St. Anne’s Episcopal School Lower School Mathematics Curriculum
Pre-Kindergarten
· Recognize numerals to 20
· Write numerals to 20
· Sequence numerals to 20
· Count with 1:1 to 20
· Count aloud sequentially to 20
· Show number combinations to 10 with manipulatives
· Count back from 10
· Identify patterns in numbers to 20
· Estimate amounts to 20
· Sort objects according to size, color or shape
· Recognize and name shapes (circle, oval, square, rectangle, triangle, star, heart)
· Recognize and Extend patterns
· None
· Make educated guesses to 20 about quantity
· Students are given opportunity to explain thinking and strategies used to solve story problems. Flexibility and a variety of strategies is emphasized.
Kindergarten
· Recognize numerals to 30
· Write numerals to 30
· Sequence numerals to 30
· Count with 1:1 to 30
· Count aloud sequentially to 30
· Combine sets and record sums up to 12
· Count back from 30
· Skip count by 5 and 10 to 100
· Identify patterns in numbers to 30
· Identify ordinal positions up to tenth
· Estimate amounts to 30
· Compare sets using terms more and less
· Sort objects according to a single attribute
· Recognize and name shapes (circle, oval, square, rectangle, triangle, hexagon and octagon)
· Recognize, extend, reproduce, create, record and label (using A,B notation) patterns
· Compare quantity on picture graph
· Record and interpret data on picture and bar graph
· Make educated guesses to 30 about quantity
· Provide solutions to story problems with quantities to ten
· Measure length using non-standard units
· Answer questions about the calendar
· Identify coins and know value
1st Grade
· Recognize numerals to 100
· Write numerals to 100
· Sequence numerals to 100
· Count aloud sequentially to100
· Add one digit numbers with speed and accuracy (18 in 2 min.) up to 18
· Find the sum of more than two addends up to 18
· Add two digit numbers without regrouping
· Count back from 100
· Subtract one digit numbers with speed and accuracy (18 in 2 min.)
· Subtract two digit numbers without regrouping
· Solve addition problems up to 18 involving missing addends
· Skip count by 2, 5 and 10 to 100
· Identify patterns in numbers to 100
· Identify ordinal positions up to twentieth
· Estimate amounts to 100
· Compares numbers to 100 using <,>,=
· Recognize a whole divided into parts (1/2, 1/4, 1/3)
· Determine 1/2 of set when given an even number of manipulatives up to 10
· Sort objects according to more than one attribute
· Describe properties of shapes
· Identify geometric solids (cylinder, rectangular prism, cube, sphere, cone, pyramid)
· None
· Uses tally marks to record data on picture and bar graphs
· Read, record and interpret data on picture and bar graph
· Check reasonable solutions using estimation
· Provide solutions to story problems with quantities to 30
· Measure length and weight using nonstandard units
· Uses standard units to measure weight and length
· Measure volume and area with manipulative materials
· Read analog clock to hour and half hour
· Count and combine coins to make equivalent values
2nd Grade
· Recognize numerals to 1000
· Write numerals to 1000
· Sequence numerals to 1000
· Add numbers with speed and accuracy (30 in 3 min.) up to 24
· Find the sum of more than 2 numbers with one and two digit addends
· Add two digit numbers with or without regrouping
· Subtract one digit numbers with speed and accuracy (30 in 3 min.) up to 24
· Subtract two digit numbers with and without regrouping
· Solve addition and subtraction with one unknown variable
· Skip count by 2, 5, 10, 3 and 4 to 100
· Uses patterns in numbers on 100 chart to solve addition and subtraction problems
· Round numbers to the nearest ten
· Compare whole numbers to 100 and balance expressions using <,>,=
· Concretely multiply using arrays
· Recognize and write proper fractions
· Determine fractional part of a set using manipulatives
· Use straight edge to construct geometric shapes
· Identify geometric solids (cylinder, rectangular prism, cube, sphere, cone, pyramid, triangular prism, hemisphere)
· Identify lines of symmetry for a given shape
· None
· Interpret picture, bar, line and pie graphs
· Determine reasonableness of response using estimation to predict outcomes
· Determine and use efficient strategies to solve problems
· Measure and compare using metric and English measurement
· Measure perimeter, area, volume and capacity
· Read analog clock to nearest five minutes
· Count mixed groups of coins and make change from a dollar
3rd Grade
· Recognize numerals to one hundred thousand
· Write numerals to one hundred thousand
· Sequence numerals to one hundred thousand
· Add numbers with speed and accuracy (95 in 10 min.) up to 24
· Solve problems using multiple addends with multiple digit numbers
· Add multi-digit numbers with and without regrouping
· Subtract one digit numbers with speed and accuracy (95 in 10 min.) up to 24
· Subtract multi-digit numbers with and without regrouping
· Solve multi-digit addition and subtraction with one or two unknown variables
· Skip count to reinforce knowledge of multiples
· Identifies patterns in numbers for multiplication
· Round numbers to the nearest hundred
· Compare numbers larger than 100 and balance expressions using <,>,=,not equal
· Move from concrete array to multiplication fact recall with speed and accuracy (95 in 10min)
· Connect multiplication facts to learn and recall division facts with speed and accuracy (95 in 10min)
· Solve 2 digit X 1 digit multiplication equations
· Extend division calculations to include division with remainders using known facts
· Compare, add and subtract proper fractions with like denominators
· Determine fractional part of a set
· Recognize equivalent fractions
· Use proper terms for polygons (triangle, square, rectangle, pentagon, parallelogram)
· Recognize/Compare/Contrast attributes of geometric solids (cylinder, rectangular prism, cube, sphere, cone, pyramid, triangular prism, hemisphere)
· Recognize the attributes of solid figure (face, edge, vertex)
· Recognize a variety of angles (acute, obtuse, right)
· Construct symmetric figures
· Identify a variety of lines (parallel, intersecting, perpendicular)
· Identify congruent figures
· Construct a circle with a compass and label parts
· Determine if shape shows slide, flip or turn
· None
· Interpret and construct different types of graphs and summarize findings
· Develop and apply strategies to problem solving and verify results
· Use metric and English measurement to record small units
· Interpret Celsius and Fahrenheit thermometer readings
· Read analog clock to nearest minute
· Calculate elapsed time to the quarter hour and half hour
· Add and subtract money in decimal form
4th Grade
· Recognize numerals to one million
· Write numerals to one million
· Sequence numerals to one million
· Add numbers with speed and accuracy (95 in 10 min.) up to 24
· Extend ability to solve problems using multiple addends with multiple digit numbers
· Extend ability to add multi-digit numbers with and without regrouping
· Subtract one digit numbers with speed and accuracy (95 in 10 min.) up to 24
· Extend ability to subtract multi-digit numbers with and without regrouping
· Extend ability to solve multi-digit addition and subtraction with one or two unknown variables
· Skip count to review multiples and create scales
· Extend patterns in numbers for multiplication
· Apply rounding rules to whole numbers, decimals and fractions
· Compare multi-digit numbers and complex expressions using <,>,=, not equal
· Recall multiplication facts with speed and accuracy (95 in 10min)
· Recall division facts with speed and accuracy (95 in 10min)
· Solve multiplication equations with two and three digit multiples
· Extend division calculations to multi-digit numbers
· Identify Roman Numerals to 10
· Compare, add and subtract proper and improper fractions with like denominators
· Determine fractional parts of a whole number
· Change fractions to equivalent form
· Change improper fractions to mixed numbers and vice versa
· Read and writes decimals to hundredths
· Add and subtract decimals to hundredths
· Relate proper fractions to decimal equivalent and vice versa
· Simplify proper fractions to lowest terms
· Name triangle, square, rectangle, pentagon, parallelogram, hexagon, octagon, quadrilateral) and identifies attributes of polygons (closed, parallel, perpendicular, obtuse angles, acute angles, right angles)
· Use protractor to identify and draw angles
· Identify all lines of symmetry for a given figure
· Identify and label lines (parallel, intersecting, perpendicular, ray, line segment)
· Distinguish between congruent and similar figures
· Construct a circle with a compass, label parts and state relationships of parts to each other
· Determine area, perimeter and volume of regular and irregular shapes
· Identify scalene, isosceles, equilateral triangle from the length of its sides
· None
· Determine mean, median and mode and draw conclusions from information on different types of graphs
· Extend strategy application to multi-step problems
· Measure and convert with metric and English units
· Distinguish between Celsius and Fahrenheit
· Measure length, weight, capacity, mass and volume
· Calculate elapsed time to five minute intervals
· Add and subtract money and make change from larger amounts
St. Anne’s Episcopal School Middle School Mathematics Curriculum
Students will proceed through the middle school curriculum in the exact order in which you see the topics listed. To best meet the needs of each student, students are separated into groups according to how quickly they grasp mathematical ideas, their grades, and recommendations from teachers. Placements will be re-evaluated periodically to determine if there is need for change for particular students. Depending on which section they are in, they will cover more or less than what you see in each grade. If a particular topic was not covered in the specific grade in which it is listed, then that topic will be discussed in the following grade.
5th Grade
· Understanding the uses of negative numbers in the world.
· Representing integers on the number line.
· Adding integers and solving problems involving addition of integers.
· Subtracting integers and solving problems involving subtraction of integers.
· Understanding and determining the absolute value of any integer.
· Multiplying integers and solving problems involving multiplication of integers.
· Dividing integers and solving problems involving division of integers.
· Determine measures of angles and identify special angle pairs (complementary and supplementary).
· Classify triangles, quadrilaterals, and other polygons according to their side lengths, angles, or both.
· Theorems involving parallel lines, alternate interior and exterior angles, vertical angles, and corresponding angles.
· Measuring the sum of interior angles of different polygons.
· Tessellations.
· Meaning of fractions as equal parts of “1”.
· Understanding and determining equivalent fractions and simplifying fractions.
· Understanding part-part, part-whole, and whole-whole ratios (rates).
· Understanding how to solve proportional situations using several different methods.
· Be able to estimate the size of a fraction to the nearest ¼, ½, ¾, or any whole.
· Understanding how to use proportional thinking when solving problems involving similar polygons (particularly similar triangles).
· Be able to order fractions using several different methods including: common denominator, common numerator, changing to decimals or percents, distance to/from, using benchmarks, and cross multiplication.
· Understand why each of the strategies for ordering fractions works.
· Meaning of decimals using place value concept and linking them to fractions.
· Be able to write decimals as fractions using expanded form and simplified forms (mixed fraction or singleton fraction).
· Be able to estimate the size of a decimal to the nearest ¼, ½, ¾, or any whole.
· Understand how to round decimals and how that affects precision.
· Understanding the base-10 metric system for metric units and be able to convert among different units within systems.
· Be able to represent numbers with powers of 10 (scientific notation and exponential form).
· Be able to represent numbers in exponential form with bases other than 10 (e.g. 81 = 34).
· Develop the meaning of percent as “out of 100”.
· Be able to estimate the size of a percent to the nearest 10%, ¼, ½, ¾, or any whole.
· Be able to convert among decimals, fractions, and percents for numbers less than 100%.
· Be able to convert among decimals, fractions, and percents for numbers less than 1%.
· Be able to convert among decimals, fractions, and percents for numbers greater than 100%.
· Understand the difference between experimental probabilities and theoretical probabilities.
· Understand how experimental probabilities eventually go to the theoretical probabilities as you do the experiment more and more times.
· Understand how to determine simple probabilities and write them as a fraction, decimal, and a percent.
· Understand how to determine the probabilities for situations involving two or more independent events and write them as a fraction, decimal, and a percent.
6th Grade
· Understand that because perimeter is a length, then we measure it by counting how many standard or non-standard units of length fit into it.
· Understand that the area of any shape is the amount of space it covers.
· Understand that because area is an amount of space, then we measure it by counting how many area units (usually squares) fit into it.
· Understand and derive the formulas for the areas and perimeters of rectangles, squares, parallelograms, triangles, trapezoids, circles, irregular shapes, and regular polygons.
· Understand that the square root function is the inverse of squaring a number.
· Be able to estimate the square root of a number.
· Understand the meaning of the Pythagorean Theorem. In particular, understand that the area of the square on one leg plus the area of the square on the second leg equals the area of the square on the hypotenuse for right triangles only.
· Understand how the Pythagorean Theorem could be used to determine the distance between any two points OR to determine lengths needed to find the areas/perimeters for different shapes.
· Be able to order decimals through estimation or through place value.
· Be able to order rational numbers and irrational numbers through estimation and thinking of where the numbers are located on the number line.
· Be able to estimate the size of addition or subtraction problems involving rational numbers using number sense and the meaning of the operations.
· Be able to determine the exact answer for addition and subtraction problems involving rational numbers.
· Be able to solve “real-world” problems involving addition and subtraction of rational numbers.
· Develop the understanding that division is repeated subtraction or how many times the divisor goes into the dividend.
· Be able to estimate the size of the answer to division problems.
· Develop an understanding of how to determine the exact answer to division problems involving fractions or decimals using a common denominator approach.
· Develop an understanding for why the “invert-and-multiply” algorithm works for dividing fractions.
· Be able to recognize and solve problems involving division of rational numbers.
· Be able to estimate the size of multiplication problems involving rational numbers by using number sense and the meaning of the operation.
· Develop an understanding for why multiplication is commutative for rational numbers.
· Develop an understanding for why the standard rule for multiplying fractions works.
· Develop an understanding for how to multiply decimals using knowledge of fractions.
· Be able to solve “real-world” problems involving multiplication of rational numbers.
· Develop an understanding of how to determine the percent of a number.
· Develop an understanding of how to find the percent given two numbers.
· Develop an understanding of how to solve problems involving percent increase and percent decrease.
· Develop an understanding of how to use the ideas of multiplication to solve problems involving conditional probabilities.
7th Grade
· Find, use, and interpret measures of center and spread, including mean, median, and mode, range, and interquartile range.
· Select, create, and use appropriate graphical representations of data, including histograms, box plots, scatter plots, and circle graphs.
· Discuss and understand the differences and similarities between data sets and their graphical representations, especially histograms, stem-and-leaf plots, and box plots.
· Use proportionality and a basic understanding of probability to make and test conjectures about the results of experiments and simulations
· Use flat patterns to help students determine the surface area of rectangular prisms, non-rectangular prisms, cylinders, pyramids, and cones.
· Develop and use formulas to determine the surface area of a sphere.
· Develop strategies that make sense for finding the volumes of rectangular prisms, non-rectangular prisms, cylinders, pyramids, cones, and spheres.
· Explore how the cube is the rectangular prism with the smallest surface area when the volume is held constant.
· Review the link between fractions, decimals, and percents.
· Develop a deeper understanding between the difference of a rational and irrational number.
· Be able to determine powers of rational numbers.
· Be able to multiply and divide powers of rational numbers.
· Develop an understanding of the difference between terminating, non-terminating repeating, and non-terminating non-repeating decimals.
· Develop an understanding of how to plot points in the coordinate plane.
· Model and solve many types of contextualized problems involving linear relationships using various representations such as graphs, tables, and equations.
· Solve one-step, two-step, and multi-step linear equations through symbol manipulation.
· Identify and describe situations with constant rates of change.
· Represent and analyze linear patterns and functions using words, tables, and graphs.
· Develop an understanding for the meaning of slope and y-intercept for linear relationships.
· Approximate and interpret rates of change from graphical and numerical data.
· Investigate how a change in one variable affects the change in another variable.
· Analyze linear relationships by investigating rates of change, intercepts, zeros, and local and global behavior.
· Draw reasonable conclusions about a linear situation being modeled.
· Determine or approximate the best-fit line for data that seem to be following a linear pattern and use this line to solve problems involving the data.
· Understand and plot points in all four quadrants of the coordinate plane.
· Make, understand, and use scale drawings and scale models.
· Understand translations, rotations, reflections, and dilations of shapes.
8th Grade
· Analyze linear relationships by investigating rates of change, intercepts, zeros, and local and global behavior.
· Draw reasonable conclusions about a linear situation being modeled.
· Develop an understanding of how to solve a system of equations using several different methods including graphical, substitution, and elimination.
· Develop an understanding of how to solve a system of inequalities graphically.
· Develop the idea of how to represent a situation with a graph that involves minimizing costs or maximizing profits when there are several constraints on a business (linear programming).
· Develop an understanding of how to solve a linear programming problem graphically.
Exponential Functions
· Identify functions as exponential and contrast their properties of tables, graphs, and equations with those of linear relationships.
· Identify and describe situations with exponential rates of change and compare them with linear relationships
· Develop the ability to write exponential equations from a table or graph of values that follow an exponential rate of change.
· Analyze exponential functions of one variable by investigating rates of change, intercepts, zeros, and local and global behavior.
· Understand the meaning of equivalent forms of exponential expressions and equations.
· Develop the ability to determine the type of exponential function that might model certain data given in tables and/or graphs.
· Develop an understanding of the different applications of exponential relationships in different scientific fields (including exponential growth and exponential decay situations).
· Model and solve contextualized problems that have exponential relationships using various representations, such as graphs, tables, and equations.
Quadratic Functions
· Identify the properties of tables, graphs, and equations that are modeled with quadratic relationships and compare them to linear and exponential functions.
· Identify and describe situations with exponential rates of change and compare them with linear relationships
· Develop the ability to write quadratic equations from a table or graph of values that follow a quadratic rate of change using the idea of second differences.
· Develop the ability to factor different types of quadratic expressions including difference of squares, binomials, and trinomials.
· Develop an understanding of what completing the square means.
· Develop an understanding of how to use the completing the square method to solve problems involving quadratic relationships.
· Develop an understanding of where the quadratic formula comes from.
· Develop an understanding of how to use the quadratic formula to solve problems involving quadratic relationships.