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See Video demonstrating of Number Line Walking approach
to solving and deriving rules for Integer Problems below.
Addition
Directions
(+) 3 ) (+) (-)
4 ) = (-) 1 )
Start on the right side at 3
Turn
Right
Walk Backward 4
End on the left side at 1
Multiplication Directions
(+) 3) (X)
(-) 2) = (-)6)
Turn Right
Walk 3 Times
Backward 2
End on the Left Side at 6
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- You can shorten the length of the numberline units and increase the range of problems by
clicking the up and down arrow buttons.
- When the second factor of a term is greater than (1), the
color of the step counter will change from yelllow to white to
count multiples of the numberline units.
- When of the two signs on the products there is an odd number
of negative signs (1) the solution is the difference of the two
products with the sign on the larger product.
- When of the two signs on the product there is an even number
of negative signs (0 or 2) the solution is the sum of the two
products with the sign on the products.
- When practicing addition, after you find a solution, click
the 'Rules' button three times to explore the multiplication and
addition of integers rules.
- See Instructions for Integer Application Below.
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- Exploring The Addition And
Multiplication Of Integers
- Each of the top two terms includes a signed number (integer)
inside the parenthesis and an signed number (integer) outside to
the left of the parenthesis.
- This arrangement indicates the multiplication of the
integers of each term. Click the 'Problem' button to display the
non-zero products below each term.
- The numberline troll is now moved with the right left arrow
buttons to find solution.
- In the steps A, B and C the words, rightside, right and
forward indicate a positive sign, and the words leftside, left
and backward indicate a negative sign.
- The sign of the product of the first term will be indicated
in step A by the side of the numberline on which the troll is to
start.
- The sign of the product of the second term will be indicated
in step B by the direction on the numberline in which the troll
is to move.
- Correct the signs on the products and solution if necessary
by placing mouse over sign.
- Position mouse over the right or left arrow button to move
the troll in the indicated direction on the numberline to the
position that represents the sum or difference of the products
of the terms.
- If the signs on the products are correct, then when the
troll reaches the position of the solution, the text of step C
will prompt you to end the troll's movement.
- When the troll moves in the direction toward the solution a
fire will burn. When the troll moves in the direction away from
the solution snow will fall
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- Multiplying Integers
- Click 'Add' to change the operation to 'Multiply' then click
'Problem'. Now all four integers are multiplied to get a
product for the single term.
- Now follow the displayed instructions for multiplication.
- Correct the signs on the products and solution if necessary.
- Then move forward or backward as indicated a number of times
equal the product of all the integers.
- The numbers on the counter will change from yellow to white
to indicate multiples of the trolls steps on the number line.
- The color of the step counter will change from yelllow to
white to count multiples of the second product.
- Download Worksheets
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