Today I'm linking up for Secondary Smorgasbord hosted by the ELA Buffet, and Desktop Learning Adventures. Well, it's never really frozen in Arizona, but considering I moved here from Michigan, I would say I am still coming out of the Deep Freeze!
This week's FREE Common Core Math Quiz domains are Number and Operations – Fractions for grades 3-5, Ratios and Proportional Relationships for grades 6-7, and Functions for grade 8. They will be added onto last week's domains in the same document.
Follow the links below the Raffle to download your grade level Quiz! (3-8)
The Raffle Winner from Week 2 is
Marcy Philo, Congratulations!!!
I will be contacting you by email to choose the grade level Assessment Bundle that you would like.
If you didn't win this time, come back next week to try again!
Fractions blocks are essential for teaching those elementary skills like modeling equivalents and performing operations, but I also use them when I teach ratios. Fractions are also ratios! and middle school kids may find this easier to master when they make this visual connection. Once that can visualize a ratio, they can always draw themselves a picture, or use manipulatives when they need to work with ratios.
Here's a fun extension activity comparing fractions and ratios. Ask kids to figure out how many groups of a fraction they will need to make a whole number, and which whole number they will get.
Example: 1/3 x 3 or 1/3, 3 times, will make 1 whole.
2/3 x 3 or 2/3, 3 times, will make 2 wholes, but it is impossible to make one whole? Why not?
What other whole numbers can be made by multiplying 2/3?
4/5 x 5 or 4/5, 5 times, will make 4 wholes… Is it possible to make 1, 2 or 3 wholes? Why not?
Do they see a pattern yet? What is it?
What other fractions will give us this pattern?
Ratios also appear when multiplying and dividing fractions by fractions.
The last few problems in the Modeling Multiplication and Division Fraction Families
project (download the preview problems and answers for free in a word document
) are especially challenging and most of my students got them wrong the first time because they don't know what to look for, or what division of fractions really means.
The Common Core standards ask students to be able to represent multiplication of fractions using a rectangular array, I like this site for online manipulatives, Fractions – Rectangle Multiplication, but I find the fraction blocks can do the same job and it's a different way to understand it.
Example: 1/3 x 1/4 = 1/12 This means 1/3 of 1/4 or 1/4 of 1/3 which is 1/12 either way. (Commutative Property).
Example: 1/3 ÷ 1/4 = 4/3 = 1 1/3 …because 1/4 fits into 1/3 one whole time, and 1/3 of a time.
1/3 divided into fourths means, “How many fourths can fit into 1/3?” What kids have to remember is that the 1/3 and 1/4 have to relate to the same whole. It does not mean 1/3 of 1/4, as in multiplication.
The ratio that exists when dividing 1/3 and 1/4 is 4:3. This can also be thought about as the common factor, 1/12. 4 x 1/12 = 1/3 and 3 x 1/12 = 1/4
The Commutative Property does not apply to division, so when the problem gets reversed, the ratio gets reversed. The ratio that exists when dividing 1/4 and 1/3 is 3:4.
Example: 1/4 ÷ 1/3 = 3/4 …because 1/3 fits into 1/4 three quarters of a time, NOT one whole time.
Whew! This is hard for me to keep track of until I can draw it out and look at it! When kids can see where the 3/4 and 1 1/3 come from based on a drawing, they have another strategy to fall back on when solving problems. The Common Core standards ask a lot of kids; and considering that 5th grade is the first and only year that all four fraction operations are taught, some middle school kids still need time to master and connect these concepts to the 6th-8th grade ratio standards.
Raffle Week 3 – $25 TpT Gift Certificate!
Sometimes you just need something different, so this week's “Happy New School Year” Raffle will be a $25 gift certificate to Teacherspayteachers.com so you can buy almost any resource from any seller you want! The winner will be notified by email and listed in the blog post for the following week.
The easiest way to keep track of the weekly Raffles is by following Mrs. L's Leveled Learning blog on Blog Lovin', by email Newsletter, or by Facebook.
a Rafflecopter giveaway
Click on the links below for this week's Common Core Domains NF and RP!
Each Quiz has one math problem for each Common Core standard in that domain. The number corresponds to the standard number. Each problem has the learning goal stated to help kids focus on the goal and make the connection between the quiz, and their work in the standards.
Check back next week for this week's raffle winner
and the next raffle and quiz domain!