This collection features resources to encourage and develop problem solving skills.
Students use their emerging writing skills to write shopping lists. They work within a budget, use problem-solving skills to create lists, and buy their favorite treats at the class store.
The inspiration for this site came from John Allen Paulos' book Innumeracy. From it Fawn Nguyen took the mathematical fun facts, etc. and created middle school mathematics critical thinking problems that relate to ratios and proportional reasoning and require students to compare stuff and really get them thinking.
Here's an example:
Tortoises have the longest lifespan among vertebrates, about 200 years.
A fruit fly's lifespan is about 45 days.
If we scaled both lifespans down so that a tortoise's 200 years is now 1 day, then what is the fruit fly's lifespan, in seconds?
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In this lesson students apply the problem solving process to three different problems in order to better understand the value of each step. They will solve a word search, arrange seating for a birthday party, and plan a trip. The problems grow increasingly complex and poorly defined to highlight how the problem solving process is particularly helpful when tackling these types of problems. The lesson concludes with students reflecting on their experience with the problem solving process. They will justify the inclusion of each step and will brainstorm questions or strategies that can help them better define open-ended problems, as this is often the most critical step.
This lesson will likely take two class periods or more to complete. The first two problems may fit into a single class period but the third will need to be moved to a second day.
Students complete two unplugged card sorting activities to explore the meaning of processing and its relationship to problem-solving. The first activity has few constraints and is used to introduce a high-level definition of processing. The next introduces more constraints that force students to develop an algorithm that will always successfully process the cards. Students iteratively develop, test, and share their algorithms with classmates. A wrap-up discussion has students reflect on the different types of problem-solving they used in these activities and the value of producing an algorithm to solve a problem.
Figure This! Math Problem Solving Challenge for Families
This site offers 4 free math activities to assist students with increasing their fluency in operations with rational number and algebraic equations. The activities include:
Activity 7.7: "Would You Rather..." Routine
There are two versions of this routine with systems of linear equations—choosing different strategies (e.g., Use Tables or Use Graphs) and making choices within a strategy (e.g., For which variable will I substitute? Or Which variables will I eliminate?).
Activity 6.10: The Transformer Game
This game is a fun way to give students opportunities to choose and use different basic transformations to start solving equations.
Activity 5.7: Worked Examples For Ratios and Proportions
Use this activity for worked examples for ratios and proportions. Correctly worked examples and partially solved worked examples benefit students so that they can understand strategy.
ACTIVITY 4.11: Quotient Connect Game
This game is an engaging way to practice division using Partial Quotients. It is played similarly to the classic board game Boggle as students find quotients through connected digits.
Four Corners Graphic Organizer for Math
Main idea, connect, brainstorm, solve, write.
If you're looking for daily fraction problems to have your students work through either as a bell buster or part of your daily math lesson, check out these 90 awesome fraction problems that will get your students thinking!
Solutions included.
“When will we ever use this in the real world?”
Real world math examples and solutions from the University of Waterloo.
Module 7 presents an opportunity for students to practice addition and subtraction strategies within 100 and problem-solving skills as they learn to work with various types of units within the contexts of length, money, and data. Students represent categorical and measurement data using picture graphs, bar graphs, and line plots. They revisit measuring and estimating length from Module 2, though now using both metric and customary units.
Module 2 uses place value to unify measurement, rounding skills, and the standard algorithms for addition and subtraction. The module begins with plenty of hands-on experience using a variety of tools to build practical measurement skills and conceptual understanding of metric and time units. Estimation naturally surfaces through application; this transitions students into rounding. In the modules final topics students round to assess whether or not their solutions to problems solved using the standard algorithms are reasonable.
Students will work in small groups to cooperatively to complete a Fermi math problem. Fermi math challenges students to solve seemingly complicated questions using estimation, rounding, approximations, analytical thinking, creative thinking, communication, and technology skills. The students will investigate the driving question: If you wanted to send a valentine card to each person in the world next year:
• how many boxes of packaged valentines will you need to purchase?
• how much will it cost for you to purchase and mail all of the cards?
• if everyone in the world sent a valentine to everyone else in the world, how many valentines in total would be sent?
Graphic Organizers to Help Kids With Math
The ABACUS International Math Challenge was launched in 1997 by Tivadar Divéki, head of Grace Church School’s Science Department. In September, 2015, we proudly changed the name of our program to Paul Erdős International Math Challenge. The program is based on a printed journal for gifted students, originating in Hungary over 100 years ago. Participants over the years included Edward Teller, Leo Szilárd and other notables in physics, computer science and mathematics. This program is designed for students of all abilities and demonstrates that mathematical talent can be stimulated and developed through individual attention, instant feedback and challenging subject matter with flexible levels of difficulty.
The Problem of the Month is intended to challenge enthusiastic high school math students. Most problems are designed with the assumption that students attempting them have a solid understanding of grade 11 math, but some problems may still be of interest to motivated younger students.
A new problem will be posted on the first Tuesday of every month starting in October. A hint will follow 10 days later, and a solution another 10 days after that.
Illuminations works to serve you by increasing access to quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers.
The website includes:
- Lesson plans
- Online math strategy games against a computer or other players across the world
- Activities
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This is a booklet containing 11 problem sets and 9 "Extra for Experts" challenges. Learners use provided textual information to determine the scale (e.g., kilometers per millimeter) for images of the lunar surface, Mars, planets, stars and galaxies and then identify the smallest and largest features in the images according to their actual physical sizes. These problems involve measurement, dividing whole numbers, decimal mathematics, and scaling principles. Each set of problems is contained on one page. This booklet can be found on the Space Math@NASA website.
The tools for educators include:
~ Problems of the Month - The Problems of the Month are non-routine math problems designed to be used schoolwide to promote a problem-solving theme at your school. Each problem is divided into five levels of difficulty, Level A (primary) through Level E (high school), to allow access and scaffolding for students into different aspects of the problem and to stretch students to go deeper into mathematical complexity.
~ Jumpstart Guide for Practitioners - guide to accompany the Problems of the Month
~ Formative Re-engaging Lessons - Formative Re-Engaging Lessons involve a cycle of inquiry, instruction, assessment, analysis, selection, and re-engagement around a mathematical concept. Each Formative Re-Engaging Lesson includes a classroom video of the lesson, downloadable lesson plan, student pages, pre- and post-assessments, and supporting instructional materials.
~ Classroom Videos
~ Resources for Social and Emotional Learning in Mathematics Classrooms
Kindergarten Math problem solving.