# Mathematics

Keys School uses the Singapore Math three-step approach. Lessons methodically progress from concrete examples to pictorial representations to more abstract concepts, mirroring the way in which students develop deep understanding. Concepts are introduced through hands-on investigation, then translated to paper-and-pencil images, and finally, into numerical and symbolic algorithms.

Instruction challenges students to apply concepts to new contexts and engage in extended exploration and discussion. Time and attention are given to sharing and evaluating one’s reasoning, as well as that of others. Math instruction spirals throughout the years, connecting current lessons to prior and future learning. Students encounter concepts and skills repeatedly, but with increasing complexity. Over time, students develop perseverance and flexibility with problem solving. Rather than memorizing isolated facts and procedures, students build skills in critical reasoning and communication, and a deep conceptual foundation.

**Highlights from the program include:**

## Kindergarten

- » Read simple graphs
- » Sort and classify by various attributes
- » Create, recognize, and extend patterns
- » Understand one-to-one correspondence
- » Deconstruct and reconstruct numbers in variety of ways
- » Use non-standard forms of measurement
- » Sequence and identify causality between events
- » Identify, describe, compare, and compose shapes

## First Grade

- » Order and compare objects, quantities, numbers
- » Use manipulatives to understand the value of numbers and the basic principles of addition and subtraction
- » Record solutions to problems using pictures, numbers, and words
- » Use multiple strategies to solve addition and subtraction problems
- » Gather, represent, and interpret simple data
- » Tell and write time

## Second Grade

- » Demonstrate number sense in whole numbers up to 1,000
- » Solve addition and subtraction problems with three-digit numbers
- » Work with equal groups as a foundation for multiplication
- » Tell time to the nearest five minutes; determine elapsed time
- » Model and solve problems involving time and money
- » Estimate, measure, and compare lengths in standard units
- » Represent and interpret data in tally charts, line plots, and graphs
- » Reason with shapes and attributes; classify and compare

## Third Grade

- » Demonstrate knowledge of place value to 100,000
- » Perform mental math using commutative, associative, distributive properties
- » Add and subtract within 10,000; solve multiplication and division problems
- » Use models to solve word problems involving the four operations
- » Measure and estimate length, mass, capacity
- » Recognize, name, compare, and order fractions
- » Calculate elapsed time
- » Represent and compare data using charts, tables, graphs
- » Conduct and analyze simple probability experiments

## Fourth Grade

- » Understand all four operations and compute efficiently
- » Use mental math and problem solving strategies flexibly and efficiently
- » Gain familiarity with factors and multiples
- » Generate and analyze numerical patterns
- » Use place value understanding to perform computations
- » Understand, order and compare fractions and decimals
- » Solve problems involving measurement; convert measurements
- » Draw, identify, classify and measure lines and angles

## Fifth Grade

- » Perform operations with multi-digit whole numbers with decimals
- » Multiply and divide fractions
- » Convert units of measurement, time
- » Understand concepts of volume and relate to multiplication and to addition
- » Graph points on the coordinate plane to solve problems
- » Understand the place value system, and standard and expanded notation
- » Find common factors and multiples
- » Understand and calculate with mixed numbers and improper fractions
- » Convert, compare, and round decimals
- » Solve problems involving perimeter, area, and volume
- » Understand percent and rate

## Sixth Grade

- » Understand and apply ratios, proportions, and percentages
- » Add, subtract, multiply, and divide decimals and fractions
- » Compute fluently with multi-digit numbers
- » Understand the system of rational numbers
- » Use bar diagrams to solve problems involving fractions, decimals, percentages
- » Develop algebraic thinking; solve one-variable equations and inequalities
- » Solve problems involving area, surface area, and volume
- » Develop understanding of statistical variability
- » Construct and analyze a variety of data displays

## Seventh Grade

- » Solve problems using algebraic expressions and equations
- » Use and apply factors, fractions, and exponents
- » Add, subtract, multiply, and divide rational numbers
- » Draw, construct and describe basic geometric concepts and properties
- » Solve problems involving angle measure, area, surface area, and volume
- » Understand and apply ratios, rates, and percentages
- » Investigate functions, graphs, and linear equations
- » Honors track allows for investigations into algebraic concepts

## Eighth Grade

- » Develop foundations for functions
- » Solve linear equations, functions, and inequalities
- » Explore direct and inverse proportion
- » Explore advanced functions, rational functions, and radical functions
- » Solve quadratic and exponential functions and equations
- » Factor quadratic and polynomial expressions
- » Use properties of rational and irrational numbers
- » Honors track deeper investigations into algebraic concepts and explorations in geometry