Ratios, they seem to be a problem. The students are having trouble connecting ratios to their equivalents. The ratio 24:36 can be reduce (very similar to reducing fractions), by dividing each side by the same number. 24:36, if I divide each side by 2 equals 12:18. I can divide that again by 2, which gives me 6:9. Now I have to divide by 3 and get 2:3. So the ratio of 24:36 can also be shown as 2:3.
When we added in rate tables and unit rates, the confusion worsened. A rate table simply puts ratios in the form of a table.
Bob's number of books 24 12 4 2
Jill's number of books 36 18 6 3
(Sorry there are no lines around it I'm at home and this computer doesn't cooperate with uploading pictures.) But whatever the ratio is for the first column in the rate table, it stays consistent throughout the table. If Bob had 8 books, Jill would have 12. If Bob had 5 books, Jill would have 7.5 (I know you can't have .5 of a book, but 2x2.5=5, so 3x2.5=7.) The ratio must remain constant.
Then we tackled unit rates. All this means is one of the numbers in the ratio or rate table is one. The problem usually tells which number should be one. With Bob and Jill and their 2:3 ratio of books, the unit rate for Bob is 1:1.5. Jill's unit rate would be 1:2/3.
I hope this helps. I'll try to get something posted sooner for our next adventure...absolute value!
When we added in rate tables and unit rates, the confusion worsened. A rate table simply puts ratios in the form of a table.
Bob's number of books 24 12 4 2
Jill's number of books 36 18 6 3
(Sorry there are no lines around it I'm at home and this computer doesn't cooperate with uploading pictures.) But whatever the ratio is for the first column in the rate table, it stays consistent throughout the table. If Bob had 8 books, Jill would have 12. If Bob had 5 books, Jill would have 7.5 (I know you can't have .5 of a book, but 2x2.5=5, so 3x2.5=7.) The ratio must remain constant.
Then we tackled unit rates. All this means is one of the numbers in the ratio or rate table is one. The problem usually tells which number should be one. With Bob and Jill and their 2:3 ratio of books, the unit rate for Bob is 1:1.5. Jill's unit rate would be 1:2/3.
I hope this helps. I'll try to get something posted sooner for our next adventure...absolute value!