Copy of Adding Integers
Marlin is searching for Nemo. He can might swim up, down, back or forward depending on the situation.
Part 1
[b]Move the blue and orange sliders to model the following situation on the number line.[/b][br]Marlin has swam 5 meters. He continues swimming for 3 more meters before he runs into Dory. How far has he gone?
Part 1 Question
In the mathematical expression in the model above [math]5+3=8[/math], what do the 5 and 3 represent?
Part 2
[size=100][b]Move the blue and orange sliders to model the following situation on the number line.[/b][br]Marlin has swam 5 meters before he meets Bruce![br]He gets scared and swims backwards for 3 meters before Bruce catches up with him.[/size]
Part 2 Question
In the mathematical expression in the model above [math]5+\left(-3\right)=2[/math], what do the 5, -3, and 2 represent?
Part 3
[size=100][b]Move the blue and orange sliders to model the following situation on the number line.[/b][br]Marlin and Dory drop the mask and swim after it for 5 meters before it gets dark.[br]Dory encourages Marlin and they "just keep swimming" down into the depths for another three meters before a strange light appears. Write an equation for how far into the depths they have swam.[/size]
Part 3 Question
In the mathematical expression in the model above [math]\left(-5\right)+\left(-3\right)=-8[/math], what do the [color=#0000ff][b]-5[/b][/color], [color=#ff7700][b]-3[/b][/color], and [b]-8[/b] represent?
Part 4
[size=100][b]Move the blue and orange sliders to model the following situation on the number line.[/b][br]Marlin and Dory swim down for 5 meters and encounter a trench.[br]Marlin ignores Dory's advice and starts swimming up instead of through it.[br]He swims up for 3 meters before encountering a jellyfish.[/size]
Part 4 Question
In the mathematical expression in the model above [math]\left(-5\right)+\left(3\right)=-2[/math], what do the [color=#0000ff][b]-5[/b][/color], [color=#ff7700][b]3[/b][/color], and [b]-2[/b] represent?
Wonder
From completing the activities, you know: [math]5+\left(-3\right)=2[/math], [math]-5+3=-2[/math], and [math]-5+\left(-3\right)=-8[/math].[br]If you were given the problem: [math]-500+300=[/math] , do you think the answer would be positive or negative and why?
Wonder
How did the easier problem help you reason that out?
Practice
For each number line below, come up with a verbal description (like Marlin's stories in the examples) that could represent the model. Try not to use Marlin or swimming as your story, be creative!
#1a
What is the numerical expression for the model above?
#1b
Write a story that could represent the model.
Practice continued
Use the number line below (optional) to help you answer the following questions.
#2
[math]-7+\left(-3\right)=?[/math]
#3
[math]7+8=?[/math]
#4
[math]-11+4=?[/math]
#5
[math]3+\left(-9\right)=?[/math]
#6
[math]-5+9=?[/math]
#7
[math]11+\left(-5\right)=?[/math]