Embedded Files
Introduction
Introduction
Watch the video for an introduction to the lesson.
Activity 1 - Dividing negative numbers
Activity 1 - Dividing negative numbers
Watch the video and learn how to divide directed numbers using counters.
Next read the information about dividing as sharing and sharing with negatives.
Then, complete the following tasks in your exercise book or folder.
Make sure you use real counters or the Color counters website to help you and then draw the counters to show your working.
Dividing Integers - with Two-Color Counters
Duration: 1:24
Dividing as sharing
Dividing as sharing
Traditionally we think of dividing as sharing objects amongst people or into groups.
Method 1
Method 1
Consider 15÷3. We can think of this as taking fifteen objects and dividing them into three groups.
Which gives us five objects in each group.
So, 15÷3 = 5
Method 2
Method 2
We can also think of 15÷3 as taking fifteen objects and dividing it into groups with three objects in each group.
This gives us five groups.
So 15÷3 = 5
Method 3
Method 3
We can also turn our division sum into a multiplication problem.
15÷3 is the same as “how many groups of three do a need to make 15?”
3× ? = 15.
3×5 = 15, so I need five groups.
Sharing with negatives
Sharing with negatives
Consider now, (-15) ÷ 3.
Using Method 1, we can think of this as taking fifteen, (-1) counters and dividing them into three groups.
Which gives us (-5) in each group.
So, (-15)÷3 =(-5)
What about, (-15)÷(-3)?
It doesn’t make sense to divide into (-3) groups, but we could make groups of (-3) counters, as in Method 2.
This would give us five groups of (-3) counters.
So, (-15)÷(-3) = 5
Task 1
Task 1
Represent these questions with counters before writing your final answer in your exercise book or folder.
Task 2
Task 2
How could you write each of the quotients (the end result of a division) in a different way?
Task 3
Task 3
How many quotients can you find with an answer of (-2)?
Task 4
Task 4
Consider your answers for Tasks 1, 2 and 3.
What do you notice?
What do you wonder?
Record your ideas in your exercise book or folder.
Activity 2 - Even more negatives
Activity 2 - Even more negatives
What about 15÷(-3)?
How can we divide fifteen, +1 counters into groups of (-3)?
The best way to tackle this problem is to turn it into a multiplication problem.
(-3)× ? = 15
When we did multiplication, we learnt that (-3) rows meant that we had to remove three rows.
What do we need to remove three rows of, to leave us with fifteen +1 counters?
If we created fifteen zero pairs, we could then remove three rows of (-1) counters, to leave us with fifteen +1 counters.
So we can remove (-5) counters out of each row, to leave us with fifteen +1 counters.
So, (-3)×(-5) = 15
or
15÷(-3) =(-5).
Task 1
Task 1
Represent these questions with counters before writing your final answer in your exercise book or folder.
Task 2
Task 2
How could you write each of the quotients (the end result of a division) in a different way?
Task 3
Task 3
How do your answers compare to those in Activity 1?
Task 4
Task 4
How many quotients can you now find with an answer of (-2)?
Task 5
Task 5
Consider your answers from Tasks 1, 2, 3 and 4.
What do you notice?
What do you wonder?
Record your ideas in your exercise book or folder.
Task 6
Task 6
In your exercise book or folder, create a summary of how to divide negative numbers (with or without counters). It should be in your own words and can use pictures or diagrams to help you.
Activity 3 - Multiplying and dividing tarsia
Activity 3 - Multiplying and dividing tarsia
Complete the Tarsia activity by using the Google doc file.
You will need:
scissors
a printer OR pencil, ruler and paper
Method 1 - If you have a printer
Method 1 - If you have a printer
Click on the embedded Google Doc and use the Grey box icon to open the Tarsia puzzle file in a new tab.
Use the Print option in the File tab to print the image onto A4 paper.
Follow the instructions in the file to cut up and complete the puzzle.
Method 2 - If you do not have a printer
Method 2 - If you do not have a printer
Use a pencil and a ruler to copy the diagram from the Google Doc onto some blank paper. Make sure the triangle sides are all equal and around 3cm long.
Carefully copy all the equations onto the same in the SAME place on the diagram. (Otherwise the puzzle won't fit together!)
Follow the instructions in the file to cut up and complete the puzzle.
Activity 4 - Arithmetic Four game
Activity 4 - Arithmetic Four game
Play “Arithmetic 4” on the Shodor website to practice your operations with integers.
Open the game in a new tab by clicking on the image of the game board.
Choose the integer options when selecting Problem types.
Activities too hard?
Activities too hard?
Play the BIDMAS Game online at the Transum website. You can play with 1, 2, 3 or 4 players.
Practise order of operations with positive integers by playing the Commit Four game. Create a copy of the game for yourself using the template.
Activities too easy?
Activities too easy?
Complete the Negative number division Venn activity by creating a copy of the document using the template.
Play Order of Operations game on the Shodor website. Select Add, Subtract, Multiply, Divide as the Problem types to start with.
Handing in your work
Handing in your work
Don't forget to hand in the work you completed today!
Your teacher will have told you to do one of the following:
Upload any digital documents you created and any photos you took of your written work to your Learning Management system (MS Teams, Google Classroom for example).
Email any digital documents you created and any photos you took of your written work to your teacher.
Make sure you keep any hand written work you did in your exercise book or folder as your teacher may need to see these when you are back in class.
Student reflection
Student reflection
Show how you feel about today's learning.
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