Valley Christian School: Mathematics Curriculum

Preschool

Pre-Kindergarten Everyday Mathematics was developed to integrate well with daily routines and activities in the early childhood classroom. Activities take place in a center-based environment with opportunities for partner, small group, and whole group interaction as well as individual investigation. With the guidance of the teacher, children participate in hands-on exploration of a wide variety of materials at a level that is most appropriate for their current stage of development.

This program is rich in problem solving everyday classroom situations. Educated guesses are a powerful tool and the preschool program encourages estimating in a variety of situations. Children are encouraged to discuss and share their thoughts, make connections among ideas and experiences, and to use their powers of reasoning and insight to solve problems.

At this level the math is incorporated into the art and music activities, circle time, games, snack time, and other daily events. The activities are designed around eight mathematical content strands:

Numeration
The stated year-end goal for oral counting is 20 and beyond. Since children learn at different rates some will not meet this goal while others will exceed it. The children will increase in their ability to oral count, recognize numbers, and perhaps even write number symbols.
Measurement
Children naturally match, compare, and measure as they go about their daily play in preschool. At this age, measurement is at the exploratory stage. Activities are based around objects that are of interest to the children, such as cooking.
Geometry
Many children are already familiar with the names of simple shapes and this math program will build on this prior knowledge and prepare children for future analysis of the properties and relationships among shapes. The children will play, trace, draw, and construct with shapes. Pattern blocks are an effective geometric tool.
Operations
Operations are the things we do to or with numbers. Children will solve concrete problems that arise from their daily preschool lives. Children will make up and act out their own number stories. This puts them in charge of their own learning.
Patterns and Functions
Pattersn are sets of elements that repeat in regular, predictable ways. Children begin to see patterns in classroom floor tiles, rows of chairs, and in leaves and flowers. Attribute activities involving selecting groups according to an attribute and sorting and categorizing various collections or things aid in the idea of patterns.
Money
The preschool children learn the differences in the size and markings of coins and how they are used as a means of exchange in activities such as playing store.
Clocks and Calendars
Many children come to school knowing their birth date, their ages, and the times of favorite television programs. They refer to days, weeks, years, hours, minutes, and seconds by they lack understanding of these measurements. Activities and games help to develop these concepts.
Data and Chance
Young children can gather information, display it and make counts and comparisons. For preschoolers the questions asked about real situations in the classroom and collecting information about daily concerns aids this process. Children can conduct surveys to generate data among their classmates. Graphing activities involve answering the question, “How many?”

The preschool activities are arranges around the following themes:

All About Me
Families at Home
A Working World
Animals All Around
Changes in Nature
Celebrations
Colors and Shapes
Dinosaurs
Foods We Eat
Growing Things
A Day at the Beach

Suggested year-end goals built into the Everyday Mathematics program are as follows:

Recognizes numbers 0-20.
Performs rote counting 1-20.
Counts 1-10 objects, actions, or sounds.
Forms groups of 0-10 objects and matches the correct number to each group.
Arranges groups of objects in one-to –one correspondence.
Compares groups of objects to determine more, less, or same/equal to using one-to-one correspondence.
Participates in solving simple addition and subtraction number stories by joining and removing objects.
Identifies and describes the similarities and differences of objects.
Sorts and classifies objects by their attributes.
Recognizes copies, extends, and generates patterns.
Locates objects using position and direction words, such as next to and behind.
Compares and sorts geometric shapes by common attributes.
Recognizes, identifies and describes 2- and 3- dimensional shapes.
Compares and orders objects by size, weight, height, and length.
Identifies and compares coins by size and markings.
Sequences events using time concepts, such as mornings/afternoon/night.
Explores the purpose and use of clocks and calendars.
Collects and displays data about people, objects, and events using objects, pictures, and graphs.

Kindergarten

Kindergarten level has many daily math routines. They include a number of the day and a growing number line; cleanup count; job chart; weather observation; building the monthly calendar; attendance; and recording the daily temperature. Activities are based around the following strands:

Numeration
Correct number sequences through counting and counting objects.
Counting on from a number, backward, skip counting.
Experiences with objects of various sizes, shapes, and arrangements.
Read and write numbers and use the term “digit”.
Operations
Using operations and relations in solving concrete problems from everyday math;
Make up and act out number stories;
Explore the inverse operations of addition and subtraction as “doing” and “undoing”;
Using relation vocabulary appropriately;
The things we “do” with numbers;
Patterns and Functions
Sorting and categorizing collections;
Exploring functions through “What’s My Rule?” games;
Counting by 1s, 2s, 5s, 10s, and so on.
Geometry
Tracing, drawing, constructing, and playing with simple shapes;
Analyze parts of shapes and relationships among sizes and shapes.
Measurement and Reference Frames
Introduce length, weight, volume, or capacity, and elapsed time through matching and comparison activities;
Using appropriate tools to measure and label carious units with U.S. customary and metric systems;
Drawing comparing and recording results;
Introduce money as a tool to explore place value, fractions, equivalence, decimal system;
Explore characteristics and values of bills and coins;
Use money incidentally;
Develop understanding of time;
Keep track of time on calendars, clocks, number lines;
Develop sense of and record sequential order and time.
Data and Chance
Collect, organize, and display data using concrete objects, tables, charts, and graphs.
Make counts and comparisons of data.

First Grade

Activities are based on the following content strands:

Numeration
Counting
Reading and writing numbers
Investigating place-value of whole numbers
Exploring fractions and money
Operations and Computation
Learning addition and subtraction facts, fact families, and extended facts;
Beginning informal work with properties of numbers and problem solving.
Patterns, Functions, and Algebra
Exploring attributes, patterns, sequences, relations, and functions finding missing numbers and rules in Frames-and-Arrows and “What’s My Rule?” problems; Studying properties of operations.
Geometry
Exploring 2- and 3- dimensional shapes.
Measurement and Reference Frames
Using tools to measure length, capacity, and weight; Using clocks, calendars, timelines, thermometers, and ordinal numbers.
Data and Chance Collecting
organizing, and displaying data using tables, charts, and graphs;
Exploring concepts of chance.

Second Grade

Second Grade Everyday Mathematics content emphasizes the following concepts:

Numeration
Counting, reading and writing numbers; identifying place-value; comparing numbers; working with fractions; using money to develop place-value and decimal concepts.
Operations and Computation
Recalling addition and subtraction facts; exploring fact families; adding and subtracting with tens and hundreds; beginning multiplication and division; exchanging money amounts.
Data and Chance
Collecting, organizing, and interpreting data using tables, charts, and graphs; exploring concepts of chance.
Geometry
Exploring 2- and 3-dimensional shapes; classifying polygons.
Measurement and Reference Frames
Using tools to measure length, capacity, weight, and volume; using U.S. customary and metric measurement units.
Patterns, Functions, and Algebra
Exploring number patterns, rules, for number sequences, relations between numbers, and attributes.

Emphasis is placed on:

A problem-solving approach based on everyday situations that develops critical thinking.
Frequent practice of basic skills through ongoing program routines and mathematical games.
An instructional approach that revisits topics regularly to ensure full concept development.
Activities that explore a wide variety of mathematical content and offer opportunities foe students to apply their basic fact skills to geometry, measurement, and algebra.

Third Grade

Third Grade Everyday Mathematics content emphasizes the following concepts:

Numeration Counting patterns; place-value; reading and writing whole numbers through 1,000,000; fractions, decimals, and integers.
Operations and Computation Multiplication and division facts extended to multi-digit problems; working with properties; operations with fractions and money.
Data and Chance Collecting
organizing, and displaying data using tables, charts, and graphs; exploring concepts of chance.
Geometry
Exploring 2- and 3-dimensional shapes and other geometric concepts.
Measurement and Reference Frames
Recording equivalent units of length; reorganizing appropriate units of measure for various items; finding the areas of rectangles; using multiplication arrays, coordinate grids, thermometers, and map scales to estimate distances.
Patterns, Functions, and Algebra
Finding patterns on the number grid; solving Frames-and-Arrows puzzles having two rules; completing variations of “What’s My Rule?” activities; exploring the relationship between multiplication and divisions; using parentheses in writing number models; naming missing parts of number models.

Emphasis is placed on a problem-solving approach based on everyday situations that develop critical thinking.

Fourth Grade

Fourth Grade Everyday Mathematics emphasizes the following content strand concepts:

Numeration
Reading, writing, and comparing whole numbers through millions, decimals through thousandths, negative numbers to -20, and fractions, Understanding relations between fractions, decimals, and percents, Locating fractions and mixed numbers on a number line, Generating equivalent fractions
Operations and Computation
Using paper-and-pencil algorithms to add, subtract, multiply, and divide multidigit whole numbers and decimals, Using mental arithmetic to compute exact answers and to estimate, Rounding from millions to hundredths, Modeling multiplication with arrays and area, Doing operations with fractions
Data and Chance
Creating, reading, and interpreting graphs, Identifying landmarks in data sets, including range, median, mode, and mean, Listing all possible outcomes in simple situations, Using fractions to quantify probabilities, Using experimental results to make predictions
Geometry
Locating points on a coordinate grid, Drawing and measuring angles, Classifying angles as acute, obtuse, or right, Classifying lines as parallel, intersecting, or perpendicular, Recognizing and using transformations, including reflections and rotations, Understanding the relationship between reflections and line symmetry, Building 3-dimensional shapes, Describing, comparing, and analyzing 2-dimensional and 3-dimensional figures
Measurement and Reference Frames
Using tools to measure length, area, volume, weight, temperature, and time, Developing personal references for inches, centimeters, feet, meters, and yards, Estimating lengths and weights, Finding areas and perimeters of rectangles, parallelograms, and triangles, Finding volumes of rectangular prisms by counting cubic units, Calculating elapsed time, Using correct units in all measurements, Calculating distances using map scales
Patterns, Functions, and Algebra
Using letters and other symbols for unknowns, Simplifying expressions containing parentheses, Creating, extending, and describing patterns, Using formulas for finding the area of simple geometric figures, Determining rules that relate numbers in pairs, Finding missing numbers in tables, Translating among verbal, numerical, and graphical representations, Understanding and writing number models for number stories

Emphasis is placed on problem solving and critical thinking, understanding the mathematical thinking and strategies of others, frequent practice of basic skills, and an instructional approach that revisits concepts regularly to ensure full understanding.

Fifth Grade

Fifth Grade Everyday Mathematics emphasizes the following concepts:

Numeration
Reading, writing, and comparing negative numbers, fractions, whole numbers through billions, and decimals through thousandths, Reading, writing, and interpreting whole-number powers of 10, Translating between exponential and standard notation, Understanding and identifying prime numbers, composite numbers, and square numbers
Operations and Computation
Using paper-and-pencil algorithms to add, subtract, multiply, and divide, multidigit whole numbers and decimals, Using mental arithmetic to compute exact answers and to estimate, Rounding from billions to hundredths, Translating among fractions, decimals, and percents, Prime factoring, Converting between fractions and mixed numbers, Adding and subtracting fractions and mixed numbers with unlike denominators, Finding least common factors, Multiplying and dividing fractions
Data and Chance
Comparing probabilities for different outcomes, Comparing theoretical and experimental probabilities, Expressing probabilities as fractions, decimals, and percents, Drawing justifiable conclusions from data, Displaying data in more than one way, Formulating a question, carrying out a survey or experiment, recording data, and communicating results, Drawing and interpreting circle graphs and stem-and-leaf plots, Understanding measures of central tendency (mean, median, mode)
Geometry
Constructing a circle with a given radius or diameter, Defining and creating tessellations, Measuring and drawing angles, including reflex and straight angles, Identifying and defining right isosceles, and equilateral triangle, Plotting points in four quadrants, Using translations, reflections, and rotations, Solving perimeter, area, and volume problems, Understanding the relationship between the volumes of cones/pyramids and cylinders/prisms, Finding the surface area of a cube and the area of a circle, Identifying angle relationships in triangles and in quadrilaterals
Measurement and Reference Frames
Measuring and estimating length, area, volume, weight and capacity, Converting and computing with common units of measure, Creating scale drawings
Patterns, Functions, and Algebra
Evaluating simple algebraic expressions, Finding rules for patterns, Finding the nth term in a sequence, Solving simple open number sentences and simple rate problems, Working with equations by doing the same thing to both sides, Understanding simple direct proportion, Using variables and equations to represent situations, Graphing ordered pairs, Translating among verbal, numerical, and graphical representations

This curriculum helps incorporate mathematics into the students’ everyday work and play. It provides the opportunity for students to obtain intuition and understanding about mathematics.

Sixth Grade

Sixth grade Everyday Mathematics emphasizes the following content strands:

Numeration
Reading, writing, and comparing whole numbers, negative numbers, fractions, decimals and percents, Reading, writing and interpreting integer powers of 10, Converting between scientific and standard notation and among fractions, decimals, percents, and mixed numbers, Renaming fractions and mixed numbers in simplest form
Operations and Computation
Using paper-and-pencil algorithms for basic operations with whole numbers, fractions, and decimals, Using mental arithmetic to compute exact answers and to estimate, Performing operations with integers and with numbers in scientific notation, Solving problems using ratios in scale drawings and size-change factors in similar figures, Rounding to any specified place, Adding and subtracting fractions and mixed numbers with unlike denominators, Multiplying and dividing fractions, Finding least common multiples, greatest common factors, and prime factors
Data and Chance
Expressing probabilities as fractions, decimals, and percents, Using tree diagrams to analyze simple probabilistic situations, Understanding that the sum of the probabilities for all possible outcomes of an experiment is 1, Making predictions based on theoretical probabilities and understanding why actual outcomes may differ from predicted outcomes, Constructing and interpreting circle graphs, Understanding how changing the scale on the axes affects a graph, Using measures of central tendency (mean, median, mode) to characterize data sets, Understanding how changes in a data set may affect the mean, median, and mode, Formulating a question, carrying out a survey or experiment, recording data, and communicating results
Geometry
Comparing and contrasting properties of 2-dimensional and 3-dimensional figures, Understanding congruence and similarity, Visualizing, describing, and using translations, reflections, rotations, and size-change transformations, Classifying angles, Identifying angle relationships in triangles and quadrilaterals, in parallel lines cut by a transversal, and in intersecting and perpendicular lines, Understanding and applying basic concepts in topology, Classifying tessellations
Measurement and Reference Frames
Measuring and estimating length, area, volume, weight, and capacity, Using formulas to compute areas, volumes, perimeters, circumferences, and surface areas, Converting and computing with common units of measure, Creating scale drawings, Measuring length to 1/16 inch and 1 mm, Measuring and drawing angles
Patterns, Functions, and Algebra
Recognizing, continuing, and describing complex patterns, Finding the nth term in a sequence, Using variables and open number sentences to represent problem situations, Writing equations to fit given tables of numbers, Evaluating algebraic expressions, Solving linear equations with one and two unknowns by performing the same operation to both sides of the equation, Representing linear functions as equations, in tables and graphs, and verbally as rules, Understanding and applying the order of operations and the distributive property

Our experience has been that our graduates are equipped for junior high math in the area public and private schools. We are even told by some alumni that seventh grade math is “easy”. This curriculum offers a thorough study of the strands of math with lots of review and allows for many different learning styles. Students who “struggle” with math begin to develop an understanding of basic math concepts. Our students exhibit a math confidence which makes for success in any school!