What do you remember?
Write two things you remember from last lesson in Math. No peeking: just what's in your head.
- Expand brackets: box it: the outside number on the side; times it by each part inside; add the parts, signs and all.
- Expand brackets: box it: the outside number on the side; times it by each part inside; add the parts, signs and all.
- Expand brackets: box it: the outside number on the side; times it by each part inside; add the parts, signs and all.
- Expand brackets: box it: the outside number on the side; times it by each part inside; add the parts, signs and all.
- Expand brackets: box it: the outside number on the side; times it by each part inside; add the parts, signs and all.
Anything you missed? That's the bit to hold on to today.
Make your first call
At camp you keep the catch in a notebook: b is one bass and t is one trout. By evening the page says 3b + 2t + 5b.
How would you write the day's catch shorter? What can you join, and what has to stay apart?
Saved. You'll come back to this at the end.
Count the same kind
Today's method is new: Collect like terms. A term is a number stuck to a letter, like 3x. Terms with the same letter part are like terms, and they join: 3x + 5x = 8x, the same way 3 bass + 5 bass = 8 bass.
Terms that aren't alike stay apart. 3x + 4 is already as short as it gets. To test any answer, put the same number in for x before and after, using 2 or 3 and never 0 or 1. If the two come out different, something slipped.
There are four short films, each with a hands-on piece and a quick check. Film 4 puts the method to work on an equation with brackets, the kind that tripped you up in Lesson 22. Then there's one problem to do on your own.
Like terms: the same letter part
Add the numbers, keep the letter
You're counting x's: 3 of them and 5 more makes 8 of them. The letter stays x, never x2, because nothing got multiplied. A lone y counts as 1y, so 4y + y = 5y.
Use it right away
7x + 2x = ?
A friend says 4y + 5y = 9y². Use fish, or anything you'd count, to explain in your own words why the answer is 9y.
Unlike terms stay apart
Put Kyle to the test
Kyle shortens 5x + 2 to 7x. You test both with x = 3. What do you find?
Use it right away
Collect the like terms in 4x + 3 + 2x.
Why is x = 1 a poor number for checking whether 2x + 6 equals 8x? Pick a better number and show what it proves.
The sign goes with its term
Right or slip?
Each one collects like terms. Watch which term owns each minus. Sort them.
Use it right away
Collect the like terms in 8x − 3x + 2.
In 4x + 9 − 6x, which term owns the minus? Collect it, then test your answer with x = 2.
Brackets in an equation: open, collect, solve
Open, collect, then hunt for x
The left side is a(x + b) + cx. Slide the outside number, the number inside, the extra x's, and a value for x. Watch the collected form and the slip version.
Predict first: 2(x + 4) + 3x collects to 5x + 8. What happens to the number part if you change the outside 2 to a 3?
Now move the sliders and see.
- Brackets first and opened-and-collected always give the same number. That's why putting x back in checks your work.
- The slip row only agrees when the outside number is 1. Any bigger and it drifts off, just like 2x + 4 did in Lesson 22.
- The number in front of x is the outside number plus the extra x's.
Use it right away
Remember Lesson 22's problem, 4(x − 3) = 20? Which row comes next, with the brackets opened?
Find x in 2(x + 5) + x = 19. Give each move a row of its own, then prove your x works.
Your turn, no help
Your turn on your own. Choose the method, then type the shortest form (like 3x + 5).
One of these comes from earlier lessons, mixed in. For each one, decide which idea it needs before you answer.
- Find the terms with the same letter
- Add their numbers, signs and all
- Leave the other terms as they are
- Find the terms with the same letter
- Add their numbers, signs and all
- Leave the other terms as they are
Only like terms join: 3x + 4 stays 3x + 4, never 7x.
- 5x + 2 − 3x + 4
- About right? A whale is about 1.5 × 108 g and a mouse about 2 × 101 g. Is the whale about 103, 107 or 109 times heavier? (type the power)
You answered both of these in the practice above. They look alike. For each one, write what you did first, and the word or sign in the question that told you to do that.
Back to your first answer
Before today, what would you have done with 6x + 5 − 2x? What do you do now, and how would you catch a slip?
In four lines
- Collect like terms: find the terms with the same letter; add their numbers, signs and all; leave the other terms as they are.
- Collect like terms: find the terms with the same letter; add their numbers, signs and all; leave the other terms as they are.
- Collect like terms: find the terms with the same letter; add their numbers, signs and all; leave the other terms as they are.
- Collect like terms: find the terms with the same letter; add their numbers, signs and all; leave the other terms as they are.
Test yourself
Answer in your head first, then tap the card.
After their kinds
God made the animals “according to their kinds” (Genesis 1:25). Bass stay bass and trout stay trout. Like terms work the same way: join what is the same kind, and keep the rest apart.
What today showed
- Your work
- Complete the lesson to see your record here.
- Standards
- 7.EE.1: Apply properties of operations to add, subtract, factor and expand linear expressions
- 6.EE.3: Apply the properties of operations to generate equivalent expressions
- 6.EE.4: Identify when two expressions are equivalent
- 8.EE.7b: Solve linear equations that need expanding brackets and collecting like terms
- MP.7: Look for and make use of structure