Two trains traveling at different speeds...

Two trains traveling at different speeds...
Two trains leave their stations at exactly the same time...

If you use 1/2 cup of sugar for every 3/4 cup of flour...

Word problems not your thing? Panic strikes when you come across yet another word problem? Starting your first year at teaching Sixth Grade Math and you're stuck on ratios? This blog will explore the secrets of breaking down word problems.

We are going to focus mostly on 6th grade level word problems involving fractions, ratios, rates, percentages, and some Common Core solution concepts including Tape Diagrams, Double Lines, and other related graphical analysis techniques. I may also explore other math-related territories as the mood strikes me, so let me know if you want to focus on some other aspect or grade level of word problems.

HOW TO USE THIS BLOG: The Blog Posts show up as the most recent ones at the top. However, I would recommend you start with the oldest Posts first and work your way to the most recent as some of the posts build on previous ones. But hey, you're the Teach...so whatever works.

The links on the side of the Blog will connect you to whatever Post you want to work on.

I hope you learn a little, and enjoy it in the process...and feel free to ask questions or offer suggestions/criticisms.

Wednesday, June 25, 2014

4. Answers to Ratio Problems

Ratio Q1:  Three boys can eat 2 pizzas.

The ratio of boys to pizzas is 3:2

The ratio of pizzas to boys is 2:3

These seem kinda obvious, so I am not sure what more to add.  If you have any questions, post a comment and I'll think of something clever.


Ratio Q2:  The ratio of pieces of sausage to pieces of pepperoni on these pizzas is 3:1.

For every   piece of pepperoni there are  3   pieces of sausage.


Ratio Q3:  Classroom #1 has 15 boys to 20 girls, or 15:20.  Break this down to its simplest form:



For Classroom #2, we need to solve for girls.  So flip the ratio so that girls "?" is on top.  In this case, we also flip the 3/4 ratio to 4/3.  So:  ? is to 12 as 4 is to 3.







 Now solve for ?, which is 16 girls in classroom 2.

For boys in classroom 3, describe the ratio with the boys "?" on top, which is now 3/4. So ? is to 12 as 3 is to 4.  Solve for the ?, which is 9 boys in classroom 3.







The final matrix is:











One important check to make sure you got the matrix correct:  The ratio of Boys on top to Girls on the bottom row is 3:4 (there are more girls than boys).  Hence, the top row must always be smaller than the bottom row.  If they are not, then you forgot to flip the ratio, or something.



No comments:

Post a Comment