University of Cambridge
University of Cambridge: Maths and Sports: Any Win for Tennis?
What are the probabilities of winning at tennis? This challenging activity is designed to be accessible to students of A-Level Maths (grades 10, 11, and 12).
University of Cambridge
University of Cambridge: Maths and Sports: David and Goliath
Does weight give shot putters an advantage? This activity encourages students to engage in statistical analysis, and is aimed at GCSE and A-level students (Key Stages 4 and 5).
University of Cambridge
University of Cambridge: Maths and Sports: What's the Point of Squash?
Squash isn't an Olympic sport (yet!) but it has an interesting scoring system. If you reach 8-all in a game of squash, when should you decide to play to 9 points rather than 10? This activity is a starting point for mathematical...
University of Cambridge
University of Cambridge: Maths and Sports: Opening Patterns
As excitement mounts ahead of the start of the London 2012 Olympic and Paralympic Games, take a look back at the opening ceremony for the 2008 Games in Beijing. What shapes and patterns can you see? This activity is aimed at young...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Triangular Tables
This task provides a good opportunity for group work and class discussions where students generate and compare equivalent expressions. In class discussion, students should be asked to connect the terms of an expression with quantities...
Illustrative Mathematics
Illustrative Mathematics: Reasoning About Multiplication
This is a good task to work with kids to try to explain their thinking clearly and precisely, although teachers should be willing to work with many different ways of explaining the relationship between the magnitude of the factors and...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Firefighter Allocation
In this students are asked to write an equation to solve a real-world problem. There are two natural approaches to this task. In the first approach, students have to notice that even though there is one variable, namely the number of...
Illustrative Mathematics
Illustrative Mathematics: Using Operations and Parentheses
The purpose of this task is to give students a chance to work creatively with three of the four fundamental arithmetic operations (addition, subtraction, and multiplication). It is well suited for helping students develop fluency with...
Illustrative Mathematics
Illustrative Mathematics: Calculator Trouble
Even though young scholars can solve this problem by multiplying, it is unlikely they will. Here it is much easier to answer the question if you can think of multiplying a number by a factor as scaling the number. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: 5.nf Fundraising
This task asks students to multiply rational numbers. Aligns with 5.NF.B.5.
Illustrative Mathematics
Illustrative Mathematics: 5.nf Grass Seedlings
For the sake of this commentary, let R be the height of Rual's seedlings (of course students do not need to use a letter to represent any number in this task). Student must compare the size of each of two products (112xR, and 34xR) to...
Illustrative Mathematics
Illustrative Mathematics: Comparing Products
The purpose of this task is to generate a classroom discussion that helps students synthesize what they have learned about multiplication in previous grades. Aligns with 5.OA.A.2.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Fishing Adventures 1
This task is the first in a series of three tasks that use inequalities in the same context at increasing complexity in 6th grade, 7th grade and in HS algebra. Students write and solve inequalities, and represent the solutions...
Illustrative Mathematics
Illustrative Mathematics: Words to Expressions 1
This problem allows students to see words that can describe the expression from part (c) of "5.OA Watch out for Parentheses." Additionally, the words (add, sum) and (product, multiply) are all strategically used so that the student can...
Illustrative Mathematics
Illustrative Mathematics: Watch Out for Parentheses 1
This problem asks the student to evaluate six numerical expressions that contain the same integers and operations yet have different results due to the placement of parentheses. It helps students see the purpose of using parentheses....
Illustrative Mathematics
Illustrative Mathematics: 6.ee Equivalent Expressions
In this problem, we have to transform expressions using the distributive, commutative and associative properties to decide which expressions are equivalent. Common mistakes are addressed, such as not distributing the 2 correctly. Aligns...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Distance to School
This task asks learners to find equivalent expressions by visualizing a familiar activity involving distance. The given solution shows some possible equivalent expressions, but there are many variations possible. Aligns with 6.EE.A.2.
Illustrative Mathematics
Illustrative Mathematics: 6.ee
The purpose of this task is to introduce the idea of exponential growth and then connect that growth to expressions involving exponents. It illustrates well how fast exponential expressions grow. Students who are just learning about...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Chocolate Bar Sales
n this task students use different representations to analyze the relationship between two quantities and to solve a real world problem. The situation presented provides a good opportunity to make connections between the information...
Illustrative Mathematics
Illustrative Mathematics: 6.ee Log Ride
In this instructional task students are given two inequalities, one as a formula and one in words, and a set of possible solutions. They have to decide which of the given numbers actually solve the inequalities. There are two solutions...
Illustrative Mathematics
Illustrative Mathematics: Bowling for Numbers
The purpose of this game is to help students think flexibly about numbers and operations and to record multiple operations using proper notation. Aligns with 5.OA.A.1.
Illustrative Mathematics
Illustrative Mathematics: 7.rp Two School Dance
The purpose of this task is to see how well students students understand and reason with ratios. This task was adapted from problem #14 on the 2011 American Mathematics Competition (AMC) 8 Test. Aligns with 7.RP.A.3. The site provides a...
Illustrative Mathematics
Illustrative Mathematics: 7.rp,ee Gotham City Taxis
The purpose of this task is to give students an opportunity to solve a multi-step ratio problem that can be approached in many ways. The site includes a task and the solution.
Illustrative Mathematics
Illustrative Mathematics: 6.ee Watch Out for Parentheses
This problem asks the student to evaluate three numerical expressions that contain the same integers yet have differing results due to placement of parentheses. Aligns with 6.EE.A.