Mathematics Updates
April 2018
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Promoting Productive Struggle in Math
Read Giardi's article and review some of the math hooks he has created. Use them as a springboard for creating your own hooks.
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Math Activities for Earth Day 2018
- Earth Day Math Games (K-1): Free printable games for grades K-1 can be downloaded from this blog. Scroll to the bottom to click on the yellow button.
- Earth Day Math Games (Grades 1-4): Download this free printable from TPT for two Earth Day math games for grades 1-4.
- Be Part of the Solution: This PBS lesson illustrates the power of multiplication when taking one small step to help the environment. Videos and activities are also available for use.
- What We Do Adds Up: This PBS lesson for grades 4-6 has students calculate the average per person trash output and how it adds up over time.
- Earth Day Math Activities Using Ratios, Unit Rates, and Data Analysis: This resource for grades 6-8 engages students in data analysis and conversations that inspire higher-order thinking about the environment.
- Population Simulation with M&Ms: In this grades 6-9 PBS lesson, simulations with M&M candies explore population growth and decay.
- Adventures with the Fish Pond - Population Modeling: Building on the population decay M&Ms activity, students in grades 7-9 write a NOW-NEXT or recursive equations in this lesson from PBS.
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Developing Understanding through Multiple Representations
Similarly, our students can develop partial understandings of mathematical concepts that they erroneously believe to be complete when they are limited to one or two representations of the concept being studied. To help our students develop a more complete understanding, it is necessary to purposefully include multiple representations in instruction and assessment.
Mathematical ideas should be evident in teaching in learning in four main ways:
- verbally,
- numerically,
- symbolically, and
- graphically.
Verbally is how we usually encounter problems in real life. Verbal representation includes word problems, contexts, descriptions, and proofs. Numerical representations are comprised of data which may be presented in a T-chart or other table. Symbolic representation is what we usually think of as "math" and includes algebraic notation. Graphical representations show the information in pictures, graphs, and/or diagrams.
Engaging with math concepts using multiple representations allows our students to develop a clearer and deeper conceptual understanding.
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Number Talks: Not Just for Elementary Students
Number Talks have been recognized as a powerful tool at the elementary level for developing computational fluency. A Number Talk is a short, ongoing daily routine planned with the expectation that students will use number relationships and the structures of numbers to add, subtract, multiply and divide efficiently, accurately. efficiently, and flexibly.
But Number Talks are not just for elementary students. Middle and high school students can benefit from this routine as well. Sherry Parrish and Ann Dominick have published a new learning resource, Number Talks: Fractions, Decimals, and Percentages.
Number Talks should be structured as short sessions alongside (but not necessarily directly related to) the ongoing math curriculum. It is important to keep Number Talks short, as they are not intended to replace current curriculum or take up the majority of the time spent on mathematics. In fact, teachers need to spend only 5 to 15 minutes on Number Talks. Number Talks are most effective when done every day.
Watch the video below to see Number Talks in action in a high school geometry class.
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Concrete-Representational-Abstract: How Students Learn
Unfortunately, too many students get far too few concrete and pictorial experiences with key concepts. It is important to note that C-R-A is for all grade levels, not just for K-2. Students in upper grades often need to go to the concrete level to develop understanding. And C-R-A is an essential part of the remediation process.
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Videos and Lessons to Inspire and Challenge
Grades K-12
Teaching requires lots of effort, but students are worth it. This short, inspirational video reminds us that it is our responsibility that students learn what we teach.
Grades K-2
A children's book sets the stage for this lesson, which encourages students to review counting back. In this lesson, children write subtraction problems and model them with cubes.
Grades 3-5
This lesson uses sports to capture student interest and motivate them to use whole numbers and fractions to calculate activities, lengths, weights, and times.
Grades 6-8
In this video, Allison Krasnow, featured in the Students Are Worth It video above, teaches a lesson on integer addition using stickers to create concrete understanding.
Grades 6-8
Students simulate a jumping-frog contest, measuring distances jumped, collecting data, and analyzing measures of center and variation.
Grades 9-12
Students use construction, consider angle measures and segment lengths, and find areas as they transform a square into a pinwheel and discover a surprising result.
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Upcoming Professional Learning Math Webinars
April 17, 2018 @ 3:30 p.m. - Webinar
Specific Strategies to Increase Mathematical Discourse in HS Math Class
Learn productive strategies for increasing classroom discourse. Dr. Christine Thomas will explain each strategy, discuss how and why it works in the classroom, and give tips for successful implementation. Register now.
What Happens When Teachers Talk Less and Students Talk More in the Mathematics Classroom
Join mathematics expert Dr. Mark Ellis for a discussion around how routines promote classroom discussion and can help increase student understanding and retention of mathematics concepts. The webinar is offered by Education Week. Register now.
April 19, 2018 @ 2 p.m. - Webinar
Bring Hands-On Coding and STEAM into Your Classroom
In this webinar, Dr. Azadeh Jamalian, head of education strategy at littleBits, discusses best practices on bringing hands-on coding and STEAM into your school. Pilot and case studies examining STEM implementation in elementary and middle schools will be reviewed, and important take-aways applicable for different educational settings will be highlighted. Teachers for grades 3-8 will benefit from attending this session offered by Education Week. Register now.
May 2, 2018 @ 7 p.m. - Webinar
Implement Tasks that Promote Reasoning and Problem Solving & Use and Connect Mathematical Representation
Effective teaching of mathematics facilitates discourse among learners to build shared understanding of mathematical ideas by analyzing and comparing approaches and arguments. How might we implement and facilitate tasks that promote productive discussions to strengthen the teaching and learning of mathematics in all our teaching settings - teaching students and teaching teacher? What types of tasks encourage mathematical flexibility to show what we know in more than one way? Register now.
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2018-2019 Pacing Guide Revision: Team Workshops
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Research base
Games 4 Learning. (n.d.). Earth Day activity: Earth Day math games. [Website]. Retrieved from https://www.teacherspayteachers.com/Product/Earth-Day-Activity-Earth-Day-Math-Games-Freebie-654794
Georgia Department of Education. (n.d.). Mathematics Georgia Standards of Excellence (GSE), [Website]. Retrieved from https://www.georgiastandards.org/Georgia-Standards/Pages/Math.aspx
Giardi, M. (2018, April 5). Promoting productive struggle in math. [Website]. Edutopia. Retrieved from https://www.edutopia.org/article/promoting-productive-struggle-math
MathHooks. (n.d.). Math hooks: Inquiry before instruction. [Website]. Retrieved from https://www.mathhooks.com/
PBS Kids. (n.d.). Cyberchase: Be part of the solution. [Website]. Retrieved from http://pbskids.org/cyberchase/activities/be-part-solution/
Public Broadcasting Service [PBS]. (n.d.). What we do adds up. [Website]. Retrieved from https://drive.google.com/file/d/1Bb9_AJw-CNH9BGFKb2npKRGTKe_GLhFs/view
Ryan, C., Slattery, I., & Weimberg, G. (Producers). (2011). What's your sign: Integer addition. [Video file]. Luna Production. Available from https://www.teachingchannel.org
Teaching Channel. (n.d.). Students are worth it. [Video file]. Available from https://www.teachingchannel.org