Chapter 4: Response Choice 1

22 Jan 2019 8:09 AM | Anonymous member

1. How are manipulatives used in your mathematics instruction?

2. In what ways are they used for multiple representations as students work on mathematics collaboratively?

3. What strategies can you use to make these tools more available to your students?


  • 24 Jan 2019 10:41 AM | Colin Bacon
    1. Depending on the level of course I teach, I incorporate what manipulatives I can to aid in instruction. In Pre-Algebra, we use hands-on activities like fraction dice, battleship, and measuring tools. Last year, we took a class outside for a number of days to measure and create a scale model of our school building. In Algebra 2 and Pre-Calculus courses, I have begun to incorporate more technology manipulatives, like Desmos activities that allow students to visualize graph transformations.

    2. The benefit of manipulatives, from my perspective, comes from both a change in class pacing and a means to reach students of different learning styles. For example, no students like to do fraction operations. But when you give them dice to roll, with a game board and some basic rules, it steps outside mundane math and can become engaging. For technology manipulatives like Desmos, applying sliders to functions allows students to physically see what different values do to the graph. Then, if we play a game that allows them to try and move balls around that are dropping onto a graph, it becomes engaging and challenging.

    When we took our pre-algebra group outside last year, it was great to divide them up into teams to work on different parts of the building. We gave each team a clipboard, a long measuring tape, and a calculator. It was really cool to see them almost self assign roles that lined well with their strengths, whilst also working together for the same task. And it was a really easy situation to answer the age old question of "when will I ever need this?", because it was an actual real-world application of scales and ratios.

    3. The downside of manipulatives mainly come from the sheer amount of planning and resource gathering required. Sure, I would love to do Desmos activities more often, but while my school isn't 1 to 1 with technology, it can become a task to try and get a computer in front of everyone. Sometimes, we have to improvise with manipulatives to make it work around materials we don't have.

    I think careful planning on planning well ahead of an activity are key. I also think I need to continue to work on incorporating ideas like the math practices, because it seems like it would help so much with those students who don't understand the "why" of what they're being asked to do.
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    • 31 Jan 2019 10:11 AM | Anonymous member
      It can definitely be hard sometime to incorporate manipulatives depending on the concept being taught. Using Desmos is a great an engaging tool for students to use. I see the challenge in using some of the manipulatives and tools you would use electronically if your students do not have 1 to 1 laptops. I love the project you did with pre-algebra, that is true application of what students were learning in the math classroom. I am sure this activity also led to mathematical discourse among students as they were working in their groups to complete different parts of the building.
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  • 24 Jan 2019 3:50 PM | Anonymous member
    I wish I could find even more ways to use manipulatives in my classroom. We are able to do some hands-on activities when working with area and circumference of circles, but not as much as I'd like.

    The one that I use the most is a manipulative model to teach integers, similar to what is described in the book. It is a game called "Zero My Hero" that I learned from Linda Jacobs. It uses red and black number dice (1-6), operation dice (add/subtract and multiply/divide) and black and red chips to show integer operations. Here is a link to the instructions:

    It does a great job of physically showing students what it is like to "add positive", "subtract positive', "add negative" and "subtract negative". They learn to use a positive and a negative to make a "Zero My Hero" in order to complete the operations.

    It is a collaborative effort because students play against each other and discuss the moves that they are making. In addition to using the chips to model integer addition/subtraction, they also use number line models.

    It takes a lot to set up the game for the students, so it would be nice if I could find a virtual game that they could play on their iPads. In addition, I think that anything on their iPad automatically becomes more engaging! For example, we recently played CMP's integer product game on paper with paper clips and markers. They weren't that into it, but then I shared a link to play it online and now they are challenging each other in their free time! (FYI:
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    • 31 Jan 2019 10:18 AM | Anonymous member
      That games sounds great. When I was teaching middle school I introduced addition and subtraction of integers with a giant number line I taped on my floor. I would have students take turns getting up and walking on the number line dependent on the equation.
      Example: 1-4=? the student would start on one facing the positive direction. Since the equation was subtraction they would have to take 4 steps back on the number line. Then when it came to 1 - -4=? The student would stand at 1, since the number they were subtracting was a negative they had to face the negative direction but it was a subtraction question so they still took 4 steps backwards. Students found this really engaging and I typically left it on my floor throughout the unit and students would periodically get up and use it when they were stuck. Just another way to help learn the same skills. Not sure this is necessarily a manipulative but it got them out of their seats and moving which they needed.
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  • 27 Jan 2019 4:50 PM | Anonymous member
    I teach 4th grade. For manipulatives we use cm cubes, counter, and fraction circles. I usually use them as I introduce a concept. For example when we started fractions we showed fractions using the fraction circles. We then found equivalent fractions using the fraction circle pieces. Then we began adding with the fraction circle pieces so students could understand why the denominator doesn't change when you add or subtract fractions. Then after the students were really good at these things with using the fraction circles, I began weaning them off the circles and into drawing them on paper and eventually using paper and pencil. I think this gives them a solid foundation and number sense before tackling math that might not make any sense to them. I did similar things with the other manipulatives like we made arrays with the counters when we started multiplication and used the cm cubes to show decimals.

    I usually start with the whole class using the manipulatives, then when my students are working with partners they use the manipulatives to solve problems. I have them draw what they do or how they use the manipulatives so I can see their thinking. They may be asked to show the problem in more than one way to show multiple representation.

    I do use the manipulatives for more than one type of math. For example I use the cm cubes for teaching volume in addition to decimals.

    The strategies I use to make these tools available are that they are introduced as a whole class so the students know what they are and how they might be used, we use them and then they are on a shelf in my classroom for students to access them as needed.
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    • 31 Jan 2019 10:45 AM | Anonymous member
      Teaching the students how to use the manipulatives is so important. Students need to know the purpose and need practice with them. You seem to really have down the gradual release part when it comes to using manipulatives; using them as a whole class, letting them use them in partners or independently, then eventually phasing them out but leaving them accessible for students that may still need or want to use them.
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    • 11 Feb 2019 4:17 PM | Anonymous member
      Hi Julie,
      We also use the same types of manipulatives. We notice that there are some students who struggle to see the transfer of content between manipulatives. For example, we teach them that a cube is one and a flat is 100 and then we tell them that a flat is a whole and the cube is .01. With fraction circles, they have trouble understanding changing the size of the whole. Do you notice that too? If you do, how do you approach that type of misconception. I look forward to seeing you in March.
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  • 28 Jan 2019 6:29 AM | Anonymous member
    I use patty paper, protractor, ruler, Geogebra, and Desmos a lot for exploration. I have students look for patterns and make conjectures and explore some more. I really like to use Desmos for the games and challenging activities. My students tend to get into the activities and don't want to stop. There is a marble slide activity that they especially enjoy. I would like for students to use Geogebra more for the drawing purposes, but it can eat up a lot of valuable class time teaching the students how to use the program. And, the next time we use Geogebra, about half have forgotten how to use the program.
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    • 01 Feb 2019 2:22 PM | Anonymous member
      Geogebra can be a great resource but I completely understand that students often forget how to use it. I wonder if there is a way to make a review video on how to use and it students can watch the review video prior to arriving to class? That could cut down on some of the having to reteach the program.
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  • 24 Feb 2019 11:39 AM | Deleted user
    Manipulatives are used often in my third grade classroom. I am fortunate in that I own a large set of Base 10 materials, hundreds of cubes, counters, dice, rulers, and various types of fraction tiles. Most often I am using manipulatives when a topic or concept is new to my students. For example, I cannot imagine teaching about multiplication being about equal groups without students using cubes
    to model equal groups. The use of fraction tiles is very helpful in teaching the essential vocabulary of halves, thirds, fourths, etc., an essential part of surface learning. This coming week I will be using fraction tiles to have students represent fractions on a number line. They are also really useful when teaching equivalent fractions. I make these tools readily available by leaving them out on the front table in my classroom.
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    • 25 Feb 2019 9:58 AM | Anonymous member
      Pat, using manipulatives to begin a new topic or concept can be so important in helping students build the conceptual understanding. Leaving those manipulatives out and available also helps students that may still be struggling and need the resource to solve problems while others may no longer need them. How often do you find students accessing the resources that are left out for them?
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  • 20 Mar 2019 9:45 PM | Anonymous member
    Teaching mostly higher level classes I find it a challenge to find activities that utilize manipulatives for many of the concepts I teach. This is extremely frustrating to me because I believe manipulatives can be life changing for students who struggle with abstract ideas. Being able to physically hold an object and see the abstract in concrete terms can open the doors that have seemed closed to them. When I was learning the rules for integers I was never given any reason why they worked, so it was memorizing the rules and having nothing concrete. Much later I was introduced to algebra tiles and for the first time truly understood why a negative times a negative equals a positive. Being able to see a concrete physical representation would have allowed me a solid understanding of the concept with no need to 'memorize rules'. It is heart breaking to me when I have Algebra II students that never used algebra tiles to explore factoring. I see their eyes light up with 'aha' moments when I do a quick demonstration. I always have algebra tiles available in my classroom if a student wants to break them out at any time.
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