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.
β
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 equationsβchoosing 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.
βWhen will we ever use this in the real world?β
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.Β Students represent categorical and measurement data using picture graphs, bar graphs, and line plots.Β 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. Β 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.Β Estimation naturally surfaces through application; this transitions students into rounding.Β In the moduleΒs 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:
β’ how many boxes of packaged valentines will you need to purchase?
β’ how much will it cost for you to purchase and mail all of the cards?
β’ 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 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.
This link will work when you are IN A SUN WEST BUILDING (otherwise, you will be prompted to log in to your account. Refer to the document "Accessing Resources at Sun West" that was sent to you via email and Friday File for username and password).
This link will specifically organize the math resources available in Learn360.
Use the tabs along the top to locate:
Videos
Audio resources (songs etc)
Printables
STEM Lessons - these are really interactive activities and full lessons.
You can also filter by grade at the top of the page.
Keep in mind you can always use the search feature to find something specific quickly.
Math so fun, we do it on Saturdays!
Finallyβ¦a structure for 1 hour math blocks that include
Building Community & Relationships
Math Routines
Math Task
Rich Mathematical Discussions
A great source for number talks
These prompts can be used at school or at home!
"Math Before Bed is a collection of prompts that can inspire mathematical discussions that you and your children can have before bed, at dinner, or anytime.
Each prompt on this site shows you and your child a perplexing problem. Sometimes there is one right answer and sometimes there are many right answers. The purpose of each question is to generate a discussion about HOW you determined an answer. If you find one answer, try to find another. You could complete one prompt a night, or many prompts."
You can filter prompts using the STRANDS tab at the top of the page into number sense, patterning, geometry, measurement or probability.
Run by the University of Regina in Canada, this site offers free resources for math teachers and their students, including a database where users can search for the answers to math questions.
Their Mathematics with a Human Face page includes information about careers in mathematics as well as profiles of mathematicians.
"Named in honour of the mathematician Emmy Noether, this free online project aims to encourage the participation of both teachers and students at the Grade 5 and 6 level in solving problems for enjoyment and satisfaction. The 'circle' symbolizes an inclusive and collaborative setting, open to a variety of ability levels, wherein mutual support enhances individual investigations.
Each Circle is a set of six problems, plus hints, suggestions, and solutions. The problems can be used individually, or as a set, as time permits. While group work is a major focus, most problems are also accessible to students who prefer to work on their own."
Original math puzzles, games and problems - organized by grade.
You may find this site will not work directly from the site - If the page doesn't work copy and paste this URL into a web browser http://mathpickle.com/
The Problem of the Week is designed to provide students with an ongoing opportunity to solve mathematical problems.
Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up.
Sign up to get the weekly problem sent right to your email!
Current week and past problems with solutions are available.
"The Problem of the Week is designed to provide students with an ongoing opportunity to solve mathematical problems. Each week, problems from various areas of mathematics will be posted here and e-mailed to teachers for use with their students from grades 3 and up."
This is great way to stretch your mathematical muscle and develop good problem solving skills (Understand, plan, solve, reflect).
Solutions are always provided!
Archives of past questions are also available.
A great collection of sample rich tasks or activities and exemplars of student answers by Dr. Marian small.
"CEMC at Home has been developed to support teachers, students and parents during these challenging times. Most weekdays, we will post something for each of four grade levels: Grade 4 to 6, Grade 7/8, Grade 9/10 and Grade 11/12. The goal is to provide a wide variety of fun and educational ways to do mathematics and computer science while at home practicing social distancing. The resources will include games, new problems to solve, applications, videos, pointers to existing materials and more."
Subscribe to have the new activity emailed directly to you daily!
This award winning math site is searchable by grade level (6-8, 9-10, 11-12), course content and activities. It encourages:
Active Learning
- The unique content format makes learning more interactive than ever before. Students can explore, discover and actively engage in problem solving and creativity.
Personalization
- The content can seamlessly adapt to different students, allowing everyone to achieve mastery. A virtual personal tutor gives real-time hints and encouragement.
Storytelling
- Every course has a captivating narrative and is full of colourful illustrations. Discover all the real-life applications of mathematics, and why it is incredibly beautiful.
Just a few topics include:
- Virtual manipulatives (including Canadian money)
- multiplication flash cards
- Fractals
- timeline of mathematics
- graph theory
- Pascal's triangle
- Factris
- Fibonacci
- circles and pi
- origami
- Platonic Solids
- Symmetry
- Probability
- Cylinders
"Free videos and downloadable worksheets to help adult learners improve their calculation and numeracy skills."
Math tutorials that include videos & worksheets for:
*number sense
*calculations
*percent and fractions
*measuring
*shapes
*graphs
πNOTE: to access the "Downloadable Factsheets" available for each skill, RIGHT-CLICK ON THE FILE AND CHOOSE TO OPEN IN A NEW WINDOW! π
THIS IS A GREAT SITE TO SHOW STUDENTS THE PRACTICAL APPLICATIONS OF THE MATH YOU TEACH THEM.
Get DEEPER Math learning from your students. Get them thinking.
Grades K-12
Worksheets and THINKING activities are organized by strand on the right side of the website.
There is a great worksheet called "Open Middle Worksheet" on the top right for kids to document their process for problem solving. It gives them up to 6 attempts and the ability to explain what they have learned and how they need to change their approach for the next attempt.
This site accompanies the book "Open Math" by Robert Kaplinsky, but you do NOT need the book to benefit from these excellent questions.
Click "Get Our Favorite Problems" to get started (you will need to enter your info.) or use the menu organized by grade and strand on the right side of the page.
Free webinars are also recorded and available for elementary and secondary teachers to help "rethink classwork"
Example Question - Grade 3 - How many numbers are there between 1 and 3? (great way to introduce fractions).
Photomath is the ultimate educational tool for a smartphone or tablet. With over 300-million downloads, students and families around the world are using Photomath to check their homework, study for tests, and are building their math confidence every month.
Teachers can use Photomath to:
- Reinforce concepts learned in the classroom.
- Check homework assignments.
- Accelerate individual learning.
Get the easy to use Photomath app today! Head on over to Google Play or Apple to download the app and get started!
Students apply what they have learned about the engineering design process to a real-life problem that affects them and/or their school. They chose a problem as a group, and then follow the engineering design process to come up with and test their design solution. This activity teaches students how to use the engineering design process while improving something in the school environment that matters to them. By performing each step of the design process, students can experience what it is like to be an engineer.
Students use a hundred board to eliminate numbers after reading each clue. Students must apply their knowledge of even-odd, multiples and place value to successfully eliminate numbers until the solution is revealed.
SNOT Problem Solving: Self, Neighbour, Other, Teacher
Same or Different? is a routine that provides students opportunities to construct arguments when comparing objects, such as numbers or shapes.
A routine like Same or Different? provides accessible opportunities for even youngest students to learn how to talk about various features of mathematical objects β quantity, shape, color, orientation, and arrangement, to name a few.
Open-ended questions to differentiate math instruction.
This is a collection of different types of questions you can use for problem solving that differentiate to meet the varied needs of your classroom.
Some potential number talks are included in the "What one doesn't belong" section.
Two sample open-ended math questions are provided for each grade K-7.
Slow Reveal Graph (#slowrevealgraph) is an instructional routine that promotes sensemaking about data. This highly engaging routine uses scaffolded visuals and discourse to help students (in K-12 and beyond) make sense of data. As more and more of the graph is revealed, students refine their interpretation and construct meaning, often in surprising ways. This routine increases access for students without sacrificing rigor or engagement.
You will find all types of graphs for all ages of learners from elementary to high school.
Here are the steps:
- It starts with a graph that has been stripped of context: its numbers, its labels, its title.
- The teacher facilitates a discussion around what students notice and wonder. (The slides give discussion suggestions)
- Then another slide is revealed.
- Students identify what information is new.
- Then another slide is revealed.
- Again, students identify what information is new (the title) and discuss how this changes their understanding of the graph.
- As more slides are added, more insight into this data representation is revealed.
The introductory page for the graph also offers more information about the context for this graph, other content connections, and paired texts for students to explore.