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Elementary Math Curriculum
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Middle School Math Curriculum
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High School Math Curriculum
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Elementary Math Curriculum Overview

  • Kindergarten
  • Grade 1
  • Grade 2
  • Grade 3
  • Grade 4
  • Grade 5
Elementary Math Students

Elementary Curriculum Overview
Beginning in kindergarten, students receive instruction in all five major math content areas:  number and operations, algebra, geometry, data analysis and probability, and measurement.  Students have the opportunity to learn each concept and how the concepts are interrelated as they build upon their knowledge in all areas from grade to grade. Student experiences in mathematics promote understanding, connections to the real world, and deeper thinking skills.

Elementary Mathematics Resources

  • Bridges in Mathematics

What students should know and be able to do

Kindergarten

Numbers and Operations

  • Read, write and represent numbers up to at least 31.
  • Count forward to 31, backward from 31.
  • Count the number of objects in a set and identify the quantity.
  • Recognize the number of objects up to 6, without counting.
  • Compare the number of objects in two or more sets.
  • Given a number, identify one more or one less.
  • Add and subtract whole numbers up to 6, using concrete objects.

Algebra

  • Sort objects in a set by one attribute such as size, shape, color or thickness.
  • Identify an object that does not belong in a set.
  • Recognize, describe and extend repeating, growing and/or shrinking patterns involving up to three elements using objects, pictures, sounds or movements.

Geometry

  • Sort two- and three-dimensional shapes according to their geometrical attributes.
  • Locate and describe placement of objects with terms such as:  on, inside, outside, above, below, over, under, beside, between, in front of, behind, next to, top, bottom.

Measurement

  • Compare and order objects by length, weight or size and use appropriate vocabulary such as longer than, holds more, smaller.
  • Compare and order events based on time and use appropriate vocabulary such as yesterday, today or tomorrow to describe relative time.

 

Process Standards

  • Create and solve word problems using actions, objects, words, pictures, or numbers.
  • Estimate and check that answers are reasonable.
  • Explain to others how a problem was solved.

Grade 1

Numbers and Operations

  • Read, write and represent numerals up to 120
  • Count by 2s to 30 and by 5s to 120.
  • Count forward or backward to or from any given number up to 120.
  • Demonstrate understanding of odd and even quantities up to 12.
  • Represent whole numbers up to 20 in various ways, maintaining equality.
  • Find numbers that are 10 more or 10 less than a given number.
  • Use one-digit addition and subtraction to solve real-world and mathematical problems.
  • Find the sum of three one-digit numbers.
  • Use counting and comparison skills to create and analyze bar graphs and tally charts.

Algebra

  • Sort, classify and compare objects in a set in more than one way.
  • Recognize, describe and extend repeating, growing and/or shrinking patterns involving up to four elements.
  • Determine if addition and subtraction equations are true.
  • Identify a missing number in an equation.

Geometry

  • Sort and describe two- and three-dimensional shapes according to their geometrical attributes.

Measurement

  • Estimate and measure length using non-standard units.
  • Tell time to hour and half-hour on analog and digital clocks.
  • Using a calendar, identify the date, day of the week, month, year, yesterday, today and tomorrow.
  • Combine pennies, nickels or dimes to equal one dollar.

Process Standards

  • Create and solve word problems using actions, objects, words, pictures, or numbers.
  • Estimate and check that answers are reasonable.
  • Explain to others how a problem was solved.

Grade 2

Numbers and Operations

  • Read, write with numerals, compare and order numbers to 999.
  • Count by 2s, 5s, and 10s from any given whole number.
  • Understand and demonstrate the significance of groups of 10 in the base 10 number system.
  • Represent numbers in equivalent ways.
  • Recognize, name, compare and represent unit fractions with drawings or concrete materials.
  • Demonstrate understanding of the relationships between odd and even numbers in addition and subtraction such as, odd + odd = even or odd – even = odd.
  • Understand the concept of multiplication as repeated addition or in rectangular arrays. 
  • Understand the concept of division as repeated subtraction or sharing equally.
  • Use one- and two-digit addition and subtraction to solve real-world and mathematical problems.

Algebra

  • Recognize, create and extend repeating, growing and shrinking patterns using numbers, concrete objects and pictures.
  • Describe what happens when zero is added to a number or subtracted from a number.
  • Understand that adding two numbers in any order results in the same sum.
  • Understand that grouping numbers in multiple addend problems, in any order, results in the same sum.
  • Generate equivalent expressions for a given number such as 24 = 17 + 7 or 24 = 100 – 76.
  • Determine the truth-value of an equation such as: true or false? 7 = 5 + 1.

Geometry

  • Sort, classify, compare and describe two- and three-dimensional shapes according to their geometrical attributes.
  • Investigate and predict the results of putting together and taking apart two- and three-dimensional shapes.
  • Create symmetrical patterns and designs.

Measurement

  • Read and write amounts of money using $ for dollar, ¢ for cents, and proper placement of the decimal point with amounts of money.
  • Know relationships among units of time such as minutes in an hour, days in a month and weeks in a year.
  • Tell time to the quarter hour, half-hour and hour using analog and digital clocks, distinguishing between a.m. and p.m.
  • Estimate standard and nonstandard linear measurements, then measure to check answer.
  • Combine coins to create amounts up to one dollar.

Data Analysis and Probability

  • Collect and record categorical data.
  • Create pictographs and real-object graphs to represent data.
  • Identify patterns in graphs or data sets.

Process Standards

  • Create and solve word problems using actions, objects, words, pictures, or numbers.
  • Estimate and check that answers are reasonable.
  • Explain to others how a problem was solved.

Grade 3

Numbers and Operations

  • Read, write with numerals, compare and order whole number to 100,000.
  • Know how fractions are related to the whole, such as four-fourths equal a whole or three fourths equal three of four equal parts of a whole.
  • Represent and write fractions with pictures, models and numbers.
  • Demonstrate an understanding of the multiplication facts through 10 using concrete models.
  • Use models to solve multiplication and division problems and use number sentences to record the solutions.
  • Use the inverse relationship of addition and subtraction to compute and check results.
  • Demonstrate mastery of basic addition facts for addends 0 through 9, without a calculator.
  • Demonstrate mastery of subtraction facts that are inverses of the basic addition facts, without a calculator.
  • Use subtraction with up to three-digit whole numbers in real-world and mathematical problems.
  • Use addition of up to three whole number addends, containing up to four digits each in real-world and mathematical problems.

Algebra

  • Create, describe and apply input/output rules.
  • Use the properties of addition and subtraction that involve ordering, grouping and the number 0, to do simple computations with whole numbers.
  • Identify a missing number or operation in a simple arithmetic equation such as 3 ? 4 =  7 or 9 - ? = 2.

Geometry

  • Sketch polygons with a given number of sides or corners.
  • Identify parallel and perpendicular lines in geometric shapes.

Measurement

  • Know relationships between units of length in a system of measurement, such as 12 inches equals 1 foot or 100 centimeters equals 1 meter.
  • Select an appropriate tool and identify the appropriate unit to measure time, length, weight and temperature.
  • Find the perimeter of a polygon with whole number sides.
  • Tell time to the minute using digital and analog time.
  • Determine elapsed time to the minute.
  • Make change using as few coins as possible up to a dollar.
  • Determine temperature using a thermometer.

Data Analysis and Probability

  • Collect data using observations or surveys and represent the data with pictographs and line plots with appropriate title and key.
  • Read and interpret data from circle graphs using halves, thirds, and quarters.

Process Standards

  • Solve problems by distinguishing relevant from irrelevant information, sequencing and prioritizing information and breaking multi-step problems into simpler parts.
  • Evaluate the reasonableness of the solutions by considering appropriate estimates and the context of the original problem.
  • Know when it is appropriate to estimate and when an exact answer with whole numbers, fractions or decimals is needed.
  • Communicate, reason and represent situations mathematically.
  • Support mathematical results using pictures, numbers and words to explain why the steps in a solution are valid and why a particular solution method is appropriate.
  • Express a written problem in suitable mathematical language, solve the problem and interpret the result in the original context.

Grade 4

Numbers and Operations

  • Compare and order whole numbers.
  • Read and write whole numbers to 100,000, in numerals and words.
  • Use the inverse relationship of multiplication and division to compute and check results.
  • Demonstrate mastery of multiplication facts for the numbers 0-10, without a calculator.
  • Multiply single-digit multiples of powers of 10 such as 300 x 60 or 70 x 3, mentally.
  • Use addition and subtraction of multi-digit whole numbers to solve multi-step real-world and mathematical problems.
  • Add up to three whole numbers containing up to 3 digits each, without a calculator.
  • Subtract whole numbers containing up to 3 digits each, without a calculator.
  • Use multiplication and division of whole numbers to solve simple real-world and mathematical problems.
  • Use rounding and estimation with whole numbers to solve real-world and mathematical problems.
  • Use fractions and decimals to solve problems representing parts of a whole, parts of a set and division of whole numbers by whole numbers in real-world and mathematical problems.

Algebra

  • Examine and describe patterns in tables and graphs.
  • Use the properties of arithmetic that involve ordering, grouping and the numbers 1 and 0, to do simple computations with whole numbers.
  • Identify a missing number or operation in a simple arithmetic equation such as 3 ? 4 = 12 or 45 / ? = 9.

Geometry

  • Identify, describe and classify two- and three-dimensional shapes by their attributes.
  • Identify congruent and similar figures.
  • Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.
  • Identify parallel and perpendicular lines.

Measurement

  • Understand that rectangles with the same area can have different perimeters and that rectangles with the same perimeter can have different areas.
  • Make change using as few coins and bills as possible up to $20.
  • Find the area and perimeter of a rectangle by measuring, using a grid, or using a formula, and label the answer with appropriate units.

Data Analysis and Probability

  • Collect data using observations or surveys and represent the data with tables and graphs with labeling.
  • Use mathematical language to describe a set of data.
  • Use physical models and pictures to represent possible arrangements of 2 or 3 objects.
  • Express outcomes of random experiments verbally and numerically such as 3 out of 4 or 3/4.

Process Standards

  • Solve problems by distinguishing relevant from irrelevant information, sequencing and prioritizing information and breaking multi-step problems into simpler parts.
  • Evaluate the reasonableness of the solutions by considering appropriate estimates and the context of the original problem.
  • Know when it is appropriate to estimate and when an exact answer with whole numbers, fractions or decimals is needed.
  • Communicate, reason and represent situations mathematically.
  • Support mathematical results using pictures, numbers and words to explain why the steps in a solution are valid and why a particular solution method is appropriate.
  • Express a written problem in suitable mathematical language, solve the problem and interpret the result in the original context.

Grade 5

Numbers and Operations

  • Read and write numbers up to three decimal places in numerals and words.
  • Recognize equivalent common fractions, decimals and percentages.
  • Interpret percents as a part of a hundred.
  • Represent and compare positive and negative integers symbolically and on the number line and use them to solve real-world and mathematical problems.
  • Use addition, subtraction, multiplication and division of multi-digit whole numbers to solve multi-step, real-world and mathematical problems.
  • Add and subtract numbers with up to two decimal places in real-world or mathematical problems.
  • Add and subtract, without a calculator, numbers containing up to five digits such as 546.23 – 84.1.
  • Model simple problems, arising from concrete situations involving the addition and subtraction of common fractions and mixed numbers as well as fractions where the common denominator equals one of the denominators.
  • Divide, without a calculator, a three-digit whole number or decimal by a one-digit whole number or decimal such as 3.51 divided by 3.
  • Multiply, without a calculator, a two-digit whole number or decimal by a two-digit whole number or decimal, such as 3.2 x 3.4.
  • Use a variety of estimation strategies such as rounding, truncation, over- and underestimation and decide when an estimated solution is appropriate.

Algebra

  • Identify patterns in numbers, shapes, tables, and graphs and explain how to extend those patterns.
  • Evaluate numeric expressions in real-world and mathematical problems.

Geometry

  • Sort three-dimensional objects according to number and shape of faces, number of edges and vertices.
  • Classify polygons as regular or irregular.
  • Classify, compare and identify acute, right and obtuse angles.
  • Know the sum of the angles in triangles and quadrilaterals.
  • Identify reflection and rotation symmetries in two-dimensional shapes and designs.

Measurement

  • Use a two-dimensional pattern of a cube or rectangular box to compute the surface area.
  • Select and apply the appropriate units and tools to measure perimeter, area and capacity.
  • Find the area and perimeter of a triangle by measuring or using a grid, and label the answer with appropriate units.

Data Analysis and Probability

  • Collect data using measurements, surveys, or experiments and represent the data with tables and graphs with labeling.
  • Determine whether or not a given graph matches a given data set.
  • Find mean, mode, median and range of a data set.
  • Use fractions and percentages to compare data sets.
  • Represent all possible outcomes for a simple probability problem with tables and grids, and draw conclusions from the results.

Process Standards

  • Solve problems by distinguishing relevant from irrelevant information, sequencing and prioritizing information and breaking multi-step problems into simpler parts.
  • Evaluate the reasonableness of the solutions by considering appropriate estimates and the context of the original problem.
  • Know when it is appropriate to estimate and when an exact answer with whole numbers, fractions or decimals is needed.
  • Communicate, reason and represent situations mathematically.
  • Support mathematical results using pictures, numbers and words to explain why the steps in a solution are valid and why a particular solution method is appropriate.
    • Express a written problem in suitable mathematical language, solve the problem and interpret the result in the original context.

     

     





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