# Mathematics

Our workshop model for math instruction allows for independent practice on projects, and problems designed specifically for small-group instruction. The program challenges students at their individual level so they can continue to develop with full and flexible understandings.

## Preschool

### Approach to Mathematics

Preschoolers are concrete thinkers and mathematical learning is practiced every day. Students are provided with varied opportunities to engage in sorting, classifying, counting, patterning, and geometrical awareness.

### Goals

To prepare students for their mathematics learning in the years ahead, the preschool classroom includes materials that will later be part of direct math instruction, providing the students with a chance to meet, play with, and get to know cuisinaire rods and unifix cubes, for example. Their natural curiosity leads preschoolers to experiment with these materials in mathematical ways. Over the course of the year each student builds context for mathematical concepts motivated by self-propelled inquiry and experiential learning.

### Topics

• Saying number names up to twenty
• Counting with one-to-one correspondence
• Understanding that numbers signify a quantity
• Using “bigger,” “smaller,” and “the same” to describe differences between collections of objects
• Using informal language to describe shapes
• Recognizing when a story involves mathematics

## Kindergarten

### Approach to Mathematics

Math is integrated throughout the kindergarten program. Kindergarteners keep track of the days of school, noticing patterns in the base-10 number chart as they work towards the 100th day. They create graphs about community members as they learn about their identities and the identities of others, comparing and contrasting with peers.

### Goals

In planning topics of inquiry for the class, teachers find ways to integrate mathematics. They look for opportunities to differentiate instruction on counting, sorting, comparing, collecting and representing data, measuring, adding, and subtracting.

### Topics

• Counting principles
• Reading, writing, and saying numerals
• Comparing collections of objects
• Solving story problems with small quantities
• Adding and subtracting within 5
• Classifying objects by different attributes
• Describing measurable attributes of objects
• Identifying and describing shapes

## 1st

### Approach to Mathematics

First grade students move from concrete, hands-on experimentation with counting, sorting, and acting out mathematical work, toward more symbolic and abstract thinking required for writing equations and understanding our number system. Students work independently, with partners, and in teacher-led small groups, which allows for differentiated instruction and practice to meet each student where they are developmentally.

### Goals

In 1st grade, the primary goals are to develop number sense, an understanding of place value, the skill to combine and separate quantities, and the ability apply mathematical thinking to real-life situations and represent their mathematical thinking.

### Topics

Number sense: Students recall addition and subtraction facts within 10 with speed and accuracy; understand place value to the hundreds place, and understand that quantities can be combined and separated flexibly.

Data analysis: First graders learn to gather, collect, organize, and interpret data on various graphs.

Measurement: They use tools to measure, tell time to the nearest hour and half hour, name coins, know values, and count money.

Geometry: Students identify names and attributes of 2-dimensional and 3-dimensional shapes.

Problem solving: First grade students identify, choose, and use an appropriate strategy to solve and explain a problem, and use models, pictures, numerals, and words to illustrate thinking process when problem solving.

Algebra: They understand the relationship between addition and subtraction; identify unknowns in equations, and use addition, subtraction, and equals symbols to write equations to match mathematical models and scenarios.

## 2nd

### Approach to Mathematics

A developmental approach guides mathematics curriculum in 2nd grade. Because students develop mathematical understandings across a broad continuum, they are challenged in a just-right fashion so they will continue to develop with full and flexible understandings. They are provided with a workshop model for math instruction, which allows for independent practice on projects, and problems designed specifically for small-group instruction. Students receive instruction in both whole group settings and small flexible groupings.

### Goals

In 2nd grade, the primary goals are supporting students to make sense of mathematics, and helping them learn that they can be mathematical thinkers. They are guided to understand the reasoning behind mathematical ideas.

The focus in 2nd grade is on computational fluency with whole numbers. This includes substantive work in many areas of mathematics, and helping students understand the connections among them, including rational numbers, geometry, measurement, data, and early algebra.

### Topics

Numbers: Students develop the ability to read, write, and understand the meaning, order, and relative magnitudes of whole and fractional numbers. This is foundational for all future mathematics and is an ongoing process.

Operations: They build an understanding of the meaning, use, and connections between addition, multiplication, subtraction, and division.

Calculations: Students choose and use a repertoire of mental, paper, and calculator computational strategies for each operation, meeting needed degrees of accuracy and judging the reasonableness of the results.

Geometry: They visualize, draw, and model shapes, locations, and arrangements in order to predict and show the effect of transformations on them; solve problems, and justify solutions.

Measurement: Each student develops confidence and proficiency in using direct and indirect measurement and estimating skills to describe, compare, evaluate, plan, and construct.

Data analysis (probability and statistics): Students understand and use the everyday language of chance and make statements about how likely it is that an event will occur based on experience, experiments, and analysis. They collect, organize, summarize, and represent data in order to draw conclusions, taking into account data collection techniques and chance processes involved.

## 3rd

### Approach to Mathematics

In third grade, students learn to make sense of mathematical problems and persevere in solving them. They discuss problem-solving strategies and recognize the connections between them, and learn to construct viable arguments and critiques of the reasoning of others. Students explain their own thinking, respond to others' explanations, and ask appropriate questions.

### Goals

Students in 3rd grade learn to use precise mathematical language. The attention to precision informs their approach to problem-solving, and the ways they communicate about mathematics in their discussions and critiques. They learn that accuracy is essential not only in their calculations and measurements, but in the ways they speak, write, and use mathematical concepts.

The 3rd grade mathematics curriculum builds on the previous year’s instruction by introducing students to new and advanced concepts in decimal numbers, fractional numbers, operations, calculations, algebraic reasoning, measurement, geometry, and data analysis.

### Topics

Operations: Third graders use the four values (addition, subtraction, multiplication, and division) to solve two-step word problems. They use place value to fluently add and subtract within 1,000, and multiply and divide within 100, and understand the relationship between multiplication and division. Students know from memory all products of multiplication with two one-digit numbers.

Fractions: Third grade students demonstrate understanding of fractions as numbers on a number line; recognize and generate simple equivalent fractions, and learn to compare two fractions with the same numerator or denominator.

Measurement: They measure and estimate time, length, volume, and weight using standard units. Students can measure and explain the area and perimeter of two-dimensional shapes.

Graphs: Students learn to draw a scaled picture graph and scaled bar graph to represent a data set with several categories. They solve one- and two-step problems using information presented in scaled bar graphs.

Geometry: They identify and categorize the attributes of two- and three-dimensional shapes.

Strategies: When solving a problem, students understand which tools are the most appropriate to use (including objects, diagrams, and estimation), and use those tools strategically. Students make sense of problems and discuss problem-solving strategies.

## 4th

### Approach to Mathematics

In 4th grade, students begin to develop understanding of mathematical concepts that are complex, abstract, and powerful. They are increasingly capable of solving a wide variety of real-world problems. They engage in hands-on, experiential learning to develop a deep and flexible understanding of math.

### Goals

Students become autonomous and self-motivated in their mathematical activity. They gain knowledge from whole group instruction, independent explorations, reflection on their process, and participation in discussions.

Students engage in a wide variety of experiences where they generate conjectures that lead to experiments, reflection, and adaptation. Math workshops include sharing problem solving strategies and receiving feedback from peers.

### Topics

Surveys and graphs: Fourth grade students use data and graphs to understand the world and represent their ideas.

Place value, number sense, and large numbers: They work with large numbers and deeply understanding the place-value system.

Multiplication and division: Students develop concepts and multiple ways to model multiplication and division.

Money, decimals, and fractions: They understand fractional numbers and their real-world application.

2D and 3D geometry: Fourth graders create array models to understand calculations of area and how these concepts can help them conceptualize volume and 3D geometry.

Probability and statistics: Students collect and analyze data to help them see patterns and experiences more clearly.

Hands-on algebra: They work with the properties of mathematics to establish a foundation for algebra.