The DCPS Mathematics Department  is proud to offer Eureka Math as its K-11 mathematics curriculum. Eureka Math is a high quality Common Core aligned curricular resource that allows students the opportunity to engage in mathematics in a coherent, focused, and rigorous manner.

Math Cornerstones are fully aligned to Eureka modules, and make meaningful real-world connections through engaging and rigorous content, taught through proven, high-impact instructional models.

Search for materials by standard, grade level, or instructional model, or browse the full collection below.

## Kindergarten Math - Designing Monuments

Eureka Math Kindergarten Module 3

Inquiry / 5E

In this Cornerstone, students will take on the role of monument designers. Students will examine monuments from the National Mall, create their own unique monuments, and compare them to their peers’ creations. Following the 5E instructional model, students will be challenged to apply their understanding of describing and comparing attributes of objects and shapes. Students will have the opportunity to construct viable arguments and attend to precision as they plan and create their monuments. Teachers will guide students and provide feedback with targeted questions and prompting support. Click here to access the full Cornerstone on Canvas.

Standards

K.MD.A.1 Describe measurable attributes of objects such as length or weight. Describe several measurable attributes of a single object.

K.MD.A.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/ “less of” the attribute, and describe the difference.

K.G.B.4 Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).

K.G.A.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to.

## Kindergarten Math - Numbers Fair

Eureka Math Kindergarten Module 1

Inquiry / 5E

In the first Kindergarten math Cornerstone, students will take on the role of mathematicians, fair staff, and fair visitors. The classroom will transform into a number fair at which students will demonstrate their expertise in numbers one through ten. Following a small group instructional model, students will be challenged to apply their understanding of counting and cardinality to create a number display and set up an interactive activity for their peers. Students will have the opportunity to plan, reason, attend to precision, and choose appropriate tools to engage in multiple number-based activities and the teacher will be able to monitor students as they create their displays. Click here to access the full Cornerstone on Canvas.

Standards

K.CC.B.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

K.CC.B.4.A When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

K.CC.B.4.B Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

K.CC.B.5 Count to answer "how many?" questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

## Grade 1 Math - Bracelet Bonds

Eureka Math Grade 1 Module 1

Inquiry / 5E

In the 1st first grade Cornerstone, students take on the role of mathematicians and designers. Students get to create a beaded bracelet using subtraction skills, utilizing number bonds as a strategy to subtract. Following a 5E instructional model, students are challenged to apply their understanding of subtraction as a way to determine how many beads are needed to complete bracelet construction. Students have an opportunity to plan, reason, design, and attend to precision as they work to create a bracelet that demonstrates a doubles fact, where some beads are missing. In addition, students will learn to provide and apply feedback as a means of creating an excellent Cornerstone product. Students will be able to look at their bracelet and recognize and explain to others that as a finished product, it shows a doubles fact where both colors are balanced. Finally, students will get to keep and wear their bracelets as a reminder of how using math skills is useful in designing their bracelet. Click here to access the full Cornerstone on Canvas.

Standards

1.OA.1 Use addition and subtraction within 20 to solve problems.

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

## Grade 1 Math - A Place Where Money Matters

Eureka Math Grade 1 Module 4

Inquiry / 5E In the 2nd first grade Cornerstone, students take on the role of mathematicians as store clerks and customers. Students will be required to show a 2-digit number as tens and ones, using dimes for tens and pennies for ones. Following a 5E instructional model, students are challenged to apply their understanding of place value in purchasing items from a classroom store with dimes and pennies. Students have an opportunity to model numbers and attend to precision as they decide how many dimes and pennies they will need to purchase items. Additionally, they create a purchase order explaining the item’s cost and the coins they used to make their purchases. Students are also expected to provide feedback to partners and apply their partner’s feedback to their work as a means of creating an excellent Cornerstone product. Finally, students will get to keep, show off, and even eat the items they have purchased. Click here to access the full Cornerstone on Canvas.

Standards

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

## Grade 2 Math - Titles

Eureka Math Grade 2 Module 3

Inquiry / 5E

In the first 2nd grade Cornerstone, students take their inspiration for their work from book titles that include numbers or number words. They begin by recognizing the intersection of literature and mathematics. Following a 5E instructional model, students are challenged to apply their understanding of place value, value comparisons, and multiple representation of amounts. Students have an opportunity to plan and express their reasoning based on their own book title selections. An engagement suggestion leading into this Cornerstone is to display several books (the same or different ones used in the activity) in the classroom before and during the activity and discuss how you can find math and numbers in books. Click here to access the full Cornerstone on Canvas.

Standards

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

2.NBT.1a 100 can be thought of as a bundle of ten tens — called a "hundred."

2.NBT.1b The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.

2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

## Grade 2 Math - Party Planning

Eureka Math Grade 2 Module 5

Inquiry / 5E

In the second Cornerstone for 2nd Grade, students will take on the role party planners, where they will be responsible for planning a birthday party of their liking to increase their fluency and accuracy with addition and subtraction word problems within 1,000. For the party, they will be given a budget of \$750. They will use their addition strategies, such as chip place value charts, regroup below notation, and the arrow notation, to calculate the prices of the items that they choose to purchase. If necessary, they will use these same strategies to reduce their total in order to meet the given budget of \$750 budget.

The final student product will be a tableau, drawn out by the student on chart paper, which displays all of the items they have purchased for their birthday party. All of the items in the drawing will be labeled with price tags to be used as evidence that the student has remained on budget. Students will use strategies, including mental math, adding or subtracting multiples of 10, using the associative property, and using other math drawings to represent addition and subtraction operations. Click here to access the full Cornerstone on Canvas.

Standards

2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties of operations. (Explanations may be supported by drawings or objects.)

## Grade 3 Math - Area Architects

Eureka Math Grade 3 Module 4

Modeling

In this Cornerstone, students will take on the roles of architects and mathematicians. Following a 5E instructional model, students begin this Cornerstone by viewing floor plans of several national and international landmarks. Next, students analyze a floor plan, measure the side lengths, and calculate the area of each room. Then, students respond to their client's request and must redesign the side lengths of each room while maintaining the original area. Students have the opportunity to share their final floor plan with their classmates and participate in an interactive discussion, defending their use of strategies and comparing/contrasting their floor plan with their peers'. Students will have the opportunity to plan, reason, attend to precision, choose appropriate tools, and model with mathematics while exploring the career field of architecture. Click here to access the full Cornerstone on Canvas.

Standards

3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).

3.MD.7 Relate area to the operations of multiplication and addition.

3.MD.7b Multiply side lengths to find areas of rectangles with whole-number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.

3.MD.7d Recognize area as additive. Find the areas of rectilinear figures by decomposing them into non-overlapping rectangles and adding the areas of the non-overlapping parts, applying this technique to solve real world problems.

## Grade 3 Math - Classroom Flag Design

Eureka Math Grade 3 Module 5

Inquiry / 5E

In this Cornerstone, students take on the role of designers. After students engage in Lesson 27 of Module 5, they will watch a short presentation of "The Principles of Designing a Flag." At the end of the presentation, they will turn and talk to discuss how after having learned about equivalent fractions, they have the skills to be able to design a flag of their choice. Following a 5E Instructional Model, students are challenged to apply their understanding of equivalent fractions using partitioning of a whole to design a class flag into their own creative representation of their classroom flag. Students have an opportunity to plan, design, and demonstrate mastery of equivalent fractions by being able to "redesign" their own class flag original design. Finally, using an evaluation checklist, students evaluate their work product against criteria during a Class Flag exhibition. They will explain the meaning and the symbolism behind their creation, adding academic vocabulary to their written explanation. Click here to access the full Cornerstone on Canvas.

Standards

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

3.NF.3b Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

## Grade 4 Math - Theater Seating

Eureka Math Grade 4 Module 3

Inquiry / 5E

In the 1st grade 4 Cornerstone task, students serve as advisors to city council as they take on the role of architects and apply their understanding of factors, multiples, and divisibility to determine all possible seating arrangements for a 100-seat movie theater6. Students then select a seating arrangement and recommend it to city council. The task culminates with students building the seating arrangement that they have recommended. Students receive feedback on the seating arrangement model based on one of the craft quality indicators. The task is structured into a 5-E instructional model. Click here to access the full Cornerstone on Canvas.

Standards

4.OA.4 Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1-100 is prime or composite.

## Grade 4 Math - Let's Have a Ball

Eureka Math Grade 4 Module 5

Inquiry / 5E

In the 2nd fourth grade Cornerstone task, Let’s Have a Ball, students participate in a basketball shooting investigation to collect data that will be used to compare and order fractions. Students create a basketball trading card that synthesizes their understanding of comparing and ordering fractions. The task is structured into a 5-E instructional model. Students use a checklist and descriptive feedback from the teacher to support them in producing a quality product (the basketball trading card). Click here to access the full Cornerstone on Canvas.

Standards

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, data-preserve-html-node="true" and justify the conclusions, e.g., by using a visual fraction model.

## Grade 5 Math - Dream Makerspace

Eureka Math Grade 5 Module 2

Inquiry / 5E

In this Cornerstone, students learn how to purchase items within a budget as they evaluate and select Makerspace technologies, tools, and gadgets for their dream makerspace. Students will apply content knowledge of decimal multiplication as they calculate the total price. Through project based learning, students will (1) review a list of technologies, tools, and gadgets; (2) select products and calculate the price using decimal multiplication; and (3) create a makerspace layout. Students will use the quality indicator rubric as they create their final product; additionally, students will receive feedback from their peers and teacher. Ted Talks and videos of other classroom makerspaces will be used as resources for this Cornerstone. Click here to access the full Cornerstone on Canvas.

Standards

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

## Grade 5 Math - Larger and Smaller

Eureka Math Grade 5 Module 4

Inquiry / 5E

In this Cornerstone, students will take on the roles of illustrators and storytellers. Students begin this Cornerstone by reading excerpts from Alice in Wonderland, in which she eats pieces from a magical mushroom that lets her grow or shrink, and they then see examples of scaling in other forms of media, such as from the films Ant Man and Honey, I shrunk the kids!. Using project-based learning, students will explore the mathematical concept of the ways in which factors (greater or smaller than one whole) can make a product larger or smaller with respect to the other factor, and then they will create a comic strip that illustrates a character who can grow and shrink (with mathematically correct drawings), as well as a “behind the scenes” page that includes mathematical, visual, and written proofs of how multiplication can function as a scale factor. Students will use a rubric and engage in a process of feedback via a series of revisions as they work towards their final product. As a supplement to the concept of growing or shrinking, teachers may incorporate mini-lessons about how scale can be used in architectural drawings or plans. Click here to access the full Cornerstone on Canvas.

Standards 5.NF.5 Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (nxa)/(nxb) to the effect of multiplying a/b by 1.

## Grade 6 Math - Camp Minihaha

Eureka Math Grade 6 Module 3

Inquiry / 5E

In this Cornerstone, the 6th grade is planning its annual Outdoor Education trip. As campsite planners, students will design the campsite while following specific criteria. Students are tasked with using their knowledge of the coordinate plane to plot the amenities, determine the location of various activities, and plan the distances between locations strategically. Following a 5E instructional model, students are challenged to demonstrate their understanding of rational numbers and the coordinate plane. Students have an opportunity to plan, solve problems, collaborate, and attend to precision as they create a map of the campsite and explain their mathematical reasoning. Click here to access the full Cornerstone on Canvas.

Standards

6.NS.C.6: Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

6.NS.C.6.B: Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

6.NS.C.6.C: Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.C.7: Understand ordering and absolute value of rational numbers.

6.NS.C.8: Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.

## Grade 6 Math - Design a Robot

Eureka Math Grade 6 Module 5

Modeling

In this Cornerstone, students will take on the role of toy developers and design a robot. The final task will ask students to create a prototype of a robot made of several 3-dimensional shapes to convince the toy company to use their design for the toy. Following a project based instructional model, students will plan the dimensions for each of the robot’s body parts, find the surface area and volume to know how much material is needed and finally create the prototype using nets cut from cardstock filled with modeling clay. Students are challenged to apply their understanding of nets, surface area and volume, of rectangular prisms and cubes, to model a real-life situation and construct an argument to defend their product. As toy developers for the same company, students will nominate the best robot prototype, based on given criteria, to be printed from a 3-dimensional printer. Click here to access the full Cornerstone on Canvas.

Standards

6.G.A.2Find 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.

6.G.A.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problem.

## Grade 7 Math - Super Pencil

Eureka Math Grade 7 Module 1

Inquiry / 5E

In this Cornerstone, students take on roles of investigators and mathematicians. Using proportional reasoning, students will justify how large a super hero is. Following the 5E instructional model, students work together to justify the height of their hero, based on the pencil that he left behind. Students have the opportunity to create and evaluate equations as they work to determine if the pencil the hero left behind is proportional to their own. Finally, students work to find the new height of their hero’s pencil after a percent decrease. Click here to access the full Cornerstone on Canvas.

Standards

7.RP.2 Recognize and represent proportional relationships between quantities.

7.RP.2.A Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.

7.RP.2.C Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

7.RP.3.A Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error.

## Grade 7 Math - One Scoop or Two

Eureka Math Grade 7 Module 3

Inquiry / 5E

In this Cornerstone, students algebraically explore the prices at ice cream shops as customers and shop owners. Students first examine pricing models as consumers and then switch their perspectives as consultants for a shop owner. They use their mathematical reasoning and critical thinking skills to make recommendations to address the shop manager’s concerns and increase revenue. Following the 5E instructional model, students are challenged to apply and extend their understanding of expressions, equations and inequalities. Students have the opportunity to solve problems, reason, and attend to precision as they examine aspects of an ice cream shop as mathematicians. Click here to access the full Cornerstone on Canvas.

Standards

7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

7.EE.B.4. Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities.

7.EE.B.4.A Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

7.EE.B.4.B Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid \$50 per week plus \$3 per sale. This week you want your pay to be at least \$100. Write an inequality for the number of sales you need to make, and describe the solutions.

7.RP.A.2 Recognize and represent proportional relationships between quantities.

## Grade 8 Math - H2Whoa!

Eureka Math Grade 8 Module 4

Inquiry / 5E

In this Cornerstone, students will take on the role of a food truck owner and determine where to buy water bottles to stock their truck. The final task will ask students to write a report to a business partner that proposes which wholesale store is best to purchase a membership and water bottles. Following a 5E instructional model, students will research the cost of memberships and water bottles from various wholesale distributors, create equations to mathematically represent the costs, graph the system of equations, and make a final decision of where to buy water. Students are challenged to apply their understanding of systems of equations to model an authentic real-life situation and construct an argument to justify their conclusion. Using laptops or tablets, students will explore prices and graph the system using specified websites. Click here to access the full Cornerstone on Canvas.

Standards

8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed.

8.EE.C.8 Analyze and solve pairs of simultaneous linear equations. Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously.

1. Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations.
2. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6.
3. Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

## HS Algebra I - Algebraic Advocacy

Eureka Math Algebra I Module 2

Inquiry / 5E

Students will use statistics to advocate for an issue that has a personal impact on members of their school community. Students will collect and analyze data on two quantitative variables, employ statistical methods in order to select the most effective ways to organize and display their data, and form a valid argument as the foundation of their advocacy campaign. Students will examine the elements of successful advocacy campaigns, apply these elements to their own campaigns, and then undergo a peer review process, engaging them in discourse about the issues they selected. Finally, students will present their findings and potential solutions to an audience comprised of school and community stakeholders. Click here to access the full Cornerstone on Canvas.

Standards

S-ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.A.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S-ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S-ID.B.6 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.

S-ID.B.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related

S-ID.C.9 Distinguish between correlation and causation.

## HS Algebra II - Sunrise to Sunset

Eureka Math Algebra II Module 2

Modeling

In the Sunrise to Sunset Cornerstone, students take on the role of business development consultants working to advise Amazon.com on where to build a new solar powered facility. Students will collect and analyze astronomical data from the US Naval Observatory to determine a trigonometric model that best represents the number of daylight hours for three different cities and represent it numerically, graphically and algebraically. Students will work on a team and discuss how to fit the data to mathematical models, and then will independently use a graphing calculator to conduct a regression analysis on the same data and compare the two models. While the focus of this Cornerstone is sinusoidal data modeling, concepts of astronomy will be included to provide a point of reference for the students. Click here to access the full Cornerstone on Canvas.

Standards

F-lF.C7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases, and using technology for more complicated cases.

F-TF.B5 Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

S-lD.B6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.