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Home

CHALLENGING MATH PROBLEMS WORTH SOLVING

DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL

WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS?

HERE'S OUR GROWING COLLECTION

WANT TO SHARE OPEN MIDDLE WITH OTHERS?

CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK

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CHALLENGING MATH PROBLEMS WORTH SOLVING DOWNLOAD OUR FAVORITE PROBLEMS FROM EVERY GRADE LEVEL Get Our Favorite Problems Take The Online Workshop WANT GOOGLE SLIDE VERSIONS OF ALL PROBLEMS? HERE’S OUR GROWING COLLECTION Get Google Slide Versions WANT TO SHARE OPEN MIDDLE WITH OTHERS? CHECK OUT THESE FREE WEBINARS TO HELP TEACHERS RETHINK CLASSWORK Elementary Version

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Illuminations provides standards-based resources and materials that illuminate the vision of NCTM for school mathematics and improve the teaching and learning of mathematics for each and every student. Lessons and activities on Illuminations have been developed in alignment with NCTM’s Principles and Standards for School Mathematics and the Common Core State Standards.

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Illuminations Home - National Council of Teachers of Mathematics

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Homepage | Silicon Valley Mathematics Initiative!!!

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Learning tasks (not scored)

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Create a new spreadsheet and edit with others at the same time -- from your computer, phone or tablet. Get stuff done with or without an internet connection. Use Sheets to edit Excel files. Free from Google.

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An Instructional Routine to Promote Sense making about Data.

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Slow Reveal Graph 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.

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Draft created and shared publicly for grade 3-8

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Classroom tasks and resources for learning (not summative)

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Performance Assessment Tasks by Grade (Grades 2-High School)

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These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifying the tasks.

The tasks for 3rd Grade through High School were developed by the Mathematics Assessment Resource Service (MARS) of the Shell Centre for Mathematical Education, University of Nottingham, England. The tasks for 2nd Grade were developed by the Silicon Valley Mathematics Initiative's Mathematics Assessment Collaborative (MAC).

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Performance Assessment Tasks | Inside Mathematics

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These tasks are grade-level formative performance assessment tasks with accompanying scoring rubrics and discussion of student work samples. They are aligned to the Common Core State Standards for Mathematics. You may download and use these tasks for professional development purposes without modifying the tasks.

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from the NYT

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Graphs, maps and charts from The Times — and an invitation to students to discuss them live.

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Tasks attached to standards, which you can map forwards/backwards (within and across grades)

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The Coherence Map shows the connections between Common Core State Standards for Mathematics.

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Tasks by content standards and grade levels

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Providing instructional and assessment tasks, lesson plans, and other resources for teachers, assessment writers, and curriculum developers since 2011.

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Lessons to develop number sense

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How do I get started? 1 USE THE FREE MATH LESSONS Estimation 180 Tasks 3-Act Tasks 2 SUBSCRIBE Email Newsletter Podcast

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

Which One Doesn't Belong?

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This is Which One Doesn't Belong?, a website dedicated to providing thought-provoking puzzles for math teachers and students alike. There are no answers provided as there are many different, correct ways of choosing which one doesn't belong. Enjoy!

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National Library of Virtual Manipulatives

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National Library of Virtual Manipulatives

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Number & Operations (All Grade Bands)

Virtual manipulatives for Number & Operations.
Number & Operations (Grades Pre-K - 2)Number & Operations (Grades 3 - 5)Number & Operations (Grades 6 - 8)Number & Operations (Grades 9 - 12)

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Number & Operations (All Grade Bands) Virtual manipulatives for Number & Operations. Number & Operations (Grades Pre-K - 2) Number & Operations (Grades 3 - 5) Number & Operations (Grades 6 - 8) Number & Operations (Grades 9 - 12)

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The Project‘s materials are of two complementary kinds:

Summative tests or tasks exemplify the performance targets that the standards imply.

Classroom Challenges are lessons that support teachers in formative assessment.

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1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e. g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

4: Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

5: Understand that positive and negative numbers are used together to describe quantities having opposite directions or values ( e. g., temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.

a: Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e. g., -(-3) = 3, and that 0 is its own opposite.

a: Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation "Subtract y from 5" as 5 - y.

b: Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2 (8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.

c: Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole- number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas V = s³ and A = 6 s² to find the volume and surface area of a cube with sides of length s = 1/2.

4: Identify when two expressions are equivalent (i. e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

7: Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

8: Write an inequality of the form x > c or x < c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams.

9: Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation d = 65t to represent the relationship between distance and time.

2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.

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1: Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e. g., by using visual fraction models and equations to represent the problem.