Equivalent Fractions on a Multiplication Chart

There's no getting around it, fifth grade math can be really challenging- especially for kids that are still struggling to understand the foundational skills. I have had so many kiddos over the years that could not master adding and subtracting fractions with unlike denominators just because they did not know their math multiplication facts. Math facts are super important, but as a teacher I always felt it was my duty to find a way to help them understand the more abstract concept of equivalent fractions. So, I started using multiplication charts to help my struggling learners understand and create equivalent fractions- but maybe not in the way you are thinking.

We all know that kids who haven't memorized their math facts benefit from multiplication charts. That is no surprise! The process for using a multiplication chart to find equivalent fractions is time consuming, though. You have to find the correct product for 2 numerators and 2 denominators- that is 4 separate math problems to solve before you can even begin to solve the problem. That is a challenge for kids with low attention spans, processing speed issues, or even just kids who are easily distracted. Instead, I have my kiddos use the multiplication chart as a reference sheet for equivalent fractions for benchmark fractions.

If you look at the chart, you can use the factors listed on the left hand side as the numerator and denominator. In my example above, the rows colored red show fractions that are equivalent to 1/2: 2/4, 3/6, etc. The rows that are colored blue show fractions that are equivalent to 3/4, yellow shows fractions equivalent to 5/6, and so on. I train my kids to find the benchmark fraction they are looking for, and then look at all the equivalent fractions shown for the original fraction. We talk about why this works, too, which is an incredibly important part of understanding so this doesn't become just a "trick" that they will memorize without any value or meaning behind it. Since both the numerator and denominator are multiplied by the same number, it creates an equivalent fraction. To deeper understanding for all of my kiddos, we talk about the identify property of multiplication and the fact that it relates to all numbers- fractions included! Since you are multiplying both the numerator and denominator by the same number, for example 2, that is the same as multiplying the whole fraction by 2/2, or 1 whole. 

In the past, I have printed a blackline box on cardstock to help kids track the fractions. The guide works to help kids with tracking issues to follow the equivalent fractions across the page. It also helps students with focus or attention trouble stay on task with a reduced amount of visual "clutter." On the colored multiplication chart, I like to use a white guide and on a white multiplication chart I like to use colored cardstock.

If you want to give this idea a shot, I've created a freebie with a blank multiplication chart, a color coded chart, and several variations of those. The freebie also includes a template to cut the paper guides to help students track the fractions across the page!  To download it, click here.

Calendar time in the upper grades

Calendar time is well known among the younger grade teachers. It's a time tested tradition- the kiddos gather at the carpet,  talk about the date, days of the week, months, weather, etc. It's a great opportunity to focus the kids and get them ready for their day. By the upper grades, the kids are past the point where they would benefit from this kind of calendar time. They know the days of the week and months of the year, so it is just no longer needed. As an upper grade teacher, though, I know that my kiddos still need a focus activity at the beginning of the day. They need to do something to get them into "learning mode" - especially during the crazy days leading up to Christmas vacation! As I was thinking about this, I was also receiving training on the PARCC test, which my district will be taking this year. That's right- straight up taking the test. Not optional, not piloting, not "testing it out". It counts for us. I noticed that the fifth grade math practice test is mainly fractions. This got my gears turning- I decided to link fraction practice with my new morning focus activity- calendar time!

Don't mind the messy writing- I let a kiddo fill it in each morning!

Every afternoon before we leave, I have a student post the date for the next day using this format:

Today is (date). 

It is the number day of school out of 180.

When the kiddos come in each morning, they check out the morning message and make a fraction. Easy enough, right? Then, they simplify the fraction. After that, they convert it into a decimal (rounded to the nearest hundredth because we have not yet learned about repeating decimals). Then, they convert it into a percentage as a bit of enrichment. After that, they figure out how many days are left of school and repeat.

I love this for so many reasons. First, it reinforces core concepts. The kids are expressing their understanding of fractions by creating a fraction using the numbers given. They are simplifying the fractions (though not always successfully, especially with large or uncommon numbers). Converting the fraction to a decimal reinforces decimal/fraction relationship knowledge, and also helps to reinforce the idea of the fraction bar representing division. The percentage is a bit of enrichment for the kiddos as it is a sixth grade concept. 

Another reason I love this is because it gives every student a place to be successful. The struggling kiddos can make the fractions using the numbers given and successfully compute the days remaining with subtraction. They can also feel successful as they make the second fraction with the number they found by subtracting. Typical students can simplify most of the fractions, and convert most of the fractions to decimals. Advanced students can convert the more difficult fractions to decimals and then convert those to percentages. 

After the kiddos have the chance to complete the work, we talk about it for a few minutes during "calendar time." I go over the math, and then let one student copy over the numbers to the board. After that, we've settled in and are ready to tackle our day.

This could be applied at other levels, as well. Sixth and seventh grade students could create a ratio. All upper elementary students could write equations using variables to show how to calculate the numbers of days remaining. I'm sure that there are even applications at the high school level as  "do now" type of activity. 

Do you use calendar time in your upper elementary classroom? If so, I'd love to hear about it!

March Madness and a fraction dash!

I'm about to embark upon my very own version of March Madness. Now, usually March Madness has a fun and exciting connotation- but not my version! Why, you ask? Well… it’s about to be the busiest month of my life. March happens to be the only winter month without a vacation. There is a long weekend, but it's not until the very end of the month for Good Friday. This month I will (of course) have my normal teaching responsibilities, as well as the big cheerleading game for the girls I coach, the school auction to raise money for technology, title one tutoring after school twice a week, and the last chance state-testing push. To just add to the fun, I also have a semester long state graduate course, 3 one credit educator professional development graduate courses, and a creative composition photography course- which I took "for fun." Ahh! I don't know how I will get through this.


A couple weeks ago, the teacher in the room next door retired. She was such a sweet woman, and I will miss her! She’s already off to finish the winter in Florida. So jealous! The girl who is finishing out the year for her is great, though. She is around my age, and has a similar teaching style to me. On Friday, we decided to open the wall up between our classrooms and have a “fun Friday” activity. We chose to do play the “Equivalent Fraction Dash” game I found over at Math Coach’s Corner. It was a blast! We mixed our classrooms up and split them into teams. They loved racing through the classroom and trying to beat the other team at finding equivalent fractions.

to the left is the classroom next door, to the right is my classroom. The cinderblock wall is the divider between our rooms. The wall with the fraction dash pocket chart is the collapsible wall between our rooms.

Students racing to finish the game!

 It was loud, a little rowdy, and tiring- but so worth it. The kids had a ton of fun, and they were angels the rest of the day. We told them that if they work hard, they can earn more activities together like this one. So much fun- make sure you check out the game!

Equivalent Fraction name tags

A few weeks ago, I learned a shocking statistic. Fractions are traditionally the weakest area in mathematics in America. In fact, on the 2004 NAEP fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000. True to this statistic, the students in my class have vocalized their fear of fractions repeatedly to me. "They're just hard, Mrs. B!" One girl said to me. Most of the other students nodded in agreement, supporting her statement. I was surprised to find that only three students in the class could correctly describe to me what a "denominator" was beyond "the number on the bottom of a fraction." I took a giant step back from our 5th grade curriculum, and did a few days of fraction intervention. Today, we had "equivalent fraction day." The students all got a name tag with a fraction on it. The students adopted this name for the day. Here is the kicker though- they had to simplify the fraction before they could say it! For instance, my name tag said 33/36, but the students called me Mrs. 11/12. How fun! Once we all received our name tags and simplified our own fractions, the students raced around the room and tried to simplify as many of the fraction names as they could. The student with the most, won some "hoot loot" - our classroom currency. We had a fun day!

Shocking Statistic

Today, I attended a math conference put on by Pearson Education, who presumably invited people from my district since we have recently adopted their elementary math program enVisionMATH. I was surprised and pleased at the amount of real life information and strategies provided. The one thing that stuck with me was the importance of fraction education. Did you know that on the 2004 NAEP fewer than 30% of 17-year-olds correctly translated 0.029 as 29/1000?  Completely shocked and blown away. Clearly our fraction decimal relationship instruction is lacking, as teachers. My personal new goal is to find new ways to address this! More to come...