LearnZillion Math incorporates three threads throughout grades K-8 in order to provide clear and important connections. These threads are Operations, Number, and Equivalence. The threads create a consistent focus as students progress from early work with numbers to arithmetic to algebra.

Each Unit Overview page describes how Operations, Number, and Equivalence appear in the Unit, and each lesson fosters a connection to one of the threads.

Watch this video to learn more about the Three Curriculum Threads in the LearnZillion Math curriculum.

**Operations**

**Why is Operations a thread?**

From arithmetic to algebra and beyond, students draw on a deep understanding of the four basic operations and the connections among them to solve problems. Operations is a thread throughout LearnZillion Math so that these connections are reinforced as students operate with new types of numbers in more complex situations.

**How is the Operations thread woven into LearnZillion Math?**

Students learn the meanings and connections between operations in a way that extends to using the operations with the different types of numbers they know. The structure of operations and their properties are highlighted each time the operations are used with a new type of number.

**What representations and models are used to deepen students' understanding of Operations?**

The curriculum makes use of several representations and models, providing students with multiple ways to represent and model problem situations. Area models, arrays, tape diagrams, and, of course, number lines support students as they solve problems.

**Number**

**Why is Number a thread?**

Developing number sense means learning to use numbers flexibly when reasoning abstractly and quantitatively. Number is a thread throughout LearnZillion Math because students are continually building and using number sense.

**How is the Number thread woven into LearnZillion Math?**

From their first experience with counting to their ultimate use of irrational numbers, students incorporate each new type of number they learn into their sense of "number." Students learn about uses for numbers, including counting, measuring, and scaling in a way that makes new types of numbers make sense.

**What representations and models are used to deepen students' understanding of Number?**

Number concepts are unified through extensive use of the number line, helping students to develop a "mental number line" they can draw on for reasoning about quantities.

**Equivalence**

**Why is Equivalence a thread?**

The equal sign is perhaps the most recognizable math symbol to students. However, many students see this symbol as an indicator of where to place their answer rather than as a powerful relational symbol. The use of the equal sign to symbolize equivalent values allows us to be flexible with equivalent forms of numbers and represent relationships among quantities, which are both crucial aspects of algebraic thinking.

**How is the Equivalence thread woven into LearnZillion Math?**

Very early in the curriculum students are asked whether statements of equivalence are true or false, basically "Are these two values the same or not?" Later, as students begin to solve problems and calculate with a variety of numbers, they use the equal sign to represent relationships in problem situations and to leverage the connections among the four basic operations.

**What representations and models are used to deepen students' understanding of Equivalence?**

To support their exploration and use of equivalence, students use a variety of models, including number lines, bar models, and double number lines.