A mixture uses two blue counters for every three yellow counters. To make twice as much, a learner writes four blue and five yellow. The numbers have both increased by two, but the relationship has changed. A ratio table makes that mistake easier to see.
NRICH’s discussion of ratio and proportion explores how these ideas describe relationships between quantities. For a first practical lesson, repeated groups provide a concrete route into that relationship.
Build the rows before naming the rule
Place two blue counters beside three yellow ones. Make a second identical group, then count the totals: four blue and six yellow. Three groups give six blue and nine yellow. Record each pair on one line, with clear column headings.
Ask what happened to both quantities when the number of groups doubled. Each was multiplied by two. That is different from adding two to each original quantity. The physical groups give the learner evidence for the multiplication, rather than a rule to memorise without a reason.
Use a missing entry as a question
Now write a row with eight blue counters and leave the yellow quantity blank. Eight blue represents four copies of the original two-blue group, so the matching yellow quantity is four copies of three: twelve. Invite the learner to explain the number of groups before stating the answer.
Keep part-to-part and part-to-whole comparisons distinct. In the original group, blue to yellow is two to three, while blue to all counters is two to five. Those statements concern the same objects but compare different quantities.
Try a deliberately incorrect row, such as six blue and eight yellow, and ask how it could be checked. Returning to equal groups is often more revealing than announcing that the answer is wrong.
Once the relationship is secure, remove the counters and use the table alone. Later, connect it to a drawing, fraction or graph as appropriate. The table’s purpose is not to fill a page with calculations; it is to keep one relationship visible while the scale changes.