Thursday 2nd April
How many points did you manage to get in the game yesterday? Did you remember to use the inverse to find the value of X?
Did you crack the code? We do love a maths joke!
Today is our final day on algebra and of course it will have an animal theme where possible. We are going to look at substitution today and you can do this with pictures or letters.
Each picture is given a value for you to substitute into the expression.
This is where you are given the values for the letters, for example a=4, b=2 and c=3.
You then need to put those values into the expression, for example 3c - a.
**Top tip: remember a number and letter next to each other means you need to multiply them.
So, 3c-a becomes (3x3)- 4 = 5.
Look at the examples in this picture if you need more of a reminder.
There are three activities for you to choose from today and as always we would like you to do at least one.
Have a go at playing this substitution game. It will tell you the value of X for you to then put into the number sentence. See how far you can get through the different levels.
On the PDF document are some top trump cards with expressions on them. There are lots to choose from so you might want to just choose a selection of your favourite animals.
When substituting, we recommend you use a=4, b=2 and c=5, but there are other options on the document and of course you could choose your own numbers.
Some of you will be able to print the cards, but others will be able to copy them down onto paper to solve.
There are lots of different activities you could do with these cards:
Choose 4 animals as your pictures and give them all a value. You can choose how difficult you would like to make this: one digit numbers, two digit numbers or even decimals.
Then create your own expressions using your animal pictures, you can use my examples to help you.
Finally, substitute your animal pictures with the numbers you chose to find the answers.
Here as one I did to help you. It also shows how you can make this activity easier and harder depending on how confident you feel with substitution.
Wednesday 1st April
What functions did you choose for your function machines yesterday? Did you have a go at correcting Miss Read’s mistakes? Here are the corrections for you to check your answers (you can click on the images to make them larger).
Today we are going to find the value of the unknown number, usually x or y. When we looked at this in class, we thought of it like going backwards through the function machine using the inverse (opposite) so you can always draw the equation as a function machine to help you.
X + 5 = 9
The inverse of +5 is -5 so 9 – 5 = 4
So X = 4
Or for two step equations…
3X – 5 = 13
First, the inverse of -5 is +5. 3X = 18
Then, the inverse of multiply by 3 is dividing by 3. X = 6
And for an extra challenge of equations with brackets…
3(X+3) = 15
First, the inverse of multiplying by 3 is dividing so X+3 = 5
Then, the inverse of +3 is -3 so X =2
There are two activities for you to choose from to find the value of the unknown. You can do whichever one you would like or do both. The answers for the activities will be put on tomorrow.
Activity 1 – points game
See how many points you can get by solving some or all of these equations. Look back at the examples above if you need to. Keep working backwards and using the inverse, one step at a time.
Activity 2 – code breaker
Complete the code breaker for one or two step equations, whichever level of challenge you feel most comfortable with, by finding the maths joke. Solve each equation first to find out the value of the unknown letter. Then put that number into the code.
Tuesday 31st March
How did you get on with sequences yesterday? Were you able to find the unknown value that the sequence was going up or down in? Did you challenge yourself to find more than one missing number?
Today we will be using the idea of function machines for algebra that we did look at in class. Again, there are two activities and you can do either Activity 1 or Activity 1 and 2, it is totally up to you.
Input = the number you put into the ‘machine’
Expression = an algebraic rule to represent the function machine using a letter as the starting number. For example, if the function machine was x2 then +15, the expression would be 2y+15, with y being the unknown number.
Output = the number that comes out of the ‘machine’ after calculating with the input numbers
Create your own one step or two step function machine using the pictures below to guide you. You can use equipment from around your house to represent them like the cubes in the picture if you need to.
First, choose your functions (times, divide, add or subtract).
Then, write an algebraic expression for your function machine using x or y as your unknown input number.
Now, test your function machine for different input numbers. For example, what would the output be if you put the number 12 into your function machine? You can choose how to challenge yourself here with 1 digit, 2 digit or even decimal numbers.
Finally, if you are ready for a challenge, work backwards through your function machine by using different output numbers to work out the input. For example, what would the input be, if the output was 24?
**Top tip: use the inverse! Look at my explanations of the pictures below to help you.
If the function machine wants you to multiply the input by 4, you need to divide by 4 when starting with the output.
If the function machine wants you to add 4, you need to subtract 4 to find the input.
If the function machine wants you to times by 2 then add 3, you need to take away 3 then divide by 2 to get the input.
Miss Read has made some errors when completing the algebra function machines. Can you spot the mistakes and correct them?
Even better, can you explain where she has gone wrong and what she needs to remember to do next time? Errors could include: not writing the algebraic expression correctly, adding instead of subtracting, not using the inverse when starting with the output.
There are three levels of challenge for you to choose from:
1 star = one step function machine with input numbers only
2 star = one step function machine with input and output numbers to start
3 star = two step function machine with input and output numbers to start
Monday 30th March
This week we will be revising the topic of algebra. In class, we looked at algebra and the understanding of the ‘unknown’, either as a missing number or as a letter. We know lots of you really enjoyed this topic and hope you will enjoy it just as much at home!
Today we will be looking at number sequences, working out what is happening to the numbers in the sequence (the unknown) and what number would therefore come next. There are two activities – one is online and the other is a worksheet. You can do whichever one you would like to do, or both(!), it is up to you.
Of course, the third activity is Times Tables Rockstars to take part in our Phase competition so if you do have a spare 10 minutes, you could log on and add on some points for your class.
- Are the numbers in the sequence increasing or decreasing in size? How do you know?
- How can you work out what the sequence is going up or down in?
- What can you use to help you work out the missing numbers now?
- How could you check your answers?
Have a go at playing the number sequence game online - https://mathsframe.co.uk/en/resources/resource/42/sequences
There are lots of different levels of challenge and then within that different levels of difficulty. We recommend you start on Level 10 (count on or back in steps of up to 100), but you can have a look at the other levels if you are finding Level 10 too easy or a bit too challenging as they will all help you with number sequences.
Then you can choose easy, medium, hard, very hard or genius level. These levels change by where the missing number is and how many missing numbers there are. You can always choose the easy level to begin with and then challenge yourself to the harder levels afterwards.
Here is a step by step guide for how to work out the answers when playing the game.
Choose either the 1, 2 or 3 star super sequence sheet below to complete. It is ok to start with the 1 star and think actually I can do the 2 star instead and vice versa!
On the sheet you need to work out the rule for the sequence and then find the missing numbers, just like the online activity. For example, on the online activity example the rule for the sequence would be -46.
The answers are also here for you to check your learning once you have finished.
Friday 27th March
Yesterday we looked at converting measurements. How did you do? Remember, you can always use your place value grid to help multiply and divide by 10, 100 and 1000.
Today we will continue practising converting different units.
Below are some worksheets for you to try – if you can’t print them off, you can always copy down the measurements onto some of the paper in your pack choosing your own measurements. The last two tables are trickier because you have to keep changing between grams and kilograms or between metres and kilometres, so pick the tables that you feel most confident with.
Challenge: Can you now convert your metre measurements to centimetres? Or for an extra challenge, millimetres?