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| Math Curriculum in Lower School |
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| This outline is an overview of the strands that guide our explorations in math in Lower School. This outline is drawn from Lower School staff discussions and curriculum; the work of Marcy Cook, Marilyn Burns, and others; and the standards of the National Council of the Teachers of Mathematics. The areas listed here are not separate and discrete, but overlapping. Most activities involve a number of these areas at the same time. Guided by the needs of the students, we at times explore a topic more deeply or extend it further. |
| In all of these strands we work on developing problem solving skills and on communicating through numbers, graphics, and oral and written language our understanding and our process. Much work is done with small groups of 7 to 12, some in smaller cooperative groups, and some individually. Manipulatives such as Unifix cubes, counters, tangrams, geoboards, pattern blocks, number tiles, base ten blocks, and money are used as students explore, experiment, and design and carry out projects. Manipulatives are important as a bridge from the children's concrete understandings of the world to more abstract concepts such as place value and regrouping (as in carrying in addition and borrowing in subtraction). Working with manipulatives gives children an underlying understanding to support more abstract learnign and gives a practical meaning to their understanding of abstract concelts. The CDA and Macmillan math workbook series are used as a supplement to reinforce and extend skills. |
| Math is spiral: Topics and skills are revisited over time, through different materials and activities and with ever increasing complexity. This allows the students to develop more thorough understanding as they move through advancing developmental stages. |
| A. Number Sense & Operations |
- Developing Basic Number Sense & Learning Relationships Between Numbers
- One-to-one correspondence
- Rounding and averaging
- Estimation
- Number order (to 1000 and beyond)
- Number systems
- Bases 2-10 using manipulatives
- Place value
- Skip counting (by 2's, 3's, 5's, 10's, 100's)
- Addition facts
- Subtraction facts
- <,>,=
- Discovering Properties of Numbers (even/odd, prime/composite, multiples, factors)
- Understanding and Applying Basic Operations
- Addition - 2 and 3 digit addition with and withouot regrouping
- Subtraction - 2 and 3 digit subtraction with and without regrouping
- Multiplication (beginning with manipulatives and sets and moving to pencil and paper operations, including memorizing times tables and operations of two digits times two digits)
- Division (beginning with manipulatives and sets and moving to pencil and paper operations up through long division)
- Learning how to decide the appropriate operation to apply to problems
- Understanding Fractions and Decimals
- Naming fractions, using fractional parts of wholes and fractions of sets
- Comparing fractions
- Adding and subtracting fractions with like denominators
- Finding common denominators
- Using decimal notation in working with money
- Algebraic Foundations
- Concept of an unknown
- Concept of equality
- Balancing equations
- Writing number names
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| B. Measurement |
- Time (elapsed time, clock time to nearest minute, calendar, epochs and classification of historical objects), Money (values of coins, making change), Linear, Capacity, Mass/Weight, Temperature
- Comparing objects by matching
- Measuring by nonstandard units
- Measuring with standard units (English and metric)
- Choosing suitable units for specific measurements
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| C. Geometry/Spatial Sense |
- Developing the Following Concepts in Plane and Solid Geometric Figures and Geometric Patterns
- Shape
- Size
- Symmetry
- Congruence
- Similarity
- Angles
- Parallel and perpendicular
- Perimiter and circumference
- Area
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| D. Probability and Statistics |
- Collecting Data
- Organizing and Representing Data
- Tallying and categorizing
- Making charts, graphs, etc. including pictographs, bar graphs, pie graphs, and Venn diagrams
- Interpreting Data
- Reading charts, graphs, etc.
- Assigning Probabilities
- Making Inferences
- Drawing conclusions based on data and articulating their reasoning
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| E. Logic |
- Identifying Likeness and Differences
- Classifying and Categorizing Objects, Making Connections, Determing Relationships
- Stating Generalizations, Drawing Conclusions
- Creating a Number Sentence from a Word Problem
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| F. Patterns and Functions |
- Looking for Patterns in Relationships Between Sets of Numbers or Objects
- Identifying Patterns in Math and in Nature
- Predicting Continuations of Patterns
- Generating Patterns
- Timelines
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| Problem solving is a strand that flows through all of these areas. |
| Some of the materials and activities through which these concepts, processes and skills are explored and developed are: |
- Word problems
- Explaining youre thinking
- Strategies
- Drawing pictures
- Assessing the reasonableness of an answer
- Logo computer program
- "If...then" inquirires
- Surveys
- Studies
- S'math (integrated science and math activities)
- Schedules
- Graphs and charts
- Plotting points and shapes on graphs
- Using computer databases
- Using computer spreadsheets
- Ordered pairs
- Pattern blkocks
- Patterns in nature
- Tangrams
- GeoBoards
- Woodworking
- Other manipulatives
- Clocks
- Hundred Day activities
- Measuring projects
- Design technology
- Cooking
- Inch cubes
- Scales
- Rulers
- Timers
- Cuisenaire rods
- Measuring cups
- Dice games
- Job cards
- Math games
- Counting and sorting
- Computation
- CDA math book series
- Hundred's board
- Base ten blocks (Deine's blocks)
- Chip trading
- Calendar
- Estimation of activities
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