowns and horses given the number of heads and feet.

Simultaneous Occasions: A problem which can best be solved as a pair of simultaneous equations.

Sum of the Signs: Each traffic sign stands for a number. Some of the sums of rows and columns are shown. What numbers might the signs stand for?

Summer Holidays: How many children and how many donkeys are on the beach? You can work it out from the number of heads and the number of feet!

Two Numbers: Find the two numbers whose sum and product are given.

Fruit Snacks: Work out the numbers of each type of fruit bought for snacks

Same Series Sum: Find an arithmetic series and a geometric series that have the same sum of the first five terms.

Two real numbers: The sum of the reciprocals of two real numbers is -1, and the sum of their cubes is 4. What are they?

#### Simultaneous Shopping

Find the cost of the individual items in shopping baskets (introduction to simultaneous equations).

Transum.org/go/?to=ssp

### Curriculum for Simultaneous Equations:

#### Year 6

Pupils should be taught to find pairs of numbers that satisfy an equation with two unknowns more...

#### Years 7 to 9

Pupils should be taught to use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations more...

#### Years 10 and 11

Pupils should be taught to solve 2 simultaneous equations in 2 variables (linear/linear {or linear/quadratic}) algebraically; find approximate solutions using a graph more...

Pupils should be taught to translate simple situations or procedures into algebraic expressions or formulae; derive an equation (or 2 simultaneous equations), solve the equation(s) and interpret the solution more...

#### Years 12 and 13

Pupils should be taught to solve simultaneous equations in two variables by elimination and by substitution, including one linear and one quadratic equation more...

### Exam-Style Questions:

There are almost a thousand exam-style questions unique to the Transum website.

### Feedback:

Comment recorded on the 25 June 'Starter of the Day' page by Inger.kisby@herts and essex.herts.sch.uk, :

"We all love your starters. It is so good to have such a collection. We use them for all age groups and abilities. Have particularly enjoyed KIM's game, as we have not used that for Mathematics before. Keep up the good work and thank you very much
Best wishes from Inger Kisby"

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"An absolutely brilliant resource. Only recently been discovered but is used daily with all my classes. It is particularly useful when things can be saved for further use. Thank you!"

Comment recorded on the 21 October 'Starter of the Day' page by Mr Trainor And His P7 Class(All Girls), Mercy Primary School, Belfast:

"My Primary 7 class in Mercy Primary school, Belfast, look forward to your mental maths starters every morning. The variety of material is interesting and exciting and always engages the teacher and pupils. Keep them coming please."

Comment recorded on the 19 October 'Starter of the Day' page by E Pollard, Huddersfield:

"I used this with my bottom set in year 9. To engage them I used their name and favorite football team (or pop group) instead of the school name. For homework, I asked each student to find a definition for the key words they had been given (once they had fun trying to guess the answer) and they presented their findings to the rest of the class the following day. They felt really special because the key words came from their own personal information."

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"A Maths colleague introduced me to your web site and I love to use it. The questions are so varied I can use them with all of my classes, I even let year 13 have a go at some of them. I like being able to access Starters for the whole month so I can use favourites with classes I see at different times of the week. Thanks."

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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Thanks for such a great resource!"

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"3 NQTs in the department, I'm new subject leader in this new academy - Starters R Great!! Lovely resource for stimulating learning and getting eveyone off to a good start. Thank you!!"

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"I think these are great! So useful and handy, the children love them.
Could we have some on angles too please?"

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"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

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Thanks again"

Comment recorded on the 1 February 'Starter of the Day' page by M Chant, Chase Lane School Harwich:

"My year five children look forward to their daily challenge and enjoy the problems as much as I do. A great resource - thanks a million."

Comment recorded on the 1 May 'Starter of the Day' page by Phil Anthony, Head of Maths, Stourport High School:

"What a brilliant website. We have just started to use the 'starter-of-the-day' in our yr9 lessons to try them out before we change from a high school to a secondary school in September. This is one of the best resources on-line we have found. The kids and staff love it. Well done an thank you very much for making my maths lessons more interesting and fun."

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Comment recorded on the 3 October 'Starter of the Day' page by Mrs Johnstone, 7Je:

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### Notes:

This topic covers simultaneous equations with two different variables. The starters pose real world problems which can be solved using the techniques taught at school or by other intuitive methods.

Though there are many formal strategies for solving simultaneous equations the skill of forming the equations from real life situations is a very important stage in working towards a solution.

Algebraic methods are the most efficient for solving basic simultaneous equations but graphical methods, probably using a graphic display calculator or computer software package, may be more suitable for less standard sets of simultaneous equations.

### Simultaneous Equations Activities:

Simultaneous Shopping: Find the cost of the individual items in shopping baskets (introduction to simultaneous equations).

Algebra In Action: Real life problems adapted from an old Mathematics textbook which can be solved using algebra.

Pentadd Quiz: Find the five numbers which when added or multiplied together in pairs to produce the given sums or products.

Recurring Decimals: Change recurring decimals into their corresponding fractions and vica versa.

Simultaneous Equations: A self-marking, multi-level set of exercises on solving pairs of simultaneous equations.

Simultaneous Solutions: Arrange the given pairs of simultaneous equations in groups to show whether they have no solution, one solution or infinite solutions.

Unbeknownst: Some picture grid puzzles which can be solved by using simultaneous equations.

Using Graphs: Use the graphs provided and create your own to solve both simultaneous and quadratic equations.

Window View: Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.

Three Unknowns: Solve these sets of three simultaneous, linear equations to find the values of the variables.

Alternatively, for the more advanced student, there is an ever-growing collection of Exam-Style Questions with worked solutions on the topic of Simultaneous Equations.

### Simultaneous Equations Investigations:

Window View: Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.

### Simultaneous Equations Videos:

Transum's Simultaneous Equations Video

Simultaneous Equations Video: Learn to solve simultaneous equations from the very basic to those containing quadratics. This video is to help you do the online, self-marking exercise.

Simultaneous Equations (Elimination): This video demonstrates how to solve simultaneous equations by elimination.

Simultaneous Graphs Video: A short video which explains how to use graphs to solve simultaneous equations.

### Simultaneous Equations Worksheets/Printables:

Simultaneous Equations Examples: These are the examples used in the help video for the Simultaneous Equations online exercise.

Simultaneous Equations Extension Exercise: An exercise that appeared in an algebra book published in 1895. It starts with basic questions but soon gets tricky!

Links to other websites containing resources for Simultaneous Equations are provided for those logged into 'Transum Mathematics'. Subscribing also opens up the opportunity for you to add your own links to this panel. You can sign up using one of the buttons below:

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#### Three Unknowns

Solve these sets of three simultaneous, linear equations to find the values of the variables.

Transum.org/go/?to=threeunknowns

### Teaching Notes:

Many Transum activities have notes for teachers suggesting teaching methods and highlighting common misconceptions. There are also solutions to puzzles, exercises and activities available on the web pages when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page.

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