LO Adding and subtracting with negative numbers RAG Key Words: Positive, Minus 11-Nov-18 Look at the set of questions on the starter activity sheet. Attempt to answer all of them. Don’t worry if you’re not sure if your answers are correct. You will get the opportunity to change your answers at the end of the lesson. You can use the number line to help you.

(+8) – (+3)= (–8) + (–3)= (–3) + (+8)= (+3) – (+8)= (+8) – (–3)= Starter Activity (+8) – (+3)= (–8) + (–3)= (–3) + (+8)= (+3) – (+8)= (+8) – (–3)= (–8) – (–3)=

(+8) – (+3)= (–8) + (–3)= (–3) + (+8)= (+3) – (+8)= (+8) – (–3)= Starter Activity (+8) – (+3)= (–8) + (–3)= (–3) + (+8)= (+3) – (+8)= (+8) – (–3)= (–8) – (–3)=

Keep a record of your answers, you may want to change them at the end of the lesson. Mini whiteboards ready – one between two, you must agree you answer with your partner.

Why is this ‘4’? Class Discussion – really important to read these notes before teaching Ideally get them to think/pair/MWB Can you explain why this diagram is showing 4? Students may be confused if they have not encountered anything like this before, as there are 8 objects. If no one has any idea, you could ask: Can you describe what you see in the picture? Someone will mention words such as ‘plus’, ‘positive’, ‘minus’ and ‘negative’. If the students are really stuck you could cover with your hand everything except the right-hand pair of one negative and one positive, and ask the class: How much is there here? They might say ‘two’, but someone will realize that the answer is ‘nothing’. Returning to the original question (by removing your hand), students may comment on ‘a plus and a minus cancelling each other out’ or on there being four more ‘pluses’ than ‘minuses’. When a positive charge and a negative charge cancel each other out, this corresponds to the fact that (+1) + (–1) = 0. You could illustrate this by crossing out a pair of opposite charges, although some students might find crossing out hard to understand. You don’t need to wait for everyone to grasp the idea – as soon as a few seem to understand move on to the next slide, as the model will become clearer with more examples. 4

How much is this? Ideally get them to think/pair/MWB If students say ‘plus three’ or ‘positive 3’, that is fine.)

Show me another way of making 3. Can you do one using 11 charges altogether? Select examples to share with the whole class to check they work, if they don’t what do we need to do to correct it?

How much is this? These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How much is this? –2 These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How much is this? These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How much is this? These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How much is this? These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How much is this? +3 These slides are intended to help students see the need for placing a + or – before each number, and you should stress the importance of this.

How would you describe what happens here? These slides show: (+4) + (-2) = +2

How would you describe what happens here? These slides show: (+4) + (-2) = +2

How would you describe what happens here? These slides show: (+4) + (-2) = +2 (+4) +

How would you describe what happens here? These slides show: (+4) + (-2) = +2 (+4) + (-2) =

How would you describe what happens here? These slides show: (+4) + (-2) = +2 (+4) + (-2) = +2

Task A Match each diagram with one of the calculations, write the calculation in the space beneath the diagram. Write the answer to the calculation after the equals sign. Check that the answer matches what you see in the drawing. Some pupils can be moved onto task C without completing task B. They will need an explanation first, this can be given individually or is a small group whilst other pupils are working on task B. (+5) – (+2) = (+5) + (+2) = (+5) + (-2) = (-5) – (-2) = (-5) + (-2) = (-5) + (+2) =

Draw diagrams to represent the following calculations. Task B Draw diagrams to represent the following calculations. (-2) + (-4) = (+ 4) + (-5) = (+ 7) + (-3) = (+8) - (+ 3) = (-8) + (- 3) = (-6) + (+3) = Most pupils will complete task B to consolidate their understanding of task A. Some pupils will move straight on to task C.

Task B Now draw diagrams to represent your own calculations.

What about this? And these slides run through: (+2) – (–1) = (+3) +2

What do we get when we take away a negative? What about this? And these slides run through: (+2) – (–1) = (+3) What does the crossing out take away? How would we write that? What do we get when we take away a negative?

What about this? (+2) - And these slides run through: (+2) – (–1) = (+3) (+2) -

What about this? (+2) – (–1) = And these slides run through: (+2) – (–1) = (+3) (+2) – (–1) =

What about this? (+2) – (–1) = (+3) And these slides run through:

Another example You could make use of the MWB here and get pairs of students to write up each step and ‘show me’ A further example. If not everyone understands the subtraction of negatives at this stage, that is fine, as the first collaborative task does not involve this and students will have opportunity later to think about this more. (+1) – (–2) = (+3)

Another example A further example. If not everyone understands the subtraction of negatives at this stage, that is fine, as the first collaborative task does not involve this and students will have opportunity later to think about this more. (+1) – (–2) = (+3) +1

Another example (+1) – (–2) A further example. If not everyone understands the subtraction of negatives at this stage, that is fine, as the first collaborative task does not involve this and students will have opportunity later to think about this more. (+1) – (–2) = (+3) (+1) – (–2)

Another example (+1) – (–2) = +3 A further example. If not everyone understands the subtraction of negatives at this stage, that is fine, as the first collaborative task does not involve this and students will have opportunity later to think about this more. (+1) – (–2) = (+3) (+1) – (–2) = +3

How can I draw (+2) – (+5)? How can I draw (+2) – (+5)?

How can I draw (+2) – (+5)? Another way of thinking of (+2)…

How can I draw (+2) – (+5)? And another... How can I draw (+2) – (+5)?

How can I draw (+2) – (+5)? And another... Do you agree that this is still (+2)?

How can I draw (+2) – (+5)? How can I take away (+5)?

How can I draw (+2) – (+5)? How can I draw (+2) – (+5)? (+2) – (+5) =

How can I draw (+2) – (+5)? (+2) – (+5) = (-3)

Task C Match each diagram with one of the calculations, write the calculation in the space beneath the diagram. Write the answer to the calculation after the equals sign. Check that the answer matches what you see in the drawing. (+2) - (+5) = (-2) - (-5) = (+5) - (-2) = (-2) - (+5) = (+2) - (-5) = (+2) - (+5) =

Always True Sometimes True Never True Extension Task Split your page into three columns, like below. For each statement decide if the statement is sometimes true, always true or never true. You must give reasons for your answers. Always True Sometimes True Never True

Extension Task

Answers (1) Class Discussion You can just show the answers if you feel the class are ready to move on quickly. Run through the questions below if you feel there are still lots of misconceptions to clear up. Which calculations did you find easiest/hardest? Why? What drawing did you make for this calculation? Why? Can you explain what your drawing shows? Did anyone else do the same or something different? Which drawing do we prefer? Why? What answer did you obtain for this calculation? Why? Did anyone obtain a different answer? Why? Is there a difference between the calculations (+5) – (+2) and (+5) + (-2)? These calculations give the same answer but have different diagrams and students could talk about how they envisage the two processes differently. They may also comment on the fact that two of the other calculations give the same answer and talk about why. There are interesting patterns here to discuss.

Calculations (2) Conduct a whole-class discussion about what has been learned and explore the different diagrams that have been drawn. Have you noticed some interesting misconceptions as you circulated among the groups? If so, you may want to focus the discussion on these. Which calculations were easiest/hardest this time? Why? What drawing did you make for this calculation? Why? Can you explain in words what your drawing shows? Does anyone have a different way of explaining it? Did anyone else do the same or something different? Which drawing do you prefer? Why? Who agrees/disagrees? Why? What answer did you obtain for this calculation? Why? Did anyone obtain a different answer? Why? What do other people think? There are two pairs of calculations with the same answer. Can you explain why this happens? What else is the same about some of the diagrams? What is different?

Look back at your answers for the starter activity. Do you want to change any of your answers?

Using a number line (+8) – (+3)=

Using a number line (–3) + (+8)=

Using a number line (+8) – (–3)=

Using a number line (–8) + (–3)=

Using a number line (+3) – (+8)=

Using a number line (–8) – (–3)=

Finish up with pupils trying this task, if possible alone, without help from you or their peers. This will need marking alongside the ‘Common Issues’ sheet. You might want to use the time for a starter in your next lesson to go through any issues they need to respond to from your marking.

Teacher Slide You might want to refer to some of the questions on the common issues sheet as you circulate during the starter Or Use these to run a MWB response to some of the starter questions

Teacher Slide