Tools4NCTeachers is designed to support North Carolina's Standard Course of Study for K-5 mathematics. The resources are supplemental, intended to serve as model lessons and tasks. They are not a curriculum with a scope and sequence for daily instruction.

The grade level resources are organized around the North Carolina Collaborative for Mathematics Learning (NC2ML) Instructional Frameworks. Each grade's Instructional Framework contains 7-9 clusters, designed to foster student' understanding and the making of connections among mathematical ideas and procedures.

Unit 6: Expressions and Equations
Lesson 2: Truth and Equations

Students begin the lesson by digging into what it means for an equation to be true or not true. They expand previously-held understandings of equations by thinking about the assumption that equations are always true. Students learn that a letter standing in for a number is called a variable. Students learn that, for an equation with a variable, a value of the variable that makes the equation true is called a solution of the equation. They find solutions to equations by using tape diagrams or reasoning about the meaning of "solution" once an equation is written.

This lesson is where "next to" notation is introduced (for example, 10m means 10 x m).

This Nrich game is designed to get children used to moving along a number line either side of a central point adding and subtracting within 27. It can help to introduce the idea of negative numbers or practice fluency with negatives by changing the midpoint to 0.

In order to show the world that the completed Brooklyn Bridge was strong enough, P.T. Barnum and his twenty-one elephants parade across to prove to everyone that the bridge is safe. The resource includes a lesson plan/book card, a design challenge, and copy of a design thinking journal that provide guidance on using the book to inspire students' curiosity for design thinking. Maker Challenge: Build a bridge between two tables or chairs that will hold one elephant per student in the class. Each student designs their own “elephant” using materials in the classroom.

A document is included in the resources folder that lists the complete standards-alignment for this book activity.

This Nrich problem introduces an intriguing trick which provides a context for practicing manipulation of fractions. Watching the video, or perhaps trying the trick out for themselves, can engage students' curiosity, and lead to some intriguing mathematics to explore and explain.

Unit 6: Expressions and Equations
Lesson 16: Two Related Quantities, Part 1

This lesson is the first of two that apply new understanding of algebraic expressions and equations to represent relationships between two quantities. Students use and make connections between tables, graphs, and equations that represent these relationships.

In this lesson, students revisit and extend their understanding of equivalent ratios. A familiar scenario of mixing paints in a given ratio provides the context for writing equations that represent the relationship between two quantities. Students then create a table of values that shows how changes in one quantity affect changes in the other, and graph the points from the table in the coordinate plane. They are invited to notice that these points lie on a line. Students will study proportional relationships in more depth in grade 7.

Students learn that relationships between two quantities can be described by two different but related equations with one quantity, the dependent variable, affected by changes in the other quantity, the independent variable. When people engage in mathematical modeling, which variable is considered independent and which is considered dependent is often the choice of the modeler (though sometimes the situation suggests choosing one way over the other). The context in this lesson was intentionally chosen because the context does not suggest a preference about which quantity is chosen as the independent variable.

Unit 6: Expressions and Equations
Lesson 17: Two Related Quantities, Part 2

In this second lesson on representing relationships between two quantities, walking at a constant rate provides the context for writing an equation that represents the relationship. Students use and make connections between tables, graphs, and equations that represent the relationship between time and distance. They use their representations to compare rates and consider how each of the representations would change if the independent and dependent variables were switched.

This Nrich problem is a fantastic opportunity for learners to apply knowledge of place value and offers a context for learning and practicing the relevant vocabulary (odd, even, multiple). The interactivity will help learners satisfy their curiosity in the sense of finding a 'better' solution, as it enables them to play around with the digits without having to commit anything to paper. This act of deciding whether one solution is better than another also provides a meaningful context in which to compare and order numbers.

This Nrich investigation is one that uses the very popular multilink cubes. It gives a wonderful opportunity for pupils to explore ways of recording. This activity is also designed to nurture children's curiosity by introducing mathematics into a familiar non-mathematical context. Children might end up pursuing different ideas from each other and this freedom to explore may well encourage learners to persevere more than they might usually. In this way, they will immerse themselves in the particular number sequence they have chosen to use, which will help them gain a deep understanding of its structure. This activity lends itself to pupils posing their own questions in the form “I wonder what would happen if...?”

This unit explores the introduction into Subtraction using the Common Core Format (Whole-Part-Part/Missing Part) and higher level thinking. This unit is being developed because I have found that it is a hard transition for students to go from addition to subtraction. Some portions will not be accessible as it is for District Supported Accounts through our Math Curriculum, Pearson envisionMath. The students will have the opportunity to explore independently, in small groups, in whole groups and one-on-one with myself. The various clips will allow a look into how to subtract using visuals and manipulatives. Students will also explore with partners and manipulatives to gain knowledge and understanding of the concept.
Many of my students are ELL or first timers, to a school setting, since Kindergarten is not required here in Michigan. This unit takes this into consideration that we have to start at base zero as if all of the students are at a lower level. Differentiation of groups and instruction/review will take place once the material is introduced and students' working levels are observed and assessed.

Unit 8: Data Sets and Distributions
Lesson 17: Using Box Plots

In the previous lesson, students analyzed a dot plot and a box plot in order to study the distribution of a data set. They saw that, while the box plot summarizes the distribution of the data and highlights some key measures, it was not possible to know all the data values of the distribution from the box plot alone. In this lesson, students use box plots to make sense of the data in context (MP2), compare distributions, and answer statistical questions about them.

Students compare box plots for distributions that have the same median but different IQRs, as well as box plots with the same IQRs but different medians. They recognize and articulate that the centers are the same but the spreads are different in the first case, and the centers are different but the spreads are the same in the second case. They use this understanding to compare typical members of different groups in terms of the context of the problem (MP2).

Unit 7: Rational Numbers
Lesson 18: Using Common Multiples and Common Factors

In this lesson, students apply what they have learned about factors and multiples to solve a variety of problems. In the first activity, students to use what they have learned about common factors and common multiples to solve less structured problems in context (MP1). The two activities that follow are optional. The optional activity "More Factors and Multiples" allows students to explore common factors and common multiples of 3 whole numbers and present their findings. The optional activity "Factors and Multiples Bingo" allows students to practice finding multiples and factors.

Unit 8: Data Sets and Distributions
Lesson 18: Using Data to Solve Problems

This lesson is a good opportunity for students to use the information they have learned in the unit and apply it to different situations, but may be shortened to fit time constraints.

In this lesson, students compare the center and spread of different distributions. They determine what these different measures (mean and MAD or median and IQR) represent in context. They select an appropriate representation for the distribution based on the structure of the data, an appropriate set of measures of center and spread, and interpret their meaning in the context (MP4).

For students who are curious why we are asking them to compute measures of center and variation by hand when computers would be more efficient and accurate, tell them that understanding the meaning of the values and knowing what questions to ask are skills computers have not yet mastered. By practicing with calculations on small data sets, students are becoming familiar with these measures as well as questioning skills so they can correctly interpret results from computers in the future. If students do not raise the question themselves, this point may be left until the topics are revisited in later grades.

Unit 5: Arithmetic in Base Ten
Lesson 1: Using Decimals in a Shopping Context

In previous grades, students learned how to add, subtract, multiply, and divide whole numbers and decimals to the hundredths place. In this unit, they will extend this knowledge to include to all positive decimals.

This lesson activates students’ previous experiences with the four operations, all in the context of planning for a party while staying within a budget (MP4). To do so, students make reasoned estimates and then compare them to actual calculated values. The lesson offers insights into students' understanding of operations and the structure of base-ten numbers before new concepts are introduced.

Unit 4: Dividing Fractions
Lesson 6: Using Diagrams to Find the Number of Groups

This is the second lesson in a series of three lessons exploring the “how many groups?” interpretation of division in situations involving fractions.
In the preceding lesson and in this one, the number of groups in each given situation is 1 or greater. In the next lesson, students find the number of groups that is less than 1 (“what fraction of a group?”).

Students have used different diagrams to represent multiplication and division. In this lesson, tape diagrams are spotlighted and used more explicitly. They are more abstract and more flexible than other representations students may have chosen for thinking about division problems that involve fractions. Because they use measurement along the length of the tape, tape diagrams are closer to the number line representation of fractions, and ultimately help students visualize division problems on the number line. (Students are not required to do that in this lesson, however.)

Students continue to make the journey from reasoning with concrete quantities to reasoning with abstract representations of fraction division (MP2).

Unit 5: Arithmetic in Base Ten
Lesson 2: Using Diagrams to Represent Addition and Subtraction

This lesson is optional. Prior to grade 6, students have added and subtracted decimals to the hundredths using a variety of methods, all of which focus on understanding place value. This lesson reinforces their understanding of place-value relationships in preparation for computing sums and differences of any decimals algorithmically.

In this lesson, students use two methods—base-ten diagrams and vertical calculations—to find the sum and differences of decimals. Central to both methods is an understanding about the meaning of each digit in the numbers and how the different digits are related. Students recall that we only add the values of two digits if they represent the same base-ten units. They also recall that when the value of a base-ten unit is 10 or more we can express it with a different unit that is 10 times higher in value. For example, 10 tens can be expressed as 1 hundred, and 12 hundredths can be expressed as 1 tenth and 2 hundredths. This idea is made explicit both in the diagrams and in vertical calculations.

Unit 5: Arithmetic in Base Ten
Lesson 7: Using Diagrams to Represent Multiplication

Students continue to use area diagrams to find products of decimals, while also beginning to generalize the process. They revisit two methods used to find products in earlier grades: decomposing a rectangle into sub-rectangles and finding the sum of their areas, and using the multiplication algorithm.

Students have previously seen that, in a rectangular area diagram, the side lengths can be decomposed by place value. For instance, in an 18 by 23 rectangle, the 18-unit side can be decomposed into 10 and 8 units (tens and ones), and the 23-unit side can be expressed as 20 and 3 (also tens and ones), creating four sub-rectangles whose areas constitute four partial products. The sum of these partial products is the product of 18 and 23. Students extend the same reasoning to represent and find products such as (1.8) x (2.3). Then, students explore how these partial products correspond to the numbers in the multiplication algorithm.

Students connect multiplication of decimals to that of whole numbers (MP7), look for correspondences between geometric diagrams and arithmetic calculations, and use these connections to calculate products of various decimals.

Unit 8: Data Sets and Distributions
Lesson 5: Using Dot Plots to Answer Statistical Questions

In this lesson, students continue to use dot plots to develop their understanding of center and spread—by identifying values of center, describing spread, comparing centers and spreads of different distributions, and making use of the structure of the distributions (MP7) to understand them in the context of situations (MP2). In future lessons, they will make their descriptions and analyses more precise, as they learn about measures of center and spread.

Students will use the Educreation App to work on two-step equations recording their voice to explain their thinking.

Unit 8: Data Sets and Distributions
Lesson 7: Using Histograms to Answer Statistical Questions

In this lesson, students create, read, and interpret histograms (MP2). They characterize the distribution displayed in a histogram in terms of its shape and spread, and identify a measurement that is typical for the data set by looking for the center in a histogram (MP7). Students also use histograms to make comparisons and to better understand what different spreads and values of center mean in a given context.