## More on Double Numberlines and Fractions

Here are some examples of modeling subtraction of fractions with double numberlines. Remember that with any model, teach it in the whole group, practice it in small guided math groups and math workstations.

Happy Mathing,

Dr. Nicki

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## Build, Sketch and Record – Must See Charts!

These charts are great for any grade level (they are flashing underneath the heading Content Standard Posters). First the students build a model of whatever they are studying, then they sketch it and finally they record it with calculations! Simple and Brilliant! Try it and let me know how it goes!

Happy Mathing,

Dr. Nicki

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## Modeling Fractions! A Whole Unit to Teach in Guided Math Groups

Modeling the Math seems to be a sticky area for a great deal of people that I meet. Here is a good unit that shows modeling of fractions. Do these lessons in small guided math groups and do follow-up activities in math centers. Most people wrestle with fractions and the more opportunities that students have to discuss them and see them modeled in small groups is really important. So, spend some time working with the concrete and pictorial representation of fractions in small groups before you get to the algorithm. BUILD THE CONCEPTUAL UNDERSTANDING!!!

Happy Mathing,

Dr. Nicki

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## More Elapsed Time Activities!

Here is another way to think about elapsed time. Remember that this standard is now introduced in 3rd grade in the math CCSS. I would use elapsed time rulers as well.

Happy Mathing,

Dr. Nicki

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## Great Examples of Mathematical Modeling

I travel to a lot of different states. Everywhere I go, everyone seems to be grappling with this idea of mathematical modeling. The New Math Common Core has placed a particular emphasis on Mathematical Modeling throughout. Whether or not you are aligning your curriculum to the CCSS, its explanation is revelatory. It states that:

*Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. …Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation…They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense… *

Given this criteria, are your students mathematically proficient? Do they have a repertoire of models to make sense of their mathematical thinking. Here is a great resource with plenty of examples to get you started. I found this online from the publisher. These explanations of mathematical thinking are in the front of a great series of books on problem solving using bar diagrams. When I use these books I start with a grade level below the grade level I am teaching. I would even start at the beginning of the series so the students have a conceptual understanding and procedural fluency so when they get to the more difficult problems they have a strong foundation. See the resource page below of the different types of models and let me know what you think!

Happy Mathing,

Dr. Nicki

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