# Mathematics

###### Kindergarten Mathematics

FOCUS: Building foundations for mathematical understanding.

CONCEPTS: Number sense; patterns; attributes; measurement; place value to hundreds.

SKILLS: Comparing and ordering numbers; identifying even and odd numbers; forward and backward counting; skip counting; creating and extending patterns; reading and writing numbers to 100; estimating; graphing; sorting; recognizing math symbols, and integrating mathematical concepts into everyday situations.

CONCEPTS: Sorting and counting, number sense, basic geometry, measurement, place value, addition and subtraction

SKILLS: Reading and writing numbers; identifying place value, skip counting by 2s, 5s, and 10s; using tally marks; solving addition and subtraction stories and equations; using mathematical symbols; reading and creating graphs.

CONCEPTS: Students focus on addition and subtraction, place value, shapes, and length measurement. They practice working with time, money, and data collection and representation. They are introduced to the concept of equal groups of objects to gain foundations for multiplication.

SKILLS: Become fluent with addition and subtraction facts with numbers to 20; add and subtract with numbers up to 1,000; measure length and solve problems involving lengths; identify, describe, compare, put together, and take apart shapes.

FOCUS CONCEPTS: Operations & Algebraic Thinking (multiplication and division); Number & Operations in Base Ten (multi-digit addition and subtraction); Number & Operations—Fractions; Measurement & Data; Geometry.

MATHEMATICAL PRACTICES: Make sense of problems and persevere in solving them; Reason abstractly and quantitatively; Construct viable arguments and critique the reasoning of others; Model with mathematics; Use appropriate tools strategically; Attend to precision; Look for and make use of structure; Look for and express regularity in repeated reasoning.

SKILLS: Represent and solve problems involving multiplication & division; Understand properties of multiplication and the relationship between multiplication and division; Multiply and divide within 100; Solve problems involving the four operations, and identify and explain patterns in arithmetic; Use place value understanding and properties of operations to perform multi‑digit arithmetic; Develop understanding of fractions as numbers; Solve problems involving measurement and estimation of intervals of time; Represent and interpret data; Geometric measurement: understand concepts of area and relate area to multiplication and to addition; Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures; Reason with shapes and their attributes.

FOCUS: Problem solving, algebraic and logical reasoning, data collection and interpretation, geometry, measurement, fractions, decimals, multi-digit multiplication, place value to the millions.

CONCEPTS & SKILLS: Developing and using thinking routines, estimating, making generalizations, measuring area and perimeter, representing and comparing fractions and decimals, communicating mathematical thinking, developing automaticity with multiplication and division math facts, recognizing patterns, applying concepts to real world math situations.

CONCEPTS: Problem solving with very large and very small numbers, relative magnitudes of numbers, representation and manipulation of parts of a whole as decimal numbers, fractions, and percentages; measurement of plane and solid figures; data collection and presentation; estimation; synthesis and application of mathematical problem-solving skills in real-world situations.

SKILLS: Multiply and divide with large numbers; long division with multi-digit divisors; compare very large numbers; prime factorization; measure and calculate area and perimeter of polygons and complex plane shapes; measure and calculate surface area and volume of solid figures; collect and analyze data; represent data graphically; communicate mathematical thinking verbally and through writing.

FOCUS: To gain an understanding of data collection, analysis and representation; sampling and probability; integer operations; order of operations; introduction to variables and writing expressions; fraction and decimal operations; percent calculations; application of variables to algebraic patterns; introduction to proportional reasoning; introduction to coordinate graphing and linear functions; deriving formulas for area and volume of right prisms.

PROCESS + SKILLS: Students develop a repertoire of strategies for solving problems and work to explain their processes in order to learn from and with classmates who may approach problems differently. Different ways of seeing, thinking, and reasoning are encouraged, celebrated, and explored in order to deepen connections and further develop understanding.

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