Model and guided practice
Equivalent ratios — learn
Equivalent ratios — learn · page 1 of 2
Before scaling: what does 3:5 mean?
In this lesson, 3:5 means 3 star stickers for every 5 circle stickers. In this stars:circles ratio, the first number counts stars and the second counts circles. For any ratio, keep the order of its named quantities. One complete group has 3 stars and 5 circles. Two complete groups have 6 stars and 10 circles. You may draw labeled groups instead of using counters. Changing the number of complete groups keeps the stars-to-circles relationship.
Teacher model: two complete groups
A pattern uses 3 star stickers for every 5 circle stickers. It needs 6 stars. How many circles keep the same relationship?
Complete groups | Stars | Circles |
|---|---|---|
1 | 3 | 5 |
2 | 6 | 10 |
Think aloud: Six stars is two groups of three stars. Each group needs five circles, so two groups need ten circles. I changed the number of complete groups, not the match between stars and circles.
Contrast: The proposal 6 stars and 8 circles adds 3 to both original counts. It does not make two complete 3-and-5 groups. Adding another complete group of 3 stars and 5 circles is valid; adding the same amount to unequal parts is the problem here.
Worked example
Watch the complete-group model for 3 stars for every 5 circles. Explain why 6:10 keeps the relationship and 6:8 does not.
Mentor Teaching · Copy edition October 1, 2026
Equivalent ratios — guided practice
Equivalent ratios — guided practice · page 2 of 2
Guided task 1
A pattern has 3 stars for every 5 circles. If it has 9 stars, how many circles keep the relationship? Show groups or a table.
Guided task 2
The same pattern has 20 circles. How many stars keep the relationship? Explain starting with the circles.
Guided task 3
Which pairs keep 3 stars for every 5 circles: 6:10, 6:8, 9:15, 12:20? Explain one pair that works and why 6:8 does not.
Mentor Teaching · Copy edition October 1, 2026