Mathematics Updates
March 2017
Strategies for increasing the Cognitive Demand of Tasks
ELEMENTARY MATHEMATICS
Rather than providing a context, ask students to write a word problem for a given expression.
Have students determine an expression to represent a situation.
Require students to provide justifications for their solutions.
Challenge students to solve problems using more than one solution method or representation.
Have students make sense of provided solution strategies by completing the solution or justifying the steps.
Make the task open ended so that multiple responses will satisfy the task. Transform a single-step problem to a multiple-step problem.
Include the use of multiple representations in a task.
MIDDLE SCHOOL MATHEMATICS
Use comparison questions. (When is one situation greater than, equal to, or less than another?)
Ask a question across multiple representations in a task.
Validate a solution pathway or approach.
Require students to provide justifications for (explain) their solutions.
Evaluate the error or reasoning in a student solution and provide a correct solution pathway.
Create a context. Ask students to write a word problem that creates a context for the given information.
Ask students to determine an expression to represent a situation.
Create an open-ended debate-type task, so that multiple student responses will satisfy a solution to the mathematical task.
HIGH SCHOOL MATHEMATICS
Find the error in a student solution, and provide a correct solution pathway.
Create an open-ended debate-type task (evaluating a student claim, for example) so that multiple responses will satisfy the task.
Rather than providing a context, ask students to write a word problem for a given expression or graph.
Ask students to determine an example to represent a situation.
Require students to provide justifications for their solution pathway or strategy (such as when comparing two quantities).
Challenge students to solve problems using more than one solution method or representation.
Ask students to make sense of provided solution strategies by completing the solution or justifying the steps.
Create the task as open ended so that multiple responses will satisfy the task.
Transform a single-step problem to a multiple-step problem.
Include the use of multiple representations in a task.
Videos of Math Instruction and Assessment Strategies
Grades 8-12
Engaging Resources for Your Students from NCTM Illuminations
Grades K-2
After Okta hides some bubbles under a shell, he then either adds more bubbles or takes some away. Students have to determine how many bubbles are left under the shell. Includes links to related resources.
Grades 3-5
Use this tool to strengthen your students' understanding and computation of numerical expressions and equality. One of the first things that students must realize is that equality is a relationship, not an operation.
Grades 6-8
Students can use tiles to represent variables and constants, learn how to represent and solve algebra problems, solve equations, substitute in variable expressions, expand and factor, flip tiles, remove zero pairs, and copy and arrange.
Grades 3-8
Calculation Nation contains more than a dozen games organized around content from the upper elementary and middle grades math curriculum. The fun games allow students to learn about fractions, factors, multiples, symmetry and more, as well as practice important skills like basic multiplication and calculating area.
Grades 9-12
The Greek mathematician Archimedes approximated pi by inscribing and circumscribing polygons about a circle and calculating their perimeters. The value of pi can also be approximated by calculating the areas of inscribed and circum- scribed polygons. This activity investigates and compares both methods.
Grades 9-12
Students challenge themselves to see how well they understand function expressions by trying to match a function to a generated graph. Related resources include a "Building Connections" lesson with activities for building quadratic and higher degree polynomial functions.
Promoting a Growth Mindset
Praising the process, not the person, is key to informative and productive feedback. Emily Diehl, a Mindset Works trainer, suggests some great prompts teachers can use to promote a growth mindset.
When a student is struggling despite a strong effort:
- "If this was easy, then you wouldn't be learning anything new!"
- "You can do this! Let's break it down into some smaller chunks."
- "Look how much progress you have made!"
When a student is struggling and needs help:
- "What parts of this was hard for you? Show/tell me ..."
- "Let's do one together. Describe your process out loud so I know your thinking."
- "Let me show you another way to try ... Maybe this will help you solve it."
When a student is making progress:
- "You are using the strategies we discussed. Keep it up!"
- "You have really stuck with this and persevered!"
- "Your hard work is really evident!"
When a student succeeds with strong effort:
- "All that hard work and effort paid off!"
- "What strategies did you use that contributed to your success?"
- "Congratulations! I am very proud of you for not giving up!"
When a student succeeds easily without effort:
- "You're ready for something more challenging!"
- "You really have that down. Let's find something that will challenge you a bit more."
- "What skill do you need to work on next?"
Free resources are available at Mindset Works. Download a copy of the poster about mistakes, in color or in black and white, to print and post.
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Looking Ahead to April Math Month
Planning ahead will allow you to plan some activities to celebrate math during the month of April. The Envision Blog lists some possibilities, and these calendars provide students with grade or grade-band appropriate challenges for each day of the month.
Math Professional Learning in March
March 7, 2017 - K-2 Math Webinar - 3pm - 4pm
Avoiding Math Misconceptions in Grades K-2
Children try to make sense of what they see and hear in terms of numbers, measurement, shapes, money, and time. And they can develop misconceptions that create issues for conceptual understanding. This session will examine some common math misconceptions children have in K-2 and discuss instructional ideas and activities that can be implemented to address these misconceptions. Register by 4 p.m. on March 6 at https://goo.gl/forms/8k010ZtYKbZEakNs1 to receive an invitation to join this session.
March 21, 2017 - Smokey Road Middle - 4pm - 5pm
Determining Power Standards
Teacher teams will apply the criteria of endurance, leverage, and readiness to grade level math standards, along with the state assessment blueprint, to determine a draft list of power standards. Teams will vertically review draft power standards at each grade level for gaps and redundancies in order to create the final list. This work is in preparation for the creation of 2017-2018 course pacing guides later in the spring. Participants are asked to bring their Chromebooks. No registration is required.
March 28, 2017 - 3-5 Math Webinar - 3pm - 4pm
Avoiding Math Misconceptions in Grades 3-5
Aside from making careless errors and having incomplete mastery of basic facts, the other mistakes students make are due to misconceptions. This session will examine some common math misconceptions children have in grades 3-5. Instructional ideas and activities that can be implemented to address these misconceptions will be discussed. Register by 4 p.m. on March 27 at https://goo.gl/forms/SgF8aASErIVH6r533 to receive an invitation to join this session.
Research Base
Briars, D.J., Larson, M.R., Kanold-McIntyre, J. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, grades 6-8. Bloomington, IN: Solution Tree.
Dixon, J.K., Adams, T.L., Nolan, E.C. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, grades k-5. Bloomington, IN: Solution Tree.
Dweck, C. (2014). The power of believing that you can improve. TEDxNorrkoping. Available from http://www.ted.com/
Envision Blog. (2016). Mathematics awareness month. Retrieved from https://www.envisionexperience.com/blog/mathematics-awareness-month
Luna Productions (Producer). (2012). Don’t give up: Plan, persevere, revise. Available from https://www.teachingchannel.org
Mindset Works. (2015). Free resources. Retrieved from https://www.mindsetworks.com/free-resources/default
National Council of Teachers of Mathematics. (n.d.). NCTM Illuminations. Reston, VA: Author.
Readdean, C. (Producer). (2012). Student-generated questions for exam prep. Available from https://www.teachingchannel.org
Sun, K.L. (2015). There’s no limit: Mathematics teaching for a growth mindset. Doctoral dissertation. Stanford, CA: Stanford University. Retrieved from https://purl.stanford.edu/xf479cc2194
Teaching Channel (Producer). (2013). Math journals: A record for students and teachers. Available from https://www.teachingchannel.org
Teaching Channel (Producer). (2015). Highlighting mistakes: A grading strategy. Available from https://www.teachingchannel.org
Toncheff, M., & Kanold, T.D. (2015). Beyond the Common Core: A handbook for mathematics in a PLC at work, high school. Bloomington, IN: Solution Tree.