Equivalent Fractions

Equivalent Fractions by NCTM Illuminations. Use the Square setting. If you get stuck, try copying the picture exactly, then sliding one green slider. After you match the fractions the app generates, try "Build Your Own" with 3/4, 2/5, 1/6, 2/3, 5/8, 4/12, and other fractions of your choice.

Melvin's Make a Match. Match equivalent fractions from pictures, etc. If the pieces look too small, hover over them to see a bigger copy.

Fraction Flag. Choose the proportions to represent some colors in a flag (for example, half one color and half another color), then design a flag that has those proportions. The design is limited to halves and quarters (fourths).

Sizes of Fractions

Dolphin Race (Comparing Fraction Size) is goofy, but it's a crowd favorite among sixth graders. It feels competitive, but gives you time to think, and there are two different levels.

Fractions Ordering Game asks you to place fractions in order of size. If you get some wrong, it gives you another chance to rearrange those. There are three levels of difficulty.

Fraction Game by NCTM Illuminations. Use equivalent fractions and estimation of fraction sizes to "play" fraction cards on fraction number lines. (Read the instructions first.) Play several times. How few cards can you use? What are good strategies to reduce the number of cards you use?

Fraction Feud on Calculation Nation (log in as guest, or at home you can set up an account) is fun for fraction masters who like strategy games. Make a fraction SMALLER or LARGER than the one you’re “jousting” against. Try to figure out which cards are generally best to use or keep for later.

Other Fractions Activities

Sheppard Software Fraction Games include a lot of "Splat" and "Mathman" (Pacman-like) games about improper fractions and mixed numbers, equivalent fractions, adding fractions, subtracting fractions, and a LOT of other choices.

Fractions Activities on NRICH. This British math (they call it "maths") site has a lot of incredibly creative games and lessons, including challenging fractions activities. If fractions are easy for you, go here and explore, and let me know which things are interesting!

IXL Fractions Activities is a for-profit site, but it lets non-members practice a few minutes. The activities are quite repetitive, but you may like them as a sort of quiz/self-check.

Speedway (Adding Fractions) on Math Playground is good mental math practice for adding and reducing fractions, if you're already comfortable with that. Speed is a big part of this one, so make another choice if that stresses you out.

With Fraction/Decimal/Percent Jeopardy and/or Decention, you can quiz yourself on converting between equivalent fractions, decimals, and percentages. Note: in Jeopardy, use "0.3..." for 0.3 with a bar (repeating decimal). I'm not totally crazy about these activities, because I don't think it's useful to think of percents without a context (percent of what?), but it's true that 3 tenths of something is 30% of that thing, so... do it if it works for you.

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As soon as I started seeing information about Hidden Figures last fall, I started wondering if we should have this field trip. The movie sounded almost too good to be true — a fun, feel-good, PG film that brings science, technology, engineering, and math (STEM) and civil rights achievements by Black women in the early 1960s into the light, shows the excitement of the intellectual accomplishments behind the space program, features stellar actors, and puts a mathematician center stage as a heroine — wow! Claire Olberding, Jason Gershuny, Ann Fournier, and Haverty Brown, the other teachers in my professional learning community at school, were also intrigued with the field trip idea and interested in working on it, and the school administrators, the school Site Council, the Equity and Climate and Culture Committees, and every other teacher who heard about it were positive and supportive.

As more previews were posted and early rave reviews came out in the media and from STEM educators, I got more and more eager to have our students see this story of courage and accomplishment. I made my screensaver into the picture of Dorothy Vaughan (Octavia Spencer) and her coworkers marching down the hall, posted about it on Twitter, and got an "I LOVE THIS!!" retweet from one of the actors in the picture (fun!!). The week Hidden Figures came out in local theaters, I showed all my math classes previews and a brief clip of the real mathematician Katherine Johnson (now 98) and told them about my own excitement. One girl had seen it before the regular release date, and had watched the previews enough that she was

It was around this point that my enthusiasm for a whole-school field trip moved to determination, especially when our principal went to see Hidden Figures and became one of the strongest proponents of a whole-school field trip, and when Katie, our school counselor, encouraged me to follow through with planning and generously shared materials, tips, and work from her experience on similar trips. The whole thing took a ton of planning and support: honestly, I might have hesitated more if I had realized how much I was asking from our secretaries Liz and Sheli and from Katie the Counselor, especially. But I could not have asked for a more positive, can-do attitude from the whole community, and it made the whole thing stay fun and inspiring. Just about the entire staff worked on organizing permission forms and payments and sponsorships, even our school nurse, who wouldn't even be at our site that day. For our professional learning community (PLC) one afternoon, Claire Olberding, Jason Gershuny, Principal Locke, and I had one of my favorite school meetings ever, as we brainstormed about curriculum for teachers to use the afternoon of the movie viewing. Staff, students, and parents thanked me so many times for leading this effort that I lost count, and it was so encouraging to know they were happy about it. Even the National Council of Teachers of Mathematics president, Matt Larson, was talking about Hidden Figures on his NCTM blog the same week as our trip!

The day of the trip, I was a little edgy as our large crowd walked to the theater, wondering how it would go, but the kids were in excellent spirits and great fun, and I don't think I heard any complaints on the 3/4 mile walk, even though it rained all the way (our native Portlanders were completely unphased by that). We actually split across two theaters, and it was pretty awe-inspiring to see how many people were there in each. I loved seeing the movie just as much the second time. The kids seemed totally absorbed during the movie, though in our theater they were quieter and more solemn than I expected (except with Octavia Spencer's line to the white supervisor, "I'm sure you believe that."... that got a vocal reaction!). I was delighted and a little relieved when they clapped as the credits rolled. It seemed fitting that the sun unexpectedly came out for our walk back. Everybody seemed happy to have this experience together and I heard such a positive response to the movie from those who had seen it for the first time, both students and adults.

After lunch, we split up into our sixth period classes, and using our PLC's discussion guide which was a lot like this one (I've edited out a few questions that originated elsewhere), we talked through these questions:

- What did you think of the movie? Did you enjoy it?
- What questions or feelings did it leave you with?
- Why do you think we spent school time seeing this movie?
- What does the term “Hidden Figures” refer to?
- In the movie, we saw many times characters were treated unfairly because they were Black. Which three examples stood out most to you?
- What character attributes and/or actions did you admire most about Katherine Johnson (the mathematician), Dorothy Vaughan (the manager who taught herself how to program the computer), and/or Mary Jackson (the engineer)? [I also ended up asking them which was their favorite; as I expected, Mary, played by the glamorous and fun Janelle Monáe, was in the lead, but I was surprised that at least a third of them picked serious, ultra-competent Dorothy Vaughan.]
- In the film, Space Task group director Al Harrison (Kevin Costner) was depicted as a heroic breaker of boundaries when he smashed down the “Colored Women” restroom sign. Unlike many of the dramatic moments in the movie, this incident was entirely made up. In real life, Katherine Johnson herself chose to use the restroom white women used. Why do you think the screenwriter and filmmakers added this incident? Do you think adding this incident improved the movie? Why or why not?
- What was most striking to you about how men treated women in this movie, and how women treated each other? What aspects of how women were treated do you think seem similar to our times, and what seemed different?

- Dorothy Vaughan and her kids were chased out of the library by the security guard (and she pays taxes for libraries!).
- Katherine Johnson's coworkers set up a "Colored" coffee pot for her... and it was empty.
- The bathrooms and drinking fountains were segregated, and the courthouse and bus had "colored seats in back." Separate was NOT equal: the things labeled "colored" were dirtier and cheaper. White people acted like this segregation was right, using words like "your kind".
- Mary Jackson couldn't access the class she needed to because of the segregated night school.
- Katherine Johnson's new coworkers assumed she was the custodian.
- Paul Stafford kept telling Katherine Johnson that computers can't be authors of technical papers. [Actually, I think the way she was restricted to being a computer was more about her being a woman, but it wasn't completely clear.]
- Mrs. Mitchell claimed to Dorothy Vaughan that "I don't have anything against you all," which was obviously false (and even the way she talked about black women as if they weren't people like her was insulting).
- Dorothy Vaughan was doing a supervisor's work, but without the credit or pay.
- When the police officer approached the women by their broken-down car, he assumed they were doing something wrong, and they were scared of what he would do.

I went to the Talent Show full of fondness for my own class around me, the wonderful performers who included my present and past students, and the adults that support them in their arts and in their studies. Da Vinci teachers regularly go so far beyond classroom teaching. Our drama, dance, visual arts, music, and writing teachers do incredible work to bring our students' art to the wider community and bring professionals to the students; math teacher Mz. Daley is one of the Talent Show organizers and a mentor to the student rock band; language arts teacher Ms. Wasson organizes a yearly trip to the Oregon Shakespeare Festival in southern Oregon; our science teachers have kids work on community projects; our social studies teachers have them engage with the broader world as citizens in so many ways; our librarian Ms. Lieberman just spent many lunchtimes and a Saturday with kids doing Oregon Battle of the the Books; the list just goes on and on. I volunteer to assist with some of these events, but usually I feel like my community contributions are limited to my classroom role and General Adult Help. It was inspirational to have my own idea and to be supported and given the freedom to carry it through, which was an experience that makes me appreciate our school and its administration and staff even more. And although it's nothing new for me to get resources and ideas from my online math teacher community, this was yet another time that they helped me create something better than I ever could have on my own.

I was already elated with the entire day, but it got even better when Ms. McMillen thanked me from stage during the Talent Show for organizing it, and the whole school cheered — so sweet! As another teacher said afterwards, "What amazing kiddos we have!!" I am so proud of our kids and our community, and grateful to Hidden Figures that we are all more educated on this story than we were last year. What will happen next with our community discourse on race, gender, workplaces, schools, justice, film, math, science, technology, engineering, heck, the whole world? I don't know, but I can't wait to see where we go.]]>

Try these if you want help knowing how to rewrite fractions with different numerators and denominators, or understanding why 2/3 is the same size as 10/15.

Equivalent Fractions by NCTM Illuminations helps show why some fractions are the same size as others. I recommend using the square model rather than the circle. Try "Build Your Own" with 3/4, 2/5, 1/6, 2/3, 5/8, 4/12, etc. Equivalent Fractions by Mark Weddell is similar.

Melvin's Make a Match could work as a review game after you work with equivalent fractions for a while. (If you hover over a piece in this game, it shows it a little bigger.)

In Fraction Flag, you choose the proportions to represent some colors in a flag (for example, half one color and half another color), then design a flag that has those proportions. The design is limited to halves and quarters (fourths).

Fraction Models (by NCTM Illuminations) is, frankly, somewhat boring, but it's a great way to explore connections between fractions, mixed numbers, decimals, and percents with a visual representation.

Dolphin Race (Comparing Fraction Size) was definitely a crowd favorite among sixth graders in 2015. It feels competitive, but gives you time to think, and there are two different levels.

Fractions Ordering Game asks you to place fractions in order of size. If you get some wrong, it gives you another chance to rearrange those. There are three levels of difficulty.

In Fraction Game by NCTM Illuminations, use equivalent fractions and estimation of fraction sizes to "play" fraction cards on fraction number lines. (Read the instructions first.) Play several times. How few cards can you use? What are good strategies to reduce the number of cards you use?

Sheppard Software Fraction Games include a lot of "Splat" and "Mathman" (Pacman-like) games about improper fractions and mixed numbers, equivalent fractions, adding fractions, subtracting fractions, and a LOT of other choices.

There are some challenging Fractions Activities on NRICH, a British math (they call it "maths") site with a lot of incredibly creative games and lessons.

IXL Fractions Activities is a for-profit site, but it lets non-members practice a few minutes. The activities are quite repetitive, but you may like them as a sort of quiz/self-check.

Speedway (Adding Fractions) on Math Playground is good mental math practice for adding and reducing fractions, if you're already comfortable with that. Speed is a big part of this one.

If you already know about decimals and percents (which we will learn more about later this year), you might like Fraction/Decimal/Percent Jeopardy (quiz yourself on converting between them; use "0.3..." for 0.3 with a bar (repeating decimal)) and/or Decention (finding equivalent fractions, decimals, and percentages).

Missing Multipliers (NRICH): I love these logic puzzles where you have to figure out what factors would give a mixed-up times table with the results inside, sort of Hangman-style. The challenges listed in links at the bottom of the page really are quite challenging!]]>

First, a bit about what factors and multiples are. They're easiest to explain with examples instead of definitions.

- The FACTORS of 15 are 1, 3, 5, and 15, because 1 x 15 = 15 and 3 x 5 = 15. 7 is NOT a factor of 15, because 7 doesn't divide evenly into 15 (you'd have a remainder).
- The MULTIPLES of 8 are 8, 16, 24, 32, 40, etc. (going on forever). That's because 1 x 8 = 8, 2 x 8 = 16, 3 x 8 = 24, and so on.

- Remember multiplication tables?
**Go look at my favorite multiplication table.**Can you tell what's going on there? Great connection to area of rectangles, huh? - Another great way to represent factors is this
**visual illustration of divisor pairs**(which is prettier than it sounds). Select one or more of the factors shown and see what happens to the picture. If you can't tell what's going on, try entering 12 or 18 or 28 in the number box. - Next, check out this
**Composite Number Tree**. "Each number branches from its largest divisor," says the caption. Can you figure out what they mean? (I think it actually would be more correct to say each number branches from its*second*largest divisor.) - Now take a look at the
**number patterns**showing up here on the curves, and move your cursor around to explore. Can you tell what's going on? It may help to notice the "n=" entry at the bottom of the page.

OK, on to the games. These games help you practice multiplication facts online, but remember: if you find a game on this list is stressing you out, or you're just learning how to do some task fast but not actually improving your recall of any new math facts, the game is not making your life easier and maybe you should go do something more fun or thought-provoking! Just make sure to stop and think every once in a while about whether the game is helping with your learning goals or not, and try to check them all out at least a little bit. Anyway, on with the list:

**Multiples Frenzy**at Sheppard Software: You shoot fruit (just go with it) that shows a multiple of your target number. Math concept level: medium. Strategy level: medium. Time pressure: high.**Times Square**at Calculation Nation (where you can click on Guest Pass): Tic-tac-toe with times tables, basically. Math concept level: medium. Strategy level: medium. Time pressure: low.-
**Factor Dazzle**at Calculation Nation (where you can click on Guest Pass): Get points by finding factors, and keep your opponent's score low by giving them numbers without many factors. Can you figure out ahead of time how many points you will get from a certain move? Very similar to NCTM Illuminations' Factor Game but has a little extra fun. Be sure to read the game directions. Math concept level: high. Strategy level: medium. Time pressure: low. **Penguin Jump**and**Swimming Otters**: Crowd favorites, especially for students playing each other. For your 12 x 12 multiplication facts, check your knowledge (and speed) in a competitive way. You can join a game or create your own. If you create a private game, you can play against the computer. You can also make custom settings to play (for instance) only up to 10 x 10. Math concept level: low to medium. Strategy level: low. Time pressure: high.**Sigma Prime**at Mangahigh.com: Shoot the appropriate factors at the invading number ships. Math concept level: medium. Strategy level: medium. Time pressure: high.**KenKen puzzles**: To practice multiplication and division, be sure to select the puzzle type that only has those operations. You can also pick the size and difficulty level that works for you. Click on How to Play if you're not sure how KenKens work. Math concept level: high. Strategy level: high. Time pressure: optional.

At the end of last year I gave my Math 6 classes a survey. The last question was:

So, for you all, these are ALL of their answers, in the order they were submitted. Only the things in italics were changed (for clarity).

- Be awesome
- BRO YOU NEED TO
*CORRECT* - its not as hard as everyone says it is
- Your cool and not to stressed out. Your also not strict.
- she is totally nice
- Work Hard and Have FUN
- Ms.Wright is awesome and the best
- nwqebgyfhgwsbhjmxm bhmsecn bbbbbb
- it is FUN!
- i would tell them that it was fairly easy and fun, but there is 1 activity that is really loud.
- Ms. Wright is a fair teacher who is never too strict, and you will learn alot throughout your 6th grade year.
- Um, I guess... That.... Dont be afraid to share what you think the answer is to the class cause your probs right. And also dont be afraid to ask questions cuz its helpful to know those questions.
- the next year sixth graders gonna learn fun math next year
- zxncg;zkxfjgnb'iSKJD flaserbvgfkajdhge[orjthgajwdufgpaoisnudgoserihgskjhvd aiusyrgkhsebrgiusrhav
- That is fun and you should enjoy it and have fun
- Math isn't as bad as you probably think it is. Enjoy yourself, be creative, and you'll have a cool time!
- Ms. Wright is a great and fun teacher to have one of the best math teahcer ive ever had and when i say that i truly mean it. She taught me so many things and helped me understand in many ways. So if i didnt understand her she would teach it another way but that was only once or twice. In other words she really helps and some people may not like her but i know i do she cares about everyone no matter what they think about her.
- that you should try your best even if you dont know just put the answer that seems right to you
- math is very fun and challenging but u are really going to have fun
- Don't shout you head off, stay calm and collected.
- its pretty fun, mrs Wright is helpful, and gives good hw
- I would say, "You have the amazing opportunity to learn from an amazing mathematician, she is really cool!!!!!!!!!!!!!!!!!!!!! Don't be afraid."
- If you mess up, that's okay! you'll get it!
- it is very fun
- more math games
- Mrs Wright is very nice but may need to challenge a little more
- Ms. Wright is a very good math teacher. She helps students learn in ways that are effective and fun. She treats all students fairly and is very educated in math. She makes math fun and easy to understand.
- You really helped me learn and are super fun.
- your going to love it
- pay atenion every day if you dont you will miss something and have to do more math.
- math is cool
- Mrs Wright is a great teacher and helped me learn a lot in my sixth grade year.
- this is an amazing class work hard and do your best
- shes really nice
- Math class isnt stressful or hard if you pay attention to what the teacher is saying. if you just chat with your friends instead of learning than yes, the class will be difficult. the choice is up to you, however i recommend that you pay attention.
- Please give students who know the material something else to do!
- she is very nice and understands how to talk with others and will help you learn math in a fun way. especially at the end of the year.
- shes very nice and i like her
- nothing
- its a fun class
- try really hard to keep your grade up and make sure you do your homework because that is also helps you learn out of school and then the next day you will correct with Ms.Wrigth
- I don't like much homework and I learn well enough in class.
- julie wright was a great teacher
- Ms. Wright is the best math teacher, and you will learn a lot from being in her class.
- You will love math class with miss. Wright
- shes good
- Ms. Wright is fun
- Meh, she's okay.
- Yes, I would give them a basic outline of your curriculum such as first we had fractions etc.
- To next year 6th graders, Ms.Wright is a nice teacher and if you have a question you shouldn't be scared to ask her because she will help you.
- She is the best math teacher I have EVER HAD!!!! She is helpful, and does not give much homework. Thanks, Ms. Wright!
- It is very nice that the math teachers here are here after school to help you about anything related to math.
- I would tell sixth graders that you are super nice and a great math teacher.
- She is nice and she has a god teaching style.
- Try your best and you'll do well.
- Pay attention, do your work and be on time
- Miss Wright is Awesome
- Ms. Wrights math class is good math class for 6th grade students. Ms. Wright is a very kind person and is also understanding. If you try to the best of your abilities in her class, you will have an awesome first year at da Vinci in math.
- I think that you will learn a lot in Ms. Wrights math class, I know I did. she is a very kind teacher and is very passionate about math. It is also just a lot of fun.
- Ms. Wright is a very kind teacher. Math class was a lot of fun for me, and if you have a open mind, it will be for you too. You will learn a lot in this upcoming year, but remember to do your homework, because it will help you a lot. Good News! Ms. Wright grades homework for effort only, so give it your all, and you will have a lovely grade.
- You'll have a great year. If you're stuck, don't be afraid to ask questions and you will learn so much in your 6th grade year.
- angler fish spermz
- It's not THAT bad.
- TRUST IN LORD MEME AND LISTEN 2 MEES WRIGHT SHEZ REALLY AWESOME AND SHE LIKES SHERLOCK BE HER FREND AND BE MY FREND MY NAME IS EDEN
- DON'T SLACK OFF! IT WILL WHIP YOU IN THE BUTT LATER IN THE YEAR!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
- Actually listen.
- Mrs. Wright is completely over qualified for this job. Use this year to the best of your ability. Despite what television tells you, math can be fun.
- Pay attention and you will do great
- You are a BAWSE!
- It was nice knowin ya little friend, but I´ll see you on the other side. (Insert dead person emoji here)
- good luck, and have fun
- for the sixth graders i would say to focus and try hard
- good luck may have mercy
- do your math.
- I had a lot of fun in this class and I liked how we got to work with the students around us.
- Just do the homework taking 15 mins out of your day is not that big of a deal
- PAY ATTENTION CHILDREN, AND DON'T BE ME.
- I had a blast this year, i met lots of new friends in this class, and I hope you do as well. Ms. Wright is a very great math teacher, and I appreciate everything she has done this year.
- dear god, may you bless there souls
- Ms. Wright is super nice, children, so take her example, and don't become a cannibal like me.

You found the Class Activities Blog post that describes what you are doing on Wednesday, August 31. Great job!

Now do these things in this order:

- Write down "Math website: juliewright.weebly.com" in your planner somewhere you can find it later (near the front is probably best). Double-check the spelling!
- On this website, find the Math 6 Homework and Support page. Look at August 31 to do your homework for today. If you can't figure it out, ask questions!
- Look at the bottom of the Homework and Support page to see which day of the week Ms. Wright is usually available to help with homework after school.
- Finally, go to one of the links under Fun Math and Puzzle Websites. You can explore any of the pages listed. There are many choices! But do NOT go jumping around to pages that aren't listed, even if they have "math" in the name.

Usually, the standard and most frequently taken math sequence after Math 6 is:

- 7th grade: Common Core Math 7
- 8th grade: Common Core Math 8
- 9th grade: first-year Algebra
- 10th grade: Geometry
- 11th grade: second-year Algebra
- 12th grade: various options, such as Statistics or Pre-Calculus

There are various exceptions: for instance, I believe at one Portland high school, students take Geometry before Algebra, and many high school students take two math courses in a year, sometimes over the summer.

In middle school, some students instead take Compacted Math I and II in seventh and eighth grade. Between them, these courses cover all of the Math 7, Math 8, and first-year, high school Algebra material in two years. Students who earn Algebra credit generally take Geometry and second-year Algebra in ninth and tenth grades and further math after that.

Even for some very bright or very conscientious students, Common Core Math is a more appropriate placement than Compacted Math. With the new standards, each level of regular Common Core math has significantly more challenging content than in the past; in fact, Common Core Math 8 contains much of what used to be high school Algebra a few years ago, and each high school class now covers more advanced material as well. Compacted Math classes are fast-moving and require time commitments, academic maturity, and excellent study, classwork, attendance, and revision habits.

Placement in “regular” math class is IN NO WAY a negative statement about a student’s math achievement, ability level, or future level of mathematics study. Many middle schoolers are still building academic skills and habits that will help them achieve through high school, and many have significant commitments outside math class. Common Core Math 7 students can excel as math learners, will be challenged at about the same level as this year, and will be very well prepared for higher math in high school and college, and many of them will continue on with advanced coursework and careers in science, technology, engineering, and math (STEM). We want to avoid rushing students and leaving them with a dread of math or gaps that will cause bigger problems later, when it matters more.

Our main priority is to give every middle school student a solid grounding in mathematical concepts and habits of thought.

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- Anything on the Math You Can See page
- Game About Squares (that's right, there are no instructions!)
- SolveMe mobiles puzzles
- Anything on my Puzzles and Games page (note: the BrainBashers Puzzles link there is new)
- 1001 Math Problems
- Anything else in the Class Activities Blog post below this one or on the Math Links page

## Decimal Practice | Fruit Splat/Place Value Decimals: This game is great practice for thinking about place value in decimals and for adding using mental math. It's designed to have several different levels, and you can play in timed mode or "relaxed" mode. Flower Power: put decimals in order of size -- a nice complicated game (read the directions) Balloon Pop Decimals Level 1 and Balloon Pop Decimals Level 2: Pop the balloons from smallest decimal to largest. If a balloon won't pop, it's because you haven't found the smallest. Score is based on time, but you can ignore it if you want and still get the practice. |

## Math You Can See page | To explore math in art, nature, patterns, society, and more, go to my page called Math You Can See and go to any of the links there. (If you find any that don't work any more, please let me know.) |

## Some Math Puzzles I Like |