Math Supplement

[happynurse]

Any good, easy-to-implement resources to help explain and solidify fractions, decimals, and percents? This would be for a 4th grader doing Saxon 5/4 who is a bit math resistant. Thanks!

[SilverMoon]

The Key to ____ series could fit that need. Each level has ten small workbooks that start with super easy comprehension exercises and build up from there. 

[PeterPan]

2 hours ago, happynurse said:

Any good, easy-to-implement resources to help explain and solidify fractions, decimals, and percents? This would be for a 4th grader doing Saxon 5/4 who is a bit math resistant. Thanks!

We did this workbook around that age https://payhip.com/b/3fCN  and it was a fun, gentle, discovery-based approach to fractions. Super easy then to convert to written skills. If you don't like that workbook, something else from Didax might suit.

[HomeAgain]

We liked Fraction Formula.  It's about $20, I think, and we changed the rules as he got more proficient: removing the 1/2 cards, requiring the work to be proven, playing all cards in hand...it's really good at showing the relationships between fraction pieces.

I was reminded this morning in my Facebook Memories of a fractions ->decimals lesson we did with money.  It was an easy way to look at multiplication and converting from one to the other.  I can write it out or link the video if you're interested.

Percent has not really been an issue here.  Since we always highlight the word CENT, it's easy to think of it as a fraction (decimal or otherwise) and do the work that way.

[mathmarm]

What about fractions/decimals/percents do you want to reinforce and cement?

For Fractions:

The best way to actually understand fractions is to experience them meaningfully. A few weeks of hands on work can lay a foundation that seamlessly bleeds into an understanding that prevents fractions from becoming an arbitrary number-stew that kinda-has-a-pattern to them, that kids can never quite latch onto.

For non-decimal fractions we use a group of say, 144 small items (such as lima beans) and work on splitting the groups into different fractions.

The kids should already be comfortable with the words factor(both noun and verb), multiple, and fraction. If not, teach those words first. Kids will need to actively know and use those terms correctly.

So, we start with 144 and divide the pile into,  1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12. We note that there are no 1/5s, 1/7s, 1/10s, or 1/11th of this particular pile, and that's because 144 is not a multiple of 5, 7, 10 or 11.

Then we hone in on one of the fractions. So, let's say that we're looking at 1/6 of 144, we see that 24 is 1/6 of 144. So we can calculate 2-sixths, 3-sixths, 4-sixths, 5-sixths, and 6-sixths. We can also predict and calculate how many beans it would take to make 7-sixths, 8-sixths, 9-sixths, etc.. (fraction of a quantity)

We can compare the 2-sixths and notice it's the same amount as 1/3, 3-sixths is the same amount as 1/2. (Equivalent fractions)

We can look at 6ths on a number line (we use a single sheet of paper as the unit and divide them into 6ths, we use a few sheets of paper so that we have multiple units) and we look at how6ths compare to halves and thirds on the number line.

Rinse and repeat.

The commercial manipulatives that we like and use are c-rods and fraction-overlays. As we're working with quantities of beans, we can represent the relationship in the c-rods and keep that visual summary connecting back to whatever specific quantity  they're working on. Fraction over lays are nice for seeing those equivalent fractions, though fraction over lays may have a very short use-life.

After a a few weeks ours kids have been able to see very quickly what a fraction of a particular fraction of a particular quantity is, so this manipulative heavy phase only lasts for a few weeks, but it's been so worth it to us to do it this way.

For Decimals

For Decimals we treat them just like base-ten, place-value units. Our kids read and write tenths, hundredths, and thousandths, as a part of their daily math work. They learn to decompose and compose them just like units, tens and hundreds, They learn to compute them as a part of base-10 calculations so for them it's little different. (We compute left to right in steps) The only differences are in the way you read them, we dont say each period and the way we write them we don't put a comma or any demarcation between periods. Instead you read the entire number after the decimal point and say that last place value.

So 3.12466

is 3 and 12 thousand, 466 hundred-thousandths.

They already know the rules for adding and subtracting so a calculation like

4.2 - 2.8 is read 42-tenths minus 28-tenths, so subtract 20-tenths, then subtract 8-tenths.

42 - 20 - 8

22 - 8 | (or -2, -6, if you prefer)

14

14-tenths, so 1.4

They also multiply and divide fractions the same way that they do base-10 whole numbers. So, I don't have a suggestion for decimals other than "Teach base-10 well and decimals are already well-taught"