Lower School (Preschool - Grade 5)

# Mathematics

Lower School math instruction focuses on how and why math works so that students develop number sense, problem-solving skills, and a facility with numbers that will enable them to use math in real-life situations. We follow the scope and sequence of Math in Focus, which is the U.S. edition of the math curriculum used in Singapore, a country at the forefront of mathematics teaching and learning for the last 15 years. The Math in Focus curriculum focuses on fostering deep understanding in mathematics by exploring concepts in depth, emphasizing problem solving, and using a concrete-pictorial-abstract approach to promote mastery. Unlike traditional math instruction, which tends to focus on skill-drilling and memorization of a wide variety of math facts and functions each year, Singapore Math presents a limited number of concepts at each grade level and encourages mastery through a process that moves from concrete manipulation to pictorial representation to abstract reasoning. The goal is to help students understand math at a deeper level than that which is needed to perform well on a traditional math test. To that end, Singapore Math focuses on problem-solving and, over time, prepares students to tackle increasingly difficult topics, such as fractions and ratios, in preparation for the study of algebra and geometry in Middle School.

### List of 7 items.

• #### Early Childhood Development

Mathematical thinking in the early childhood classroom is a process of developing a strong sense of number, spatial, and pattern awareness through hands-on inquiry based experiences. We give the children many different opportunities to increase number fluency and automaticity using an extensive range math manipulatives such as Pattern blocks, Cuisenaire rods and Unifix Cubes and through daily exposure to block building work. Students learn to engage in mathematical concepts through activities such as counting leaves on a branch, counting how many teddy bears in a bowl or the amount of cups needed for each classmate. They verbalize their discoveries, naturally using words and phrases like longer than, shorter than, and equal to. They sort, count, compare, and reflect as they manipulate concrete materials. Children are encouraged to explore the materials freely to encourage independent discovery.

Math lessons are designed foster the recognition of math all around us in the everyday world. A mini math lesson will often happen intuitively at the snack table when a child is counting out how many cups or napkins the group may need. Children will have the opportunity to develop a strong number sense and to make quantity and symbol relationships. “What is a way to show how many teddy bears there are in this group?” The children learn that amounts can be showed in different visual ways either by number symbol or graph. They are beginning to make connections between number symbols and quantity. They learn to see the patterns and shapes of things and math as a meaningful part of life experiences.
• #### Kindergarten

The Kindergarten math program presents a coherent sequence of topics and gives students time to master foundational concepts, so that little repetition is required the next year. The approach begins with the concrete, progresses to the pictorial and culminates in the abstract, and forms the framework of the math program. Thus, the emphasis in the Kindergarten math curriculum is on presenting fewer topics, with each topic explored in depth.

Kindergarten students learn numbers, operations and algebra. Concepts covered in these areas are comparing and ordering, whole number computation, patterns, models, equality and inequality. In geometry, the Kindergarten program introduces size and position, and two- and three-dimensional shapes. Through measurement, students experience length and distance, weight/mass, capacity and volume. The program also lends itself to data analysis, problem solving, reasoning and proof. Students are given the opportunity to recognize connections in mathematical ideas and understand how concepts build on one another. The Kindergarten math program allows for the student to use representations to model, organize, and record.

In first grade, math instruction follows a curriculum that develops mastery through a process that moves from concrete manipulation to pictorial representation to abstract reasoning. The goal is to help students understand math at a deeper level than what is needed to perform well on traditional math tests. Among the areas covered in first grade are: sets and numbers; counting to 100; skip counting by 2s, 5s, and 10s; comparing and ordering numbers; number bonds; whole number addition and subtraction; number sentences; number stories; place value; money; estimation and mental math; shapes and solids; measurement; data analysis; problem-solving; and critical thinking. In addition, students are regularly challenged to explain their problem-solving strategies, both verbally and on paper. Based on ongoing assessments, students receive differentiated instruction, extra practice, or enrichment as needed.

In math, the objectives for the second grade support three goals for students: to become mathematical problem solvers, to be able to communicate and reason mathematically, and to make mathematical connections. Concepts are introduced and developed through the use of models and hands-on-materials. The concrete (models or manipulatives), pictorial (visual models or drawings) and abstract (symbols), the C-P-A approach, help build understanding and application of concepts taught as they focus on numbers 1-1,000. This approach is designed to provide more in-depth instruction in the math strands of number concepts, operations, math fact fluency, measurement, geometry and data collection and analysis. Students are prompted to explain their thinking when they are solving problems, and encouraged to use “math talk” when describing the strategies they used to problem solve.

The third grade math program aims to produce engaged and creative problem solvers. While continuing to develop fluency of basic math facts, third graders are required to think critically during math lessons. Using our math program and a variety of supplemental material, students are introduced to various math concepts using manipulatives, read-alouds, and a variety of hands-on experiences. Through consistent practice and reinforcement, students learn to rely less on concrete models, and begin to problem solve and think abstractly. Students begin each math unit with a review of previously taught concepts, enabling them to draw and build upon prior knowledge.

Throughout the year, third graders explore mathematical patterns, develop number sense, understand and apply concepts of multiplication and division, and solve real world problems involving all four basic operations, and enhance their understanding of fractions. Direct instruction of problem solving tools and strategies provides a clear framework for organizing information and planning to solve more complex problems. Studies of concepts relating to time and money help students see the value of math in their everyday lives. Third graders actively discuss and practice using mental math strategies during “Number Talks,” which to enable students to explain their mathematical thinking and compute numbers more efficiently. Finally, third graders often display a diversified ability in math. To ensure that students’ needs are met, pre-assessments are given for each new unit, and small group instruction is differentiated accordingly.

In fourth grade mathematics, students build a strong conceptual understanding through the use of hands-on manipulatives, as well as the reinforcement of their computational skills. In order to deepen comprehension, students begin the year with reviewing prior skills while continuing the year developing critical thinking skills and learning to solve real world problems. Topics covered range from place value to geometry.

Students become proficient in multiplying multiple digit numbers as well as fractions and decimals, in conjunction with multiplication, division of whole numbers, fractions and decimals.  Students demonstrate a clear understanding of graphs and their uses as well as interpreting data. They learn solve mathematical problems through reasoning and critical thinking. Students benefit from differentiated instruction and small group work allowing us to meet the needs of the individual child while they master each skill.