Singapore Math Classroom Diary

Singapore Math Classroom Diary

Year level: Grade 3 

Topic: Fractions 1

Today, I began teaching the grade 3 fractions unit to a group of students who require more support than the average third grader at my school. I wanted to document the sequence of lessons I taught, in part to think about how I use technology to teach the concepts in the unit.

With the faculty here, as well as in my training seminars, I try to emphasize to teachers that they need to begin their lesson planning with a foundational question: what is the most important mathematics that I need to teach today? Looking through the material I have planned, I interpret the answer to that question to be: Fractions show us parts of a whole. The parts come together to make a whole. This is what I want my students to understand and apply by the end of my 60-minute lesson.


In the textbook, this idea is taught by showing shaded and unshaded parts of fraction diagrams, using multiple representations such as fruit, circles, rectangles, triangles and other polygons. I use a 5-component lesson plan for my math classes, so I will present the lesson through the sum of its components. You can see how I used technology to help me teach concepts and skills throughout the lesson.

Mental Math

Today was the first math class after vacation. I wanted to begin reviewing multiplication and division fact practice right away to clear out any vacation cobwebs. Each student completed a 5-10 minute session with the ipad app connected an adaptive, web-based math facts practice solution that our school has been piloting this year. I am pleased with the independent and differentiated work that went on during this component of the lesson. Each child was practicing facts at their level. I was able to carefully observe one particular child who has not been making much progress. I noted that his attention wandered, and at the same time, he rushed in entering answers he knew. How can I have this child work at a more even pace. perhaps coupling that even pace with saying facts out loud?

Problem Solving

With this group, I have been remiss in keeping up with measurement skills. All this week, I have planned to use problem solving to work with telling time on an analog clock. Today, I presented a clock on my smartboard. I had each child write down the time shown (we practiced time to the nearest 5 minute) and then write down what time it would be 20 minutes later. 3 clocks were presented, one per screen. I could see children make progress with each example, and the group was independent with the task by the final example. The large and moveable clock I had designed on the smartboard was a clear and easy-to-use visual. I realize now that I could have used Matholia’s Virtual Clock Tool with even greater effect. I would be testing out a different Matholia tool later in the lesson, so this would have made more sense. Ahh, 20/20 hindsight. 

Directed Lesson

I began the directed lesson with the fruit examples right out of the textbook. We looked at fruits that had been cut up into equal parts. I emphasized how, in the example of fruit cut into fifths, the two fifths on one plate could be combined with the 3 fifths on the second plate to make 5 fifths of the fruit, which was the same as the whole fruit. This part/part/whole concept was certainly not new to these students, as we have been using this kind of language and representation with them throughout their math learning here. I made a big deal about how these pieces were cut into five equal parts, not just five parts. Fifths means five equal parts. If the parts aren’t equal, we cannot say that it has been cut into fifths.

I then digressed from the textbook and projected several circle models for fractions. I had students write down the fraction that was shaded and the fraction that was not shaded. I pointed out how the two parts (shaded and unshaded) came together to make one whole. Without really thinking about it ahead of time, I pushed the idea further into abstraction as I wrote fraction addition sentences that described each circle representation, adding the fraction shaded to the fraction unshaded and totalling to one whole. I knew that this was pushing the level of abstraction, for this group, but instinctively, I felt it was important for the kids to see the abstraction of the fraction equation right alongside the pictorial representation of the fractions.

Activity

The directed lesson then evolved into a partner activity, moving along with the text, I represented fractions with bar models. We worked through several examples on the Smartboard, with me releasing more and more responsibility to the students in the class to look at the fraction diagram, then point out the fraction shaded, the fraction unshaded, and the corresponding fraction equation.

Independent Practice

The corresponding workbook page helped the students practice the ideas that we discussed and that they had worked on with their partners. It took the group about 15 minutes to complete and partner-check the three assigned exercises.
For the last 5 minutes of class, I brought up Matholia’s Fraction Disc Tool. There, I pulled up the disc for one whole, and then pulled several unit fractions onto the screen. We were all able to see how ⅓ is actually a large piece, while ⅕ or 1/9 are actually very small pieces. The visuals helped to build foundational knowledge (without a lot of words from me) of the meaning of the denominator. On a whim, I used the rotate feature on the 1/12 piece to show how many 1/12 pieces would fit into ¼. This was a bit clunky. I didn’t want to spend a lot of time fiddling with the visual right in front of the class. Perhaps next time I will prepare a few tabs on my browser before class, that way I could quickly shift between set representations without building diagrams on the fly.

So, there it is. The lesson was a success. After having written it up, I can see how I used technology much more than I realized. Writing also gave me more ideas about how to incorporate the powerful tools in matholia and blend them with the Smartboard presentations I have already built for the lessons.

by Dr Kevin Mahoney

Dr. Kevin Mahoney is an academic researcher and Math Curriculum Coordinator for an independent school outside of Boston, MA. With over 20 years of elementary teaching experience Dr. Mahoney also works as a consultant and trainer to schools and teachers implementing Singapore Math Curricula. Read more about Dr. Mahoney at singaporemathmentor.com.

Follow the matholia blog for more classroom diaries and the latest Singapore math news.
If you have a Singapore math story, experience or teaching tip, we'd love to hear from you. Contact matt@bre.com.sg for more information on how you can contribute.