# Mathematics Curriculum Overview

The ITDS math program’s aim is to ensure all students become capable problem solvers who demonstrate confidence, success, and joy in mathematics. The Common Core State Standards for Mathematics, Illustrative Mathematics, and the Desmos math curriculum serve as guides to instruction, and we incorporate math read alouds, games, manipulatives, authentic tasks, and real-world projects to engage students in a variety of math activities and provide multiple ways for them to demonstrate their understanding of grade-level concepts. Our primary focus is on helping students make sense of mathematics. We spend significant time building a conceptual understanding of math topics so students understand the “why” behind mathematical ideas and procedures. We value student-derived strategies to solve problems and challenge our students to think flexibly about numbers and utilize increasingly efficient strategies. We use the Standards for Mathematical Practice and research in growth mindset to guide our work with students, ensuring that they become confident, capable, and successful mathematicians who see the connections between school mathematics and their world outside of ITDS.

Preschool, prekindergarten, and kindergarten: The foundations of literacy
Preschool and prekindergarten math focuses on manipulating concrete objects and tools to learn mathematical concepts and practice skills. Students will use toys, games, or other manipulatives to work on counting, one-to-one correspondence, numeracy, shapes, patterns, and sorting. As with other academic concepts, math learning is integrated throughout the day and often presented within the context of a topic of exploration (for example, sorting laundry during a unit on clothes). Math instruction occurs in whole group gatherings, small groups, and in independent play centers.

Kindergarten math focuses on two major areas- representing and comparing whole numbers, and describing shapes and space. Kindergarten students use both written numerals and sets of objects to represent and manipulate quantities. They explore and apply different strategies for answering quantitative questions such as how many in a set, and combining and taking away sets of objects. Students explore the physical world using geometric concepts. They work to identify and describe both 3D and 2D shapes, as well as recognize them within their environment. Kindergarteners are also introduced to basic measuring tools and how to use them.

Math 1-2
First and second-grade mathematics focuses on developing fluency with addition and subtraction, understanding whole number relationships and place value, using nonstandard and standard units of measurement, and exploring geometric shapes. First-grade students explore numbers within 100, learning a variety of strategies to add and subtract one- and two-digit numbers. They develop an understanding of our base-ten system and think of whole numbers between 1 and 100 in terms of tens and ones. They practice measuring the lengths of different objects and compose and decompose shapes in geometry. Second-grade students extend their knowledge of addition and subtraction and place value to explore three-digit numbers, including mental strategies for computation and practice with the addition and subtraction algorithms. Students also recognize the usefulness of standards unit of measure and begin measuring using rulers and other measurement tools. They describe and analyze shapes by examining their sides and angles.

In both grades, math read alouds, authentic math contexts, and math games play a key role in helping our students see themselves as mathematicians and engaging them in the work of mathematics. They learn to value different approaches to solving math problems and work to explain their math thinking using pictures, equations, and words.

Math 3-4
In grades 3 and 4, students develop an understanding of multiplication, division, and fractions through a variety of activities. In grade 3, students work to build fluency with their multiplication facts and learn the relationship between multiplication and division. They develop an understanding of fractions, beginning with unit fractions, and use their knowledge of numerators and denominators to compare fractions. Multiplication and fractions connect with geometry through explorations of area. In grade 4, students extend multiplication and division to larger numbers. They explore different strategies for solving multiplication and division problems, including arrays, place value charts, and algorithms, and solve multi-step problems with both operations. Key fraction concepts include operations with like denominators and fraction equivalence. Fourth graders learn key vocabulary related to 2D shapes, including parallel sides, perpendicular sides, and symmetry, and learn how to measure angles with protractors.

Math games and authentic math contexts continue to be a key feature of student learning. Students also engage in projects that connect math to the real world. In these grades, we challenge students to persevere through problems and work to balance conceptual understanding with procedural fluency.

Math 5-6
The mathematics program in grades 5 and 6 deepen student understanding of fractions, decimals, and whole number operations, as well as introduce students to ratios, proportions, expressions, and statistical distributions. In grade 5, students develop fluency with addition and subtraction of fractions and build conceptual understanding around fraction multiplication and division. They finalize their fluency with whole number addition, subtraction, multiplication, and division, and apply their base-ten understanding to operations with decimals. In geometry, students investigate volume through hands-on activities. In sixth grade, students use reasoning about multiplication and division to solve ratio and unit rate problems. They explore fraction division, with a focus on making sense of fraction division using manipulatives and models. Students extend their knowledge of the number system to the full system of rational numbers, including negative integers. They write expressions and equations with variables and solve one-step equations. In statistics, students learn different ways to measure central tendency, including mean, mean, and mode.

In both fifth and sixth grades, students engage in collaborative, hands-on activities in partnerships and small groups, giving plenty of opportunities for students to share their mathematical reasoning and listen to the reasoning of their peers. As students grow increasingly independent, their math projects become more in-depth with a wider range of student choice and connect to social justice topics.

Math 7
Students develop an understanding of proportional relationships, using their knowledge of ratios to solve single- and multi-step problems, including percent problems. Students learn how to graph proportional relationships and calculate and describe the slope of the line as a property used to describe a relationship. Students solve operations with rational numbers and begin to work with expressions and linear equations. They solidify their understanding of fractions, decimals, and percents as different ways to represent rational numbers while gaining proficiency in operations with negative numbers. In geometry, students learn to use two- and three-dimensional shapes to solve area, surface area, and volume problems. They also explore circles, developing an understanding of area and circumference of a circle. In statistics and probability, students draw conclusions about populations based on samples and compare data distributions to answer questions about different populations.

Math 8
Students learn to formulate expressions and equations, show the association of data with a linear equation, and to solve linear equations. Students use the linear equation, y = mx + b, to graph proportional relationships and understand that m represents the rate of change of the two variables and the graphs are lines through the origin. Students use linear equations to describe the relationship between two values in bivariate data. They also solve problems with one linear equation and systems with two linear equations. During a study of functions, students define, evaluate, and compare functions, and use functions to model relationships between quantities. Geometry is a core part of eighth-grade math. Students explore congruence and similarity and describe the effect of dilations, translations, rotations, and reflections of two-dimensional figures using the coordinate plane. Students understand the Pythagorean Theorem and explain why it is true. They use the theorem to find distances between points on the coordinate plane, find lengths and analyze triangles. Students complete their study of volume by learning to solve for the volume of cones, cylinders, and spheres.

Algebra
Topics introduced in Algebra 1 provide the foundation students require for future success in high school mathematics, critical thinking, and problem-solving. The primary goal in Algebra 1 is to help students transfer their concrete mathematical knowledge to more abstract algebraic generalizations. In this course, the students become proficient in recognizing and developing patterns using tables, graphs, and equations. They explore operations on algebraic expressions, apply mathematical properties to algebraic equations. Students solidify their understanding of how to solve problems using equations, graphs, and tables to investigate linear relationships. They identify structure in quadratic functions, absolute value expressions, radical expressions, rational expressions, and equations. Students also apply what they’ve learned to real-world concepts and tasks. Technology is used to introduce and expand upon the areas of study listed above. Computers and graphing calculators are incorporated whenever possible into each concept.