Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Opposite quantities cancel each other out. A deposit of $15 and a withdrawal of $15 leave a balance unchanged, and climbing 8 feet then dropping 8 feet puts you back where you began. Seventh graders build on that idea to add and subtract every kind of rational number: positive and negative integers, fractions and decimals.
On a number line, p + q means start at p and move |q| units, to the right if q is positive and to the left if it is negative. Subtraction is then defined as adding the opposite, so p - q is the same as p + (-q), which explains why 5 - (-3) = 8. The same picture shows that the distance between two numbers is the absolute value of their difference, so -4 and 9 are 13 units apart. Students finish by using properties such as commutativity and associativity to regroup terms and make calculations with signed numbers easier, and by describing what a sum like -12 + 5 means in a real situation such as elevation or temperature.
That rule belongs to multiplication. For -7 + (-7) both moves go left, giving -14. Asking students to sketch the moves on a number line separates the two rules.
Students expect any subtraction to go down, so they write 5 - (-3) = 2. Rewriting it as 5 + 3 shows the answer is 8, and a temperature story (the low went from -3 to 5) confirms it.
In -8 + 3, some students find 8 - 3 = 5 and forget the sign. The result takes the sign of the number farther from zero, so the answer is -5.
Computing -4 - 9 = -13 and calling that the distance mixes up difference and distance. Distance is the absolute value, 13.
At 6 a.m. the temperature was -4.5°F. By noon it had risen 7.25°F. What was the noon temperature, and how many degrees apart are -3°F and 5°F?
Answer: The noon temperature was 2.75°F, and -3°F and 5°F are 8 degrees apart.
Two-color counters (zero pairs) and vertical number lines such as thermometers and elevators give students two complementary models. Counters show why a number and its opposite make zero; the number line shows direction and distance. Use both before introducing shortcut rules.
Assessment questions frequently ask students to match an expression to a number line diagram or to interpret a sum in context, so ask for a sentence of explanation alongside each computed answer.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: -5
Start at -8 and move 3 to the right. You land on -5.
Answer: 3.5
Subtracting -6 is the same as adding 6: -2.5 + 6 = 3.5.
Answer: C) -7 + 7
-7 and 7 are opposites (additive inverses), so their sum is 0. The other expressions give -14, 7 and -14.
Answer: B) 13
Distance is the absolute value of the difference: |9 - (-4)| = |13| = 13.
Answer: -15 (also accepted: -15 m)
-12 + 5 = -7, then -7 - 8 = -15. She is at -15 m.
Answer: D) -1/4
Write 1/2 as 2/4. Then -3/4 + 2/4 = -1/4. The result is negative because -3/4 is farther from zero.
Answer: -9
Subtracting 9 is the same as adding its opposite, so 5 - 9 = 5 + (-9). Both equal -4.
A full lesson with slides, activities and an exit ticket on adding and subtracting rational numbers, pitched to grade 7 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 7.NS.A.1 with an answer key, ready in about a minute.
Make a worksheet →Turn adding and subtracting rational numbers into a quiz students answer online that marks itself, with a class summary for you.
Build a test →It is the opposite of a number, the number you add to get zero. The additive inverse of 6 is -6, and of -2/3 is 2/3.
Because subtracting is adding the opposite. Taking away -3 is the same as adding 3, so 5 - (-3) = 8.