6th Grade · Week 1 of 36 · Math
Ratios as comparisons; tape diagrams (CPA)
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.
A trail mix has 3 cups of nuts for every 2 cups of raisins. If you see only the bag, how could you draw what "3 to 2" means?
Then: lab → guided → quiz → teach it back. The lab is the lesson, not a decoration.
2. Teach
Understand a ratio as a comparison of two quantities and model ratios with tape diagrams (CCSS 6.RP.A.1).
Standards alignment: CCSS.MATH.CONTENT.6.RP (domain-level; works with any state’s standards)
Engineers mix concrete by ratio (for example 1 part cement : 2 parts sand : 3 parts gravel). A tape diagram shows the parts so you can scale a batch without changing the mix.
- A ratio compares two quantities: 3 to 2, 3:2, or 3/2.
- Order matters: nuts to raisins 3:2 is not raisins to nuts 2:3.
- A tape diagram uses equal-sized boxes, one box per unit of the ratio.
Concrete: put out 3 red blocks and 2 blue blocks. Pictorial: draw 3 boxes labeled N and 2 boxes labeled R, all the same size. Abstract: write N:R = 3:2.
Ratios can be part-to-part (nuts to raisins 3:2) or part-to-whole (nuts to all mix 3:5), because 3 + 2 = 5 boxes in all.
- Problem: nuts to raisins is 3:2 and the bag holds 20 cups total.
- Draw 3 + 2 = 5 equal boxes.
- 20 cups ÷ 5 boxes = 4 cups per box.
- Nuts = 3 × 4 = 12 cups; raisins = 2 × 4 = 8 cups. Check: 12 + 8 = 20.
A class has 4 boys for every 5 girls and 27 students. Draw a tape diagram and find the number of girls.
Reversing the order of the ratio, or dividing the total by one part instead of by the total number of boxes.
Recipes, paint mixes, and sports records (wins to losses) are all ratios.
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.
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
Count the boxes, divide the total by the number of boxes, then multiply by each part.
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 Ratios as comparisons; tape diagrams (CPA).
Classroom · Gradebook · Transcripts
Stay on this page. The studio, the lab, pictures, and Your work are the lesson.
6. Reflection / teach-back
Teach-back: Explain Ratios as comparisons; tape diagrams (CPA) in your own words. Give one example and name the usual mistake.