Manipulatives &/or hands-on ideas for rounding off & equivalent fractions

[Earthmerlin]

Hi there. I'm in need of ideas to teach both rounding- off & equivalent fractions that use manipulatives. I'd like to stick to concrete examples & visualizations or now--so anything that's hands-on is preferable. Many thanks!

[Cake and Pi]

Equivalent fractions -- like what decimal equals suchnsucha fraction?  Or fraction A/B equals fraction C/D?  For you might like a fraction chart or equivalency cubes for the smaller denominators.  There are also flip charts.

[Earthmerlin]

Equivalent fractions -- like what decimal equals suchnsucha fraction? Or fraction A/B equals fraction C/D? For you might like a fraction chart or equivalency cubes for the smaller denominators. There are also flip charts.

Yes, thanks, I like these ideas. I'm looking for cheaper manipulatives though--perhaps using everyday materials? I need rounding-up/down ideas & equivalent fractions ideas--i.e., 3/6 = 1/2.

[vaquitita]

For the equivalent fractions, what if you used six small toys -3 cars and 3 animals- and said I have 6 toys, 3 of them are cars, so 3/6 are cars, but I could also say half of them are cars. Something like that. Or cut two circles out of paper and cut one in half and one in sixths and let them place 3/6 on top of the 1/2?

 

For rounding ideas... Singapore uses a number line which works well. If you draw your own then you can have the whole tens or hundreds or whatever you are rounding to written larger or bolder. Have them point to 28 on the number line, then find the nearest whole tens (20&30) ask which one 28 is closer to. It is visibly apparent this way. Start with numbers closer to a whole ten first and after they get the idea then talk about 5.

[alisha]

I saw an idea for rounding once, where you draw a hill with 5 at the top and 1 and 10 on either side, and pretend a car is going up the hill. If it goes to 3, and you let go, it rolls back down to 1, and if you go to 7 and let go, it will roll to 10. Make sense (if not, I saw it on pinterest, you could just search homeschool rounding or something like that).

[Monica_in_Switzerland]

For fractions, easy options are just to draw fractions on a white board- we do this almost exclusively because it's easier than sorting through all the fiddly little pieces of a fraction circles set.  But you can easily do homemade fraction puzzle pieces too.  

 

I love the car-on-the-hill rounding idea!

[kateingr]

For equivalent fractions, try using simple hand drawn squares. Use vertical lines to subdivide the square to match the denominator of the simplest-form fraction, and shade the rectangles you make to match the numerator. Then, use horizontal lines to divide the square to match the denominator of the other fraction. 

 

The beauty of cutting squares like this is that it helps show why we multiply both the numerator and denominator by the same number to find equivalent fractions: the shaded rectangles (which represent the numerator) and the total number of rectangles (which represent the denominator) are being cut by the same lines, so they increase by the same factor. 

 

Here's a quick sketch I did to illustrate. Hope it makes sense! 

 

 

[Earthmerlin]

I truly appreciate all the ideas above & am using most already. Thanks!