Illustrative Mathematics
Illustrative Mathematics: A Ced, a Rei Basketball
In this task, two brothers track how many games they have each won. Students are asked to make calculations based on the percentage of games won. They set up a rational equation (and a rational inequality) in one variable, and then solve...
Illustrative Mathematics
Illustrative Mathematics: A Ced Buying a Car
In this task, students are asked to calculate what a car's list price would be in states with different sales taxes. Its purpose is to help students develop familiarity with different ways to solve a problem. Aligns with A-CED.A.1.
Illustrative Mathematics
Illustrative Mathematics: A Rei, a Ced Cash Box
In this task, students are asked to construct equations in two variables to determine whether a loose coin beside a ticket box belongs with the money collected for tickets. They must then explain their reasoning. Aligns with A-CED.A and...
Illustrative Mathematics
Illustrative Mathematics: A Ced Bernardo and Sylvia Play a Game
In this task about an algebra game, students must create and reason with algebraic inequalities. Aligns with A-CED.A.3 and A-CED.A.1.
Illustrative Mathematics
Illustrative Mathematics: Locating Fractions Greater Than One on the Number Line
Students locate fractions greater than one on the number line. Aligns with 3.NF.A.2. or CCSS.Math.Content.3.NF.A.1 Standard 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram....
Illustrative Mathematics
Illustrative Mathematics: 3.nf Closest to 1/2
Students find which number is closest to 1/2. Aligns with 3.NF.A.2/CCSS.Math.Content.3.NF.A.1 Standard 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.
Illustrative Mathematics
Illustrative Mathematics: 3.nf Find 1 (On the Number Line)
The purpose of this task is to assess whether students understand fractions as being built from unit fractions and whether they can accurately locate fractions on the number line. Aligns with 3.NF.A.2/CCSS.Math.Content.3.NF.A.1 Standard...
Illustrative Mathematics
Illustrative Mathematics: 3.nf Find 7/4 Starting From 1, Assessment Variation
Students find 7/4 starting from 1. Aligns with 3.NF.A.2; CCSS.Math.Content.3.NF.A.2.a Represent a fraction 1/b on a number line diagram
Illustrative Mathematics
Illustrative Mathematics: a.apr Combined Fuel Efficiency
The purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context, in this case, the fuel efficiency of a car. A-APR.D.6.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes, Factorization of Quadratic Polynomial Ii
This task is intended to help students see more clearly the link between factorization of polynomials and zeroes of polynomial functions. The argument here generalizes to show that a polynomial of degree d can have at most d roots....
Illustrative Mathematics
Illustrative Mathematics: A Apr the Missing Coefficient
The purpose of this task is to emphasize the use of the Remainder Theorem as a method for determining structure in polynomials in equations, and in this particular instance, as a replacement for division of polynomials. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: A Apr Egyptian Fractions Ii
In this task, students will rewrite fractions as a sum of distinct unit fractions. To solve the problem, students will rewrite a simple rational expression and will need to study the arithmetic of these unit fractions with a variable in...
Illustrative Mathematics
Illustrative Mathematics: 5.md Cari's Aquarium
This task supports the standard 5.MD.5.b in that it asks students to use the volume formula and conceptual understanding to solve real-world problems.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of a General Polynomial
In this task, students investigate the properties of a polynomial of degree d > 0. The task relates to the Fundamental Theorem of Algebra. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: A Apr Zeroes and Factorization of Quadratic Polynomial
This is the first of a series of problems building to an understanding of an important property of polynomial functions, that a polynomial of degree d can have at most d roots. Aligns with A-APR.B.2.
Illustrative Mathematics
Illustrative Mathematics: 3.nbt Rounding to 50 or 500
Students explore different rounding scenarios. Aligns with CCSS.Math.Content.3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
Illustrative Mathematics
Illustrative Mathematics: A Apr Trina's Triangles
For this task, students investigate polynomial identities in order to generate Pythagorean triples. Aligns with A-APR.C.4.
Illustrative Mathematics
Illustrative Mathematics: 3.md the Square Counting Shortcut
This is a rectangle subdivision task; ideally instead of counting each square. students should break the letters into rectangles, multiply to find the areas, and add up the areas. Aligns with 3.MD.C: CCSS.Math.Content.3.MD.C.6 Measure...
Illustrative Mathematics
Illustrative Mathematics: 3.nbt, 4.nbt Rounding to the Nearest 100 and 1000
This task builds off of the skill of rounding to the nearest ten and hundred in third grade. Aligns with CCSS.Math.Content.3.NBT.A.1 Use place value understanding to round whole numbers to the nearest 10 or 100.
Illustrative Mathematics
Illustrative Mathematics: 3.nbt Rounding to the Nearest Ten and Hundred
The purpose of this task is for students to practice rounding numbers to the nearest ten, connect the rules for rounding with location on the number line, and to introduce the idea of rounding to the nearest 100. Aligns with...
Illustrative Mathematics
Illustrative Mathematics: 3.oa, Md, Nbt Classroom Supplies
The purpose of this task is for students to solve problems involving the four operations and draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Aligns with 3.NBT.A.2;...
Illustrative Mathematics
Illustrative Mathematics: A Rei Pairs of Whole Numbers
The premise of this problem is simple - students must find three whole numbers with three different sums when they are added in pairs. To do this, they set up a system of linear equations in three variables. Aligns with A-REI.C.6.
Illustrative Mathematics
Illustrative Mathematics: A Rei Quinoa Pasta 3
For this problem, students must determine how much of a quinoa-based gluten-free pasta is actually quinoa. They must study the ingredient list and set up linear equations to solve the problem. Aligns with A-REI.C.6.
Illustrative Mathematics
Illustrative Mathematics: A Rei Quinoa Pasta 2
For this problem, students must determine how much quinoa and how much corn are in a type of pasta. They must study the ingredient list which shows the protein content of the pasta. They know that quinoa has more protein than corn and...