Math

The Mathematics curriculum at The Day School incorporates the activities and teaching strategies addressed in the Standards of the National Council of Teachers of Mathematics (NCTM).  The following goals are stressed at all grade levels:

  • That students utilize mathematical problem solving skills
  • That students apply critical thinking skills when performing mathematical tasks
  • That students communicate mathematically
  • That students reason mathematically
  • That students perform mathematical operations with confidence
  • That students value mathematics as a necessary component of daily life

In order to attain these goals, students are grouped for instruction based on individual strengths and needs.  These groups may be within a grade or class, or across grade lines.  Teachers in each grouping utilize the texts, materials and teaching strategies that best meet the needs of the students in the group.

Pre-K and K             Grade 1             Grade 2             Grade 3             Grade 4             Grade 5            Grade 6             Grade 7             Grade 8     

Pre-K and Kindergarten

The objective of the Pre-K and Kindergarten math program is to embed math concepts throughout the school day with meaningful and relevant experiences. This program is a developmentally appropriate, multi-sensory approach that uses manipulatives and hands-on activities.  Problem solving is integrated throughout each unit. Units at this basic level include, sorting; Positions and patterns; Comparing Sets,  Data, and Graphing; Represent and Read Numbers;  Plane shapes and fractions; Solid Shapes; Represent and Read Numbers 6-12; Using Numbers 0-12; Time; Money; Length, Weight and Capacity; Addition and Subtraction;  and "skip count" by twos, fives and tens;

  1. Objectives

The students will:

  1. Learn sorting
    1. Alike and different
    2. Sort by color
    3. Sort by size
    4. Sort by kind
    5. Sort by own rule
    6. Problem solving
    7. Learn positions and patterns
      1. Top, middle, bottom
      2. Before, after, between
      3. Left and right
      4. Inside, outside
      5. More position words
      6. Patterns with sounds and motions
      7. Extend patterns
      8. Translate pattern
    8. Comparing Sets, Data, and Graphing
      1. Math One to One
      2. Same number
      3. More, fewer, sort and graph
      4. Pictographs
    9. Represent and Read Numbers
      1. Count, read and write numbers 0-5
      2. Ordinal numbers
    10. Plane shapes and fractions
      1. Circle and rectangle
      2. Square and rectangle
      3. Patterns with shapes and positions
      4. Combine plane shapes
      5. Symmetry
      6. Equal parts, halves
      7. Likely and unlikely, predict and record outcomes
    11. Solid Shapes
      1. Sort solid shapes
      2. Identify solid shapes
      3. Build solid shapes
      4. Surfaces of solid shapes
      5. Combine solid shapes
    12. Represent and Read Numbers 6-12
      1. Names for 6-12
      2. Order 6-12
    13. Using Numbers 0-12
      1. Names for 1-12
      2. Order numbers to 12
      3. More/fewer
      4. Estimate quantities
    14. Time
      1. Time of day
      2. Days and months on the calendar
      3.  More time, less time
    15. Money
      1. Sort and graph coins
      2. Penny, nickel, dime, quarter
    16. Length
      1. Compare order by length
      2.  Measure length
      3. Estimate and measure length
      4. Explore area
    17. Weight and Capacity
      1. Compare and measure weight
      2. Estimate weight
      3. Compare capacity
      4. Order capacity
      5. Measure capacity
      6. Tools for measuring
    18. Addition
      1. Model addition
      2. Add 1 to numbers 0-9
      3. Add 2 to numbers 0-9
      4. Add pennies
      5. Practice addition
      6. Doubles
    19. Subtraction
      1. Model subtraction
      2. Subtract 1 from numbers 1-10
      3. Subtract 2 from numbers 2-5
      4. Subtract 2 from numbers 2-5
      5. Subtract 2 from numbers 6-10
      6. Subtract pennies
      7. Practice subtraction
      8. Relate addition and subtraction
    20. Numbers 10-20
      1. Count, read and write numbers 10-20
      2. Order numbers 10-20
      3. Estimating
    21. Numbers greater than 20
      1. Count, read and write numbers 21-31
      2. Order 1-31
      3. Count by twos, fives and tens.

Resources: Kindergarten Math Textbook



Grade 1

The first grade mathematics program is designed to build a bridge from concrete experimentation to a more symbolic understanding of math concepts,. Students work with a wide variety of manipulatives in an atmosphere that encourages problem solving.  Children solve problems in a variety of ways and share strategies to apply mathematics to real world situations.  Language skills are used to explore mathematical concepts and word problems. Here we build the foundation for such units as: Number concepts and addition concepts; Subtraction concepts, data and graphing; Addition and Subtraction strategies; Plane Solid Shapes, Spatial Sense and Patterns; Geometry and Fractions; Numbers through 100; Time and Money and number patterns; Using Money; Addition and subtraction facts through 12; Measurement of length, weight, capacity and temperature; as well as Two digit addition and subtraction.

Grade 2

The second grade mathematics curriculum builds on concepts previously taught in grade one.  One main goal is mastering addition and subtraction facts in order to build a solid math foundation.  This program is designed with emphasis on a hands-on approach to learning. We will develop number concepts to understand numbers through 50; examine Addition and Subtraction- develop and use strategies for whole number computation; Data, graphing and probability; Number Concepts through 100 and Place Value; Plane Shapes; Fractions; Regrouping with Addition and Subtraction using 2 digit numbers and regrouping; Increasingly more complex concepts with Money, Time,  Measurement; Weight - measure weight in pounds and ounces ; measure in cups, pints, quarts and gallons; temperature -  understand that thermometers measure temperature - Read Fahrenheit and Celsius ; Choose the best tool and unit to measure length, weight, capacity and temperature

Grade 3

The third grade mathematics curriculum focuses on developing skills and strategies for problem solving and developing understanding of a variety of concepts in an age and developmentally appropriate format for all students in the program. Read, write and represent whole numbers using symbols, words,, and models through 999,000

A. 

  1. Expand numbers through 999,000
  2. Compare, order and describe whole numbers with or without symbols through 999,000
  3. Identify and use cardinal and ordinal numbers to 99
  4. Round numbers to the nearest ten
  5. Round numbers to the nearest 100
  6. Identify odd and even numbers
  7. Identify, describe, extend and create patterns and functions

B.    Addition and Subtraction facts

  1. Analyze number relations and compute addition and subtraction facts
  2. Use commutative, associative, and zero property of addition
  3. Use mental math
  4. Use problem solving strategies
  5. Use fact families
  6. Solve and write word problems

C.    Addition with greater numbers

  1. Add mentally using strategies
  2. Estimate sums by rounding
  3. Use place value models
  4. Add up to 5 digit numbers with and without regrouping
  5. Add up to 4 columns of 4 digit numbers
  6. Use problem solving strategies to solve word problems

D.    Subtraction of greater numbers

  1. Subtract numbers using mental math strategies
  2. Estimate differences by rounding numbers
  3. Use place value models to explore subtracting digits up to 4 digit numbers with and without regrouping
  4. Subtract 4 digit numbers with regrouping across zeroes
  5. Use problem solving strategies

E.    Money

  1. Explore identifying and writing money through half-dollars
  2. Explore identifying and writing money in dollar amounts through $999,000
  3. Compare, order and round money
  4. Give change
  5. Add up to 5 digit money amounts
  6. Estimate change
  7. Subtract money up to 5 digits
  8. Money word problems

F.    Measurement and time

  1. Explore reasonable time estimates
  2. Tell time to the nearest minute and as AM or PM
  3. Make and use schedules involving elapsed time
  4. Get information and find patterns in calendars
  5. Solve word problems

G.    Graphing

  1. Collect, organize and display data using tallies
  2. Organize and display data to make a pictograph
  3. Organize and display data to make a bar graph
  4. Interpret graphs
  5. Organize and display data on a line graph

H.    Number computation and multiplication

  1. Represent multiplication facts through the 9’s
  2. Identify and use properties of multiplication- commutative, associative, zero and of one.
  3. Understand multiplication as repeated addition
  4. Multiply multiples of 10 and 100 mentally
  5. Use place value models to explore multiplication
  6. Solve word problems

I.    Number computation- division

  1. Represent division basic facts through 81/9=9
  2. Relate multiplication to division fact families
  3. Explain division as the opposite of subtraction
  4. Use place value models to explore finding 2 or 3 digit quotients with or without remainders
  5. Solve division word problems

J.    Measurement

  1. Read customary and metric units
  2. Estimate to determine length
  3. Estimate and read temperature in Fahrenheit and Celsius
  4. Estimate and determine weight of objects
  5. Measure length and width
  6. Measure capacity
  7. Measure weight
  8. Estimate and determine measurement of perimeter, area and volume
  9. Identify equivalent units of length
  10. Solve word problems

K.    Geometry

  1. Identify and describe points, lines, line segments, rays and angles
  2. Identify and describe polygons, quadrilaterals, triangles, rectangles and squares
  3. Identify right angles
  4. Identify and describe cubes, rectangular prisms and congruence
  5. Identify and describe the results of flips, turns and slides
  6. Identify and describe symmetry

L.    Fractions, decimals and probability

  1. Explore fractions as equal parts of the whole
  2. Read and write fractions as parts of a whole
  3. Explore finding equivalent fractions
  4. Compare fractions
  5. Read and write mixed numbers
  6. Solve word problems

M.    Word Problems

  1. Identify the question
  2. Identify the clue words
  3. Determine the information
  4. Make a plan
  5. Apply a strategy
  6. Extend the solution
  7. Identify the operation and solve
  8. Use deductive or inductive reasoning

Resources:
Houghton Mifflin Mathematics, McGraw-Hill Math in my World, manipulatives, various workbooks, internet activities, Smart Board activities, games, interactive lessons.

Grade 4


I.    Course Overview
The 4th grade math curriculum focuses on a broad set of skills and concepts and uses age and developmentally appropriate texts, activities and lessons to meet the range of needs of the students in the program.
II.    Objectives
The students will:
A.    Understand place value and the reasonableness of numbers

  1. Numbers to thousands
  2. Compare and order numbers
  3. Determine if a number is reasonable
  4. Round numbers
  5. Numbers to millions
  6. Solve problems by interpreting data

B.    Money, addition and subtraction

C.    Time, data and graphs

  1. Time and elapsed time
  2. Range, median and mode
  3. Pictographs and bar graphs
  4. Ordered pairs and line graphs
  5. Solve problems by working backwards and interpreting

D.    Multiplication and division

  1. Meaning of multiplication
  2. 2-9 as factors
  3. Three factors
  4. Meaning of division
  5. 2-9 as divisors
  6. Fact families

E.    Multiply by 1 digit and 2 digit numbers

  1. Multiplication patterns and estimating products
  2. Multiply 2 digit numbers
  3. Multiply greater numbers and money
  4. Multiply 2 digit numbers by 2 digit numbers
  5. Multiply 3 digit and greater numbers by 2 digit numbers
  6. Solve multi-step problems, interpret data, use estimation and alternate methods

F.    Measurement

  1. Use customary and metric units
  2. Rename customary units of length
  3. Perimeter
  4. Capacity and weight (mass) in customary and metric units
  5. Solve problems by using logical reasoning or checking for reasonableness

G.    Divide by 1 and 2 digit numbers

  1. Division patterns and estimating quotients
  2. Divide by 1 digit numbers, multiples of ten, and by tens
  3. Zeroes in quotient
  4. Divide greater numbers
  5. Solve problems by using the guess, test and revise strategy and by interpreting the quotient and remainder.

H.    Geometry

  1. 3 dimensional figures
  2. 2 dimensional figures
  3. Lines, segments and rays
  4. Angles
  5. Congruency, similarity and symmetry
  6. Slides, flips and turns
  7. Area and volume

I.    Fractions and probability

  1. Identify, read and write fractions as parts of a whole and as parts of a group
  2. Find a fractional part
  3. Simplify fractions
  4. Read and write mixed numbers to represent words and diagrams
  5. Find the probability of simple events
  6. Solve problems by conducting an experiment
  7. Solve multi-step problems

J.    Fractions and decimals

  1. Add and subtract fractions and mixed numbers
  2. Use decimals to express fractions as tenths and hundredths
  3. Add and subtract decimals
  4. Find the least common denominator
  5. Add and subtract fractions with like and unlike denominators
  6. Read and write decimals to the hundredths
  7. Read and write decimals greater than 1 to the hundredths
  8. Add and subtract decimals and money amounts

Resources:
McGraw-Hill, Math in My World, Smart Board resources, manipulative activities, on line sites and resources, teacher created materials

Grade 5


I.    Course overview
The fifth grade math curriculum focuses on a variety of skills and is taught through various methods to meet the standards as well as to prepare the students in the program for the middle school math curriculum.  The curriculum is a bridge between elementary and middle school math.  Focus is given to problem solving skills in every day life and discovery activities and manipulatives are incorporated to enhance student understanding of each concept.
II.    Objectives
The students will:
A.    Learn the place value of numbers and decimals

  1. Whole numbers to millions, decimals to thousands
  2. Comparing and ordering
  3. Equivalent decimals
  4. Rounding whole numbers and decimals

B.    Add and subtract whole numbers and decimals

  1. Add and subtract decimals
  2. Front end estimation, estimation with decimals
  3. Addition and subtraction expressions

C.    Data, statistics and graphs

  1. Collect and organize data
  2. Range, median and mode
  3. Bar graphs, line graphs and leaf plots

D.    Multiply whole numbers and decimals

  1. Multiply whole number by 1 digit and by 2 digit numbers
  2. Estimate products
  3. Multiply decimals
  4. Use the multiplication properties

E.    Divide whole numbers and decimals by 1 digit divisors

  1. Dividing by 1 digit divisors
  2. Divisibility rules
  3. Mean
  4. Estimate quotients
  5. Divide decimals by whole numbers
  6. Divide decimals by decimals
  7. Zeroes in the quotient
  8. Division patterns

F.    Divide whole numbers and decimals by 2 digit divisors

  1. Dividing by 2 digit divisors
  2. Estimating quotients
  3. Dividing by powers of 10
  4. Dividing larger numbers

G.    Measurement

  1. Customary units
  2. Metric units
  3. Units of time
  4. Units of length, capacity, weight (mass)

H.    Geometry

  1. Polygons
  2. Angles, lines, triangles, quadrilaterals, circles
  3. Congruence, motion, similar figures, coordinate graphing
  4. Definitions of all shapes, angles, lines

I.    Fraction concepts and number theory

  1. Meaning of fractions
  2. Prime and composite numbers
  3. Mixed numbers
  4. Adding and subtracting fractions and mixed numbers with a like denominator
  5. Adding and subtracting fractions with unlike denominators

J.    Multiplying and dividing fractions and mixed numbers

  1. Multiplying fractions
  2. Multiplying mixed numbers
  3. Dividing fractions
  4. Multiplying a fraction by a whole number, by a fraction, by a mixed number, multiplying mixed numbers, dividing fractions by whole numbers and fractions

K.    Perimeter, area and volume

  1. Perimeter, area, circumference and volume
  2. Perimeter and area of rectangles, triangles, parallelograms
  3. Circumference and area of circles
  4. Volume of 3-D figures

L.    Ratio, percent and probability

  1. Ratio, equal ratios and scale drawings
  2. Meaning of percent, estimate percent
  3. Probability- predicting outcomes
PREPARING CHILDREN TO THRIVE IN A COMPLEX WORLD