9th Grade · Week 1 of 36 · Math
Variables, expressions, properties of real numbers
1. Hook
- Read (or listen to) what you’re learning. Don’t jump to the quiz.
- Walk the worked example. Then use the interactive lab on this page.
- Guided set → independent set → mastery check → teach-back.
- If you write a paper, stay on campus: Citation Helper, Source Library, Paper Studio.
This is self-paced homeschool on Life Academy. Everything you need is on this page.
Is 3(x + 7) the same as 3x + 7? Prove it with a property, then check with x = 2.
Then: lab → guided → quiz → teach it back. The lab is the lesson, not a decoration.
2. Teach
Algebra is legal moves you can defend. Today's job: Variables, expressions, properties of real numbers.
Standards alignment: CCSS.MATH.CONTENT.HSN (domain-level; works with any state’s standards)
STEM this week is Variables, expressions, properties of real numbers: units, a model, and a check another student could repeat.
- 3(x + 7) = 3x + 21.
- A variable stands for a number.
- Check by substituting a number.
This week's algebra skill is Variables, expressions, properties of real numbers — do that job, not last week's job.
Legal move example: 3(x + 7) = 3x + 21. Property: distributive. Check x=2: left 3(2+7)=27; right 27. Match = honest.
A variable is a blank for a number. You do not get to skip the check because the letters look official.
Now apply the same honesty to the title: write one equation that is actually about Variables, expressions, properties of real numbers, plug in a number, and say whether the units still make sense.
- Name the week's skill: Variables, expressions, properties of real numbers.
- Distribute if needed: 3(x + 7) = 3x + 21 because a(b+c)=ab+ac.
- Write the property next to the rewrite.
- Check x=2. Left 3(2+7)=27. Right 27. They must match.
Expand 3(x + 7) with the distributive property. Then substitute x=2 and check both sides. Then say in one sentence how this week's title (Variables, expressions, properties of real numbers) uses that move.
3(x+7)=3x+7 — distributing to only one term — or ignoring this week's actual title.
Science formulas, a shop profit line, and code all use variables you must justify.
No classroom teacher today — this page is the lesson. Follow the how-to, then the lab, then the quiz. Follow Lesson Studio, then the lab, then the quiz. Open Transcripts for credits and grades.
Interactive lab (on this page)
Change one variable. Record what happened. This model is the lab — not an off-site sim.
Your work — type it here
Type the answer. Then tap Check my work. This is the assignment — not optional reading.
3. Guided practice
Try these with me — type the missing word, then check.
Reveal the thinking
Legal move, then substitute a number. Both sides must match.
4. Independent practice
Work the set. Check when finished — this is practice (mastery quiz is next).
5. Mastery check
Scored quiz — results save to your gradebook.
Show the math — don't only tap a letter
The lab is the worked example you can move. Then the quiz checks that you own Variables, expressions, properties of real numbers.
Research Desk · Transcripts · Gradebook
Honest limit: We did not film a custom movie for every core lesson. The teach-back, the on-page lab, and the campus library are the curriculum. The teach-back, the on-page lab, and Lesson Studio are the lesson.
6. Reflection / teach-back
Teach-back: Explain Variables, expressions, properties of real numbers in your own words. Give one example and name the usual mistake.