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: Drawing Pictures to Illustrate Decimal Comparisons
The purpose of this task is for students to compare decimal numbers using pictures or diagrams. Aligns with 5.NBT.A.3.b.
Illustrative Mathematics
Illustrative Mathematics: Using Volume Associative Property of Multiplication
The purpose of this task is for students to use the volume of a rectangular prism to understand the associative property of multiplication. Aligns with 5.MD.C.5.a.
Illustrative Mathematics
Illustrative Mathematics: 5.nbt Kipton's Scale
The purpose of this task is to help students recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left...
Illustrative Mathematics
Illustrative Mathematics: 5.nbt Marta's Multiplication Error
This task highlights a common misconception among students deriving the rules for multiplying a number by a power of 10. Aligns with 5.NBT.A.2.
Illustrative Mathematics
Illustrative Mathematics: 3.md Finding the Area of Polygons
The purpose of this instructional task is for students to find the area of figures that can be decomposed and then recomposed into rectangles. Aligns with 3.MD.C.6. CCSS.Math.Content.3.MD.C.7.d Recognize area as additive.
Illustrative Mathematics
Illustrative Mathematics: 3.md, 3.g, 3.nf Halves, Thirds, and Sixths
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are...
Illustrative Mathematics
Illustrative Mathematics: A Apr Egyptian Fractions Ii
In this task, young scholars 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...
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: 3.g Geometric Pictures of One Half
This task presents students with some creative geometric ways to represent the fraction one half. Aligns with 3.G.A.2.
Illustrative Mathematics
Illustrative Mathematics: 5.md Box of Clay
This task provides an opportunity to compare the relative volumes of boxes in order to calculate the mass of clay required to fill them. Aligns with 5.MD.C.
Illustrative Mathematics
Illustrative Mathematics: 3.g Representing Half of a Circle
This task asks which pictures represent half of a circle? Moving into more complex shapes where geometric arguments about cutting or work using simple equivalences of fractions is required to analyze the picture. Aligns with 3.G.A.2.
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
In 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.md Three Hidden Rectangles
The purpose of this task is for students to decompose a figure into rectangles and then find the total area by adding the area of all of its smaller, non-overlapping rectangles. Aligns with 3.MD.C.7.d.
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.nf Find 2/3
This simple-looking problem reveals much about how well students understand unit fractions as well as representing fractions on a number line. Aligns with 3.NF.A.2/CCSS.Math.Content.3.NF.A.2.a Represent a fraction 1/b on a number line...
Illustrative Mathematics
Illustrative Mathematics: 3.md Shapes and Their Insides
The purpose of this task is to help students differentiate between a polygon and the region inside of a polygon so that they understand what is being measured when the perimeter and area are being found. Aligns with 3.MD.D.