Lesson 1 of 3
Use substitution and distribution to preserve an expression’s value.
One idea at a time. Try the example, then keep going.
Big ideas · 1 of 8
Big ideas
Do this: Read one idea, then explain it in your own words.
To evaluate an expression, replace each variable with its complete value. Parentheses protect a negative input before applying powers or subtraction.
Calculate grouping and powers before multiplication or division, then addition or subtraction. Work left to right within the same priority.
The distributive property gives . A minus sign outside parentheses multiplies every inside term by −1.
Two expressions are equivalent when they agree at every input where both are defined. One matching example can support a check but cannot prove equivalence.
Step-through
Do this: Step through the example. Predict the next step before revealing it.
Worked example: keep a negative input
Whole picture, 4 steps
4 steps. Tap a number or Show me how it works.
Do this: Cover the next step and try it yourself.
The value is 15.
Do this: Cover the next step and try it yourself.
The distribution and collection of like terms establish equivalence for all real x.
Do this: Explain why the tempting shortcut fails.
Wrong idea: . The factor multiplies every term inside: . Substituting exposes the error because the two proposed forms give 10 and 5.
Worked example
Do this: Try this on paper before opening the worked answer. No online turn-in is needed.
Worked example
Do this: Predict the next step on paper, then compare the worked reasoning.
Watch
Do this: Watch the public lesson, pause to try a step, then return to your practice.
The linked video is free to watch. The creator may offer optional paid resources; they are not needed for this lesson. If YouTube is blocked, use the lesson notes and worked examples here.
Ready when you are.
Activity 1 of 6 · 0 of 6 activities done
Flashcards
Do this: Say the answer and a reason before you flip.
Card 1 of 8
0 Know it0 Still learning
The variable receives a specific value.
On the card: Enter or Space flips. Left and Right move. After revealing, 1 marks Still learning and 2 marks Know it. Tab reaches every control.
What does evaluating an expression mean?
Substitute stated values and calculate its value.
What does simplifying an expression mean?
Rewrite it in an equivalent, more usable form.
Which terms are like terms?
Terms with identical variable factors and exponents.
Simplify .
.
Expand −(x−8).
−x+8.
Evaluate .
9.
Evaluate .
−9.
Can one matching input prove two expressions equivalent?
No; equivalence requires all allowed inputs.
True or false
Do this: Choose true or false; explain what would make a false statement correct.
Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Self-test
Do this: Try each problem without a timer. Read the feedback before moving on.
6 questions. One at a time.
Practice, not a grade. No timer. Your best score stays in this browser.
Write it
Do this: Write two or three sentences, then compare with the model.
Start here if it helps: I would first identify...
Your answer is not saved anywhere. It disappears when you leave the page.
Write it
Do this: Write a mathematical argument, then compare its reasoning with the model.
Start here if it helps: My argument starts with...
Your answer is not saved anywhere. It disappears when you leave the page.
Homework · 3 points
Opening your homework…
Practice it: You did 0 of 6 activities.
You decide when you have finished. This is your study progress, not a grade.
Not marked finished yet.
One ready post. Nothing is saved or sent. Make one Classroom assignment for each step you assign, using the points shown below and its own due date. Copy its post and paste it into the assignment's instructions.
Homework
Worth 3 points.
https://gradebridge-beryl.vercel.app/learn/precalculus/essential-review/expressions-and-equivalence#homework
After students turn it in, open Check student work
Download their files from the assignment's Drive folder, then open them in Check student work.
