Solve Real-World Problems with All Four Operations on Rational Numbers

Students solve real-world and mathematical problems involving addition, subtraction, multiplication, and division of rational numbers including integers, fractions, and decimals with any sign. They interpret solutions in context and check for reasonableness.

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Grade 7 · The Number System · question 1 of 3

0 of 20

20 rungs. A star at the top.

4 × 0.5 =

How it is taught

0:00 of 3:36

Sharing a debt splits a negative amount equally.

Each person's share keeps the negative sign.

Read it: A story on the number line

The temperature was −6°C and rose 10°C. Start at −6 on the line and hop 10 to the right: −6 + 10 = 4, so the new temperature is 4°C.

Find where the story starts, and mark it on the line.
Make each change a hop: a rise to the right, a drop to the left.
Read where the last hop lands. For the change between two readings, hop from the first reading to the second, and read the hop.

A number line puts every value in order, below 0 as well as above it.

A rise adds a positive number, so it moves right; a drop adds a negative number, so it moves left.

The same change made again and again is equal hops, so it can be multiplied: the number of times × the change.

Start where the story starts: a rise hops right, a drop hops left, and the answer is where the hops land.

Hopping the wrong way for a rise: −6 − 10 = −16.

A rise of 10 hops 10 to the right: −6 + 10 = 4.

The temperature was −2°C and dropped 9°C. What is the new temperature in °C? — −11. Start at −2 and hop 9 to the left: −2 − 9 = −11.

Temperature: −3.5°F + (4 × 2.5°F)

At 6 a.m. it was negative three point five degrees. Each hour it warms up by two and a half degrees. What's the temperature four hours later?

Two operations hide in this story. First we'll multiply to find the total rise, then we'll add it to our starting temperature.

Step one: four hours, each rising two and a half degrees. That's four times two point five.

Four times two point five is ten. So the temperature rose ten degrees in all.

Step two: start at negative three point five, then add ten. Let's use a number line.

Here's where we begin — negative three point five, just left of zero.

Now we hop ten units to the right because the temperature went up by ten.

Grade 7 · A cold morning warming up

We land on positive six point five. So negative three point five plus ten equals six point five.

Does this make sense? We started below zero and warmed up a lot, so a positive answer feels right.

At ten a.m. it's six point five degrees. Real-world math, solved!

What you see

While they climb, your page writes one true line to ask about tonight, and a short note each Sunday.

MayaGrade 3 · Mathematics

Did you know?

A chessboard has 64 squares — share them out between the 8 rows and each row holds exactly 8.

Today’s goal: 1 star — one skill mastered, every rung of its ladder climbed
Climbing now: Divide within 100

An example student.

MayaGrade 3 · Mathematics

Maya earned 2 stars this week — Interpret multiplication as equal groups, which took 6 answers over 3 days before its star landed 3 days ago and Multiply by 6, 7, 8 and 9. Next up: Divide within 100.

An example week.

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