Can you visualize what it means when we divide by a fraction? If not, watch this video. New TikTok video: Did you know we can divide across fractions? New TikTok video: One of my favorite ways of finding the greatest common factor. Twitter. My 6th graders were struggling with fraction division so I gave them this @desmosclassroom activity by @davidporas today. One thanked me and said that it made division finally make sense to her. Thank you, David for this!!! □□ #mtbos #iteachmath. New math infomercial: You never have to do long division ever again! Our 5th graders will be playing around with decimal place value. Oh how I love "Decimal in between"
Twitter. Twitter. Twitter. Have some S's who don't think about whether they need to regroup for subtraction. What to do about it? Give them an open middle! We're learning how to think, not what to think! @robertkaplinsky. Twitter. Twitter. How Many Hot Dogs And Buns Should He Buy? How many packages of hot dogs and hot dog buns should he purchase so that there are no extra hot dogs or hot dog buns?
These questions may be useful in helping students down the problem solving path:How many hot dogs come in a package? How many hot dog buns come in a package? What might happen if you buy one package of hot dogs and one package of hot dog buns? How might that make someone feel? What is a guess that is too low? What is a guess that is too high? What is your best guess? In the movie clip there are 8 hot dogs and 12 hot dog buns in a package. Below I have provided images with examples of hot dogs and hot dog buns in various packaged quantities to use as an extension.
A package containing 7 hot dogs A package containing 8 hot dogs A package containing 8 hot dog buns A package containing 12 hot dog buns A package containing 16 hot dog buns Daniel Luevanos shares a wonderful reflection of how it went when he used this lesson with his students. Greg Tang sur Twitter : "Started the day early with 5th graders in Maryland. Turned word problems the kids struggle with into easy 1st grade problems! Are these problems algebra, tape diagrams, number bonds, or mental math problems? All 4 with practice! N.
[New @Desmos Activity] Using area to model decimal multiplication (with Challenge Creator) #mathchat #ITeachMath #MTBoS… Volume, From the Ground Up. If you asked a student to look at this figure and tell you how many cubes it’s made of, he might tell you 16. Can you figure out why? Well, if you think about it, he can only see 16 cubes. He’s not thinking about the ones tucked away underneath. Here in Texas, 4th grade students must “use models of standard cubic units to measure volume”, and in 5th grade they need to “connect models for perimeter, area, and volume with their respective formulas.” Notice that both standards feature the use of models. The danger is in jumping to the formula, v=l x w x h, before students have an understanding of what the formula means.
In other words, jumping to an abstract idea without concrete experiences. Give students concrete experiences with volume by comparing the process to building a building. For my fourth graders who don’t need to know the formula, they now have a strategy for determining the volume using a picture. Ready to try it with your kiddos? Fix It: An Activity for Ordering Fractions. Involving students as creators of problems for others to solve provides an experience for them that’s different from the teacher always being the source of problems. Also, when students have opportunities to solve their classmates’ problems, I find that they invest in their learning in a different way, often with added interest.
And a benefit to teachers is that reviewing the problems that students create is useful for assessing their progress. Here’s what I did with fifth graders studying fractions. I wrote five fractions on the board, as shown above, purposely writing them out of order. Then I explained to the students that they were going to create “Fix It” puzzle cards for their classmates to solve. I modeled on the board how I would follow each direction. Finally I modeled making a puzzle card by copying onto a 4-by-6-inch index card the five fractions out of order from the top of my paper. I gave one last direction. As the class worked, I circulated and observed. Multiplying Mixed Numbers by Whole Numbers | Open Middle® Multiplying Decimals.
In Texas, multiplying decimals with products to the hundredths was added to the 5th grade curriculum last year, and today I tackled it with some of our 5th graders. Shifting from multiplying whole numbers to multiplying decimals is a huge shift, so that means that the learning needs to be concrete. Time to bring out the base-10 blocks. As I was planning for my lesson, I thought through all the variations related to multiplying with decimals, and here’s what I came up with:Whole number factor times mixed number factor (eg., 2 x 1.3)Mixed number factor times mixed number factor (eg., 1.3 x 1.5)Whole number factor times a decimal factor (eg., 2 x 0.8)Mixed number factor times a decimal factor (eg., 1.3 x 0.4)Decimal factor times a decimal factor (eg., 0.7 x 0.3) I think I got them all!
Before getting into the meat of the lesson, we had to cover some basics. First, we needed to establish the value of the base-10 blocks. Next up, I asked them to model 2 x 1.3. Okay, this was a trickier one. I ❤️ constant difference with decimals... @marian_small #StenhouseMath… Just made this for Grade 5 unit on multiplication of fractions. I wanted to build reasoning into the game. Students decide where they will place each number they roll in order to make the greatest product. #iteachmath #mtbos #elemma…
Margie Pearse sur Twitter : "Playing around with this Number Sense Routine by @JohnSanGiovanni Love the idea of building fluency with decimals using the same mental math strategies used with whole numbers #iteachmath #elemmathchat #mathconceptions… https: Each student is given a different problem, when I say "SWITCH! Ready to tackle 4.NBT.1 We won't be adding zeros but seeing how the relative size and magnitude of the number increases by ten #elemathchat… 5th Grade: Decimal Place Value | Math Minds.
There are some standards I think we do such a great job developing in early elementary, but never revisit explicitly when students learn about different numbers such as fractions and decimals. I blogged about this in reference to even and odd numbers last year, but this past week I have found another: Early elementary spends SO much time building understanding of the relationships between 1’s, 10’s and 100’s, but I don’t think we do this standard justice as students build their understandings of fractions and decimals. Leigh’s 5th grade math class just started their work with decimals. To help students make connections to what they learned last year, she and I went back and brushed up on where the students should be in terms of the 4th grade CCSS.
It is always so interesting to me how the CCSS authors chose to put decimals in the NF strand in 4th grade because students are learning decimals are just another way to write a fraction with a denominator of 10 or 100. Like this: I feel like I lean toward something like 7 x 1 7 x 10 7 x 10 x 10 7 x 10 x 10 x 10 with recording that lines them up: 7 70 700 7000 How does the value the digit 7 represents change each time?… Greg Tang sur Twitter : "Kids are really liking Greg Jr's Pictarithms at every grade level. Here's a Gr 5 puzzle for adding fractions with unlike denominators. Kids have to start with parts and find whole, and start with whole and find parts. Getting them.
Saw this in one of our textbooks...I think a part of me just died □□♀️. #cpsmathandme #iteachmath @ddmeyer… What Did You Say About Cheeseburgers – Elementary Teacher in Middle School. Yes, it’s how we learned it. Yes, most people will say, “It worked for me, so it will work for them!” The standard algorithm has definitely been a bone of contention in many conversations. On another, but connected note, while watching Spiderman into the Spider Verse, my youngest was singing along with one of the songs.
A friend of mine made the comment, “Kids can hear a song once and be able to sing it, but yet they can’t remember things in school.” (With the voice of Carrie) I couldn’t help but wonder, “If concepts had more structure that is easily identified by students, would learning be more fluid”. This reminded me of a talk I watched of William McCallum on The Story of Algebra. In it he discussed finding structure within a poem to help memorize the poem. In 5th grade, students solve division of whole numbers using partial quotients. When dividing 691, students should think how many 8s are in all of 691.
“I notice there are 69 tens in 691. Like this: Like Loading... Dividing Decimals (Middle School) | Open Middle™ Multiplying Decimals (Middle School) | Open Middle™ What Is It Between? – The intricacies of teaching rounding – Elementary Mathematics – Round Rock ISD. Grade 5 Math Talks Comprehensive Bank. Teaching Adding Decimals: What If You Give the Answer First? | Marilyn Burns Math Blog. I struggle with how to teach topics that revert to learning procedures, too often without understanding. Take adding decimals. This is typically part of grade 5 math instruction. But every time I’ve given students the reminder to line up the decimal points and then add, I’m reminded of the fraction counterpart: Yours is not to question why; just invert and multiply.
My ongoing search is for ways to engage students with adding decimals in a way that promotes making sense, reasoning numerically, and solving problems, not merely learning a procedure. I chat from time to time with Nina Sudnick, a teacher at West Elementary in Athens, Ohio, now teaching math to one class of fourth graders and two classes of fifth graders. But when we’ve given students practice with adding decimals out of contexts, we’ve both found ourselves reverting to reminding students about lining up the decimal points before adding.
As Nina and I talked, I recalled an idea. I’d give time for them to complete this. Most Misunderstood Math Standards in Grade 5. In my last posts we explored the Most Misunderstood Elementary Mathematics Standards in Grades 3 and 4. I have loved the conversations I’ve engaged in with math educators and welcome more people to join in! I can be found on Twitter here: @few_rebecca or leave me a comment below! In this post, we will dive into the most misunderstood elementary school standards in Grade 5. Again, this is not about judging our colleagues, but looking deeply at the practice of mathematics instruction in Grade 5 and learning more about the standards together. How many times have we heard someone say, “When we multiply, the product is always larger” or, “When I divide, my answer is always smaller.” Probably several times during our tenure in education.
Making generalizations about mathematics that are inaccurate promote misunderstandings about important math concepts. The first one is 5.NF.B.4: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. When You Multiply by 10, Just Add a Zero? Horrors!?! | Marilyn Burns Math Blog. We Ask, We Listen, We Learn is one of the early blog posts I wrote. (I posted it on January 5, 2015.) The post includes interviews of several students answering the question: How much is 12.6 x 10? One of the video clips shows Mallika Scott interviewing Natasha, who explains how she decided on the incorrect answer of 12.60. Natasha explains, “Any number that’s times 10, you can add a zero at the end.”
Even though I wrote the blog more than three years ago, Westley Young recently posted a comment that addresses, in part, the “add a zero” strategy: Westley (who Tweets as @Cukalu) raised issues that have long concerned me. My second issue is my struggle with what to do about my concern. In elementary math, students have experiences looking for patterns. Many thoughts race through my head as I reflect on this video clip of Natasha and on Westley’s comment.
My First Thought What if I said something like this to Natasha: If Natasha answered yes, I’d want to hear why she thought that was true. When You Multiply by 10, Just Add a Zero? Horrors!?! | Marilyn Burns Math Blog.