Sign In
| 12 Theory slides |
| 9 Exercises - Grade E - A |
| Each lesson is meant to take 1-2 classroom sessions |
Here are a few recommended readings before getting started with this lesson.
Outcome | Action |
---|---|
1 | Move 1 step forward |
2 | Move 2 steps backward |
3 | Move 3 steps forward |
4 | Move 4 steps backward |
5 | Move 5 steps backward |
6 | Move 6 steps forward |
The first player to reach 36 is the winner.
Addition and subtraction are two primary operations performed between two or more integers to increase or decrease their values.
Tadeo and Magdalena bought the mystery box by combining their monthly allowances. Tadeo paid $10 out of the total cost of the box and Magdalena paid only $6.
Tadeo and Magdalena take a break from unpacking the box. They are now deciding whether to play soccer or stay in the house to watch a movie in the afternoon. The kids agree that they will stay inside if the weather is colder than 62∘F (degrees Fahrenheit) in the afternoon. The current temperature is 67∘F.
The weather app says the temperature is expected to cool down by 9∘F later in the afternoon. What will the temperature be then?Cool down
suggests a subtraction. Subtract 9 from 67 to find the expected temperature for the afternoon.
Cool downimplies subtraction — in other words, subtracting 9 degrees from the current temperature will give the temperature for later in the afternoon.
Magdalena and Tadeo spend the rest of the day watching a fantastic movie together. The movie is about a dolphin stuck in a net in the ocean. The siblings are intrigued because the main character, a kid like them, wants to save the dolphin. The kid swims 10 feet below sea level, but the dolphin is 7 feet deeper.
The siblings want to figure out how deep the dolphin is below the surface. Help them find the answer.Start by representing the main character's depth as a negative value. The seven feet further down to reach the dolphin is also negative. When adding a negative integer to another integer, change the addition sign to a subtraction sign and the negative integer added to its opposite.
Oh no! Magdalena and Tadeo were distracted by the movie and did not notice that Luna, the family pet, escaped. They must find Luna before their parents get home.
Tadeo and Magdalena live in a third-floor apartment. They decide start their search in the underground parking structure, which is a common place that Luna goes to. She particularly likes the third floor down of the parking structure, Subbasement 3.
Find the given sum or difference of integer numbers. Consider that adding a negative number is the same as subtracting its opposite. In contrast, subtracting a negative integer is the same as adding its opposite.
In this lesson, how to add and subtract integer numbers was explained. Use this information to find the positions of Tadeo's and Magdalena's pieces on the curious board game that came in the mystery box they bought. Begin by looking at the board game.
In this game, players start at 0 and take turns rolling a die 🎲 to move forward or backward based on the outcome of the roll. The rules for each of these outcomes are shown in the table.
Outcome | Action |
---|---|
1 | Move 1 step forward |
2 | Move 2 steps backward |
3 | Move 3 steps forward |
4 | Move 4 steps backward |
5 | Move 5 steps backward |
6 | Move 6 steps forward |
The first player to reach 36 is the winner.
Outcome | Action | Integer |
---|---|---|
3 | Move 3 steps forward | 3 |
5 | Move 5 steps backward | -5 |
1 | Move 1 step forward | 1 |
Outcome | Action | Integer |
---|---|---|
1 | Move 1 step forward | 1 |
1 | Move 1 step forward | 1 |
4 | Move 4 steps backward | -4 |
Find the given sum of integers.
Consider the given sum. 27+ 2 This sum is the addition of a positive integer to another integer. Let's move two units to the right starting from 27 to find the value these two numbers sum up.
The sum of 27 and 2 is 29. 27+ 2=29
Look at the given sum.
33 + ( -5)
In this case, this is a sum of a negative integer to another integer. We must change the positive sign to a subtraction sign and -5 to its opposite 5.
33 + ( -5)
⇕
33 - 5
The result is the subtraction of a positive integer from another integer. Let's move 5 units on a number line to the left starting from 33 to find the result of this subtraction.
The difference is 28, which is also the result of the initial sum. 33 + ( -5)=28 ⇕ 33 - 5=28
Let's look at the last sum.
-11 + ( -6)
This is also a sum of a negative integer to another integer. Let's change the addition sign to a subtraction sign and -6 to its opposite 6.
-11 + ( -6)
⇕
-11 - 6
We have now the subtraction of a positive integer from another integer. Let's find the result of this subtraction on a number line.
The result of this subtraction is -17. This is also the result of the initial sum. -11 + ( -6)=-17 ⇕ -11 - 6=-17
Find the result of the given subtraction of integers.
Consider the given subtraction. 4- 5 We have a subtraction of a positive integer from another integer. We can find the result of this subtraction by moving 5 units to the left on a number line starting from 4.
The result of this subtraction is -1. 4- 5=-1
Look at the given subtraction.
12 - ( -8)
In this case, we are subtracting a negative integer from another integer. We need to change the subtraction sign to an addition sign and -8 to its opposite 8 to perform this subtraction.
12 - ( -8)
⇕
12 + 8
We came to a sum of two positive integers. We can then move 8 units to the right starting from 12 to find the result of this sum.
These values add up to 20, which is also the result of the initial difference. 12 - ( -8)=20 ⇕ 12 + 8=20
Let's look at the last subtraction.
-6 - ( -7)
Again, we have a subtraction of a negative integer from another integer. Let's change the subtraction sign to an addition sign and -7 to its opposite 7.
-6 - ( -7)
⇕
-6 + ( 7)
The subtraction simplifies to an addition of two integers. Let's find this sum.
This sum equals 1, which is the result of the initial subtraction. -6 - ( -7)=1 ⇕ -6 + ( 7)=1
Dominika is practicing sum and subtraction with integers. She did the following procedure for the given sum.
There is a mistake in Dominika's procedure. Which step has the mistake?We need to find the mistake in Dominika's procedure. In step A, she added 12 and 2. These values sum up to 14, which Dominika calculated correctly. 12+2-(-5) ⇓ 14-(-5) After performing this sum, the expression simplifies to a subtraction of a negative integer from another integer. In this case, we must continue simplifying the resulting expression by changing the subtraction sign to an addition sign and -5 to its opposite 5. 14-(-5) ⇕ 14+5 We can see from Dominika's procedure that she correctly changed -5 to its opposite. However, she did not change the subtraction sign to an addition sign. This means that step step B is the one that has the mistake. Let's fix this in Dominika's procedure and find the result of this sum.
Find if the given statement is always, sometimes, or never true.
The sum of two positive integers is positive. |
The sum of an integer and its absolute value is 0. |
Consider the given statement.
The sum of two positive integers is positive.
Let's test some pairs of numbers and find their sum using a number line. That can help us to discover if this statement is always, sometimes, or never true. 3+7 In this case, we move seven units forward starting from 3 to find the sum.
The result of adding these two positive integers is also positive. Let's try with another pair of numbers. 77+5 Again, let's look at this sum on a number line.
The result is also a positive integer. Note that when adding a positive number to another positive, we always move forward starting from the first positive integer. This means that the sum will always be positive when adding two positive integers.
Let's look at the given statement.
The sum of an integer and its absolute value is 0.
We can follow a similar reasoning to find out if this statement is always, sometimes, or never true. Let's begin by considering the sum of a positive integer and its absolute value. 7 + |7| Recall that the absolute value of a positive integer is itself. This means that the absolute value of |7|=7. The previous sum simplifies to a sum of two positive integers. 7 + |7| ⇕ 7 + 7 = 14 In this case, the statement is false. Now, let's consider a negative integer and its absolute value. -3+|-3| We can simplify this sum by recalling that the absolute value of a negative integer is its opposite. The opposite of -3 is 3. -3+|-3| ⇕ -3 + 3 The sum simplifies to the sum of -3 and its opposite. Consider that the sum of an integer and its opposite is 0. -3 + 3 = 0 ⇕ -3+|-3| = 0 We have an example where the statement is false and one when the statement is true. We can then say that the statement is sometimes true.