Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
Official wording from the Common Core State Standards for Mathematics (Β© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
Negative numbers become official in sixth grade, and they arrive through situations students already know. Temperatures can be above or below zero, places can be above or below sea level, a bank account can have deposits and withdrawals, and an electric charge can be positive or negative. In each case the two signs describe quantities that go in opposite directions or have opposite values.
A key part is explaining what zero means in each context. Zero degrees Fahrenheit is just a point on a scale, not 'no temperature'; zero elevation is sea level; a zero balance means owing nothing and having nothing. Students learn to choose which direction counts as positive (usually up, above, gained or deposited) and to represent a situation with a signed number, such as -15 for a dive 15 feet below the surface or +40 for a $40 deposit. Operations with negative numbers wait until seventh grade, so the focus here is meaning and representation.
Zero on a thermometer is a temperature, and zero elevation is sea level. Ask students what zero stands for in each situation.
A loss of 5 yards is -5, but students sometimes write a debt of $20 as +20 because it is an amount. The sign shows direction relative to zero, so a debt is -20.
Students may describe -10 Β°F and 10 Β°F as the same weather. Placing both on a vertical thermometer shows they are 20 degrees apart.
A submarine is 250 feet below sea level. A plane flies 3,000 feet above sea level. Represent both with signed numbers and explain what 0 means.
Answer: Plane: 3000 feet. Submarine: -250 feet. Zero is sea level.
Vertical number lines are the natural representation here: thermometers, elevation charts and building floors with basements. Ask students to invent their own contexts and to state what zero means in each one.
Assessment items usually give a situation and ask for the signed number, or give a signed number and ask for a description. Pairs of opposite situations (gain and loss, deposit and withdrawal) prepare students for 6.NS.C.6.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: D) -12
Below zero is the negative direction, so 12 degrees below zero is -12.
Answer: -7
A loss moves the team backward, the negative direction, so the change is -7 yards.
Answer: B) The account owes nothing and holds nothing
Zero is the point between having money (positive) and owing money (negative).
Answer: -420
The opposite of climbing 420 feet is descending 420 feet, which is -420.
Answer: D) Depositing $25
A deposit increases the balance, which is the positive direction. The other three are decreases or movements below a reference point.
A full lesson with slides, activities and an exit ticket on positive and negative numbers in context, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson βA printable, differentiated worksheet on 6.NS.C.5 with an answer key, ready in about a minute.
Make a worksheet βTurn positive and negative numbers in context into a quiz students answer online that marks itself, with a class summary for you.
Build a test βNot under this standard. 6.NS.C.5 is about meaning and representation. Operations with negative numbers come in grade 7 (7.NS.A.1).
Zero is the reference point that positive and negative values are measured from. Explaining it in context shows that students understand what the sign means.