Putnam Valley Central School District

Core Content and Skills
Math Grade 1
2007-2008
BOE Approved

How Many of Each

Content

Skills

Counting and Quantity: Developing strategies for accurately counting a set of objects by ones

Counting a set of up to 20 objects by ones

Practicing the rote counting sequence forward and backwards from 1 to 30

Connecting number names and written numbers to the quantities they represent

Developing and analyzing visual images for quantities up to 10

Counting and quantity: developing an understanding of the magnitude and position of numbers

Ordering a set of numbers and quantities up to 12

Comparing two quantities up to 20 to see which is larger

Developing an understanding of how the quantities in the counting sequence are related: each number is 1 more or 1 less than the number before or after it

Number composition: composing numbers up to 10 with 2 addends

Finding and exploring relationships among combinations of numbers up to 10

Recording combinations of two numbers that make a certain total

Solving a problem with multiple solutions

Solving a problem in which the total and one part are known

Whole-number operations: making sense of and developing strategies to solve addition problems

visualizing and retelling the action in an addition situation

Modeling the action of an addition problem with counters or drawings

finding the total of two or more quantities up to a total of 20 by counting all,counting on, or using number combinations

seeing the adding the same two numbers results in the same total, reguardless of context

Whole-number operations: using manipulatives,drawings, tools and notations to show strategies and solutions

using the number line as a tool for counting

introducing standard notation for comparing quantities (greater than, less than and equal to)

introducing and using standard notation (1 and 5) to represent addition situations

recording a solution to a problem

representing number combinations with numbers, pictures and/or words

Making Shapes and Disigning Quilts (2-D Geometry)

Content

Skills

Features of Shape: Describing, identifying, and comparing 2-D shapes

Notice shapes in the environment.

Describe, compare, and name 2-D shapes

Develop visual images of and language for describing 2-D shapes.

Identify common attributes of a group of shapes.

Identify characteristics of triangles and quadrilaterals.

Identify and making triangles and quadrilaterals of different shapes sizes.

Recognize that there are many types of quadrilaterals (e.g., rectangles, trapezoids, squares, rhombi)

Decompose shapes in different ways

Features of Shape: Composing and decomposing 2-D shapes

Cover a region without gaps or overlaps using multiple shapes

Decompose shapes in different ways

Find different combinations of shapes that fill the same area

Examine how shapes can combined to make other shapes

Alter designs to use more or fewer pieces to cover the smae space

See relationships between squares and triangles

Solving Story Problems: Addition, Subtraction, and the Number System 2

Content

Skills

Number Combinations: Composing numbers up to 15 with 2 or more addends

Finding as many 2-addend combinations of a number as possible

Proving that all of the possible combinations have been found

Solving a problem in which the total and one part are known

Finding and exploring relationships among combinations of number up to 15

Developing the strategy of counting on

Whole-Number Operations: Making sense of and developing strategies to solve addition and subtraction problems with small numbers

Developing counting on as a strategy for combining two numbers

Visualizing and retelling the action in addition and subtraction situations involving removal

Finding the total of two or more quantities up to a total of 20 by counting all, counting on, or using number combinations

Estimating whether an amount is more or less than a given quantity

Modeling the action of an addition or subtraction (removal) problem with counters or drawings

Subtracting one number from another, with initial totals of up to 12

Developing strategies for addition and subtraction (removal) problems

See that subtracting the same two numbers (e.g., 6 from 10) results in the same difference regardless of context (e.g., number and dot cubes, cards, objects)

Number Composition: Representing numbers by using equivalent expressions

Generating equivalent expressions for a number

Counting and Quantity: Developing strategies for accurately counting a set of objects by ones

Practicing the rote counting sequence forward and backward, starting from any number 1-60

Develop and analyze visual images for quantities

Accurately count a set of objects by ones, up to 60

Practice the oral counting sequence from 1 to 100

Write the sequence of numbers (as high as students know)

Identify and use patterns in the sequence of numbers to 100

Whole-Number Computation: Using manipulatives, drawings, tools, and notation to show strategies and solutions

Recording solutions to a problem

Using numbers and standard notations (+, -, =) to the quantities and actions they represent

Using the equal sign to show equivalent expressions

Use the number line as a tool for counting

Develop methods for recording addition and subtraction (removal) strategies

See the 100 chart as a representation of the counting numbers to 100

What Would You Rather be? (Data Analysis)

Content

Skills

Data Analysis: Sorting and classifying

Describe attributes of objects

Use attributes to sort a set of objects

Look carefully at a group of objects to determine how they have been sorted

Data Analysis: Representing data

Make a representation to communicate the results of a survey

Make sense of data representations, including pictures, bar graphs, tallies, and Venn diagrams

Compare what different representations communicate about a set of data

Use equations to show how the sum of the responses in each category equals the total responses collected

Organize data in numerical order

Data Analysis: Describing data

Describe and compare the number of pieces of data in each category or at each value and interpret what the data tells you about the group

Understand that the sum of the pieces of data in all the categories equals the number of people surveyed

Use data to compare how two groups are similar or different

Data Analysis: Designing and carrying out a data investigation

Interprete results of a data investigation

Choose a survey question

Make a plan for gathering data

Collect and keep track of survey data

Fish Lengths and Animal Jumps

Content

Skills

Linear Measurement: Understanding Length

Understanding what length is and how it can be measured

Measuring lengths using different-sized units

Identifying the longest dimension of an object

Comparing lengths to determine which is longer

Identifying contexts in which measurement is used

Understanding the meaning of at least in the context of linear measurement

Linear Measurement: Using linear units

Developing accurate measurement techniques

Describing measurements that are in between whole numbers of units

Understanding that measurements of the same length should be the same when they are measured twice or by different people using the same unit

Understanding that measuring an object using different-length units will result in different measurements

Measuring length by iterating a single unit

Linear Measurement: Measuring with standard units

Using inch tiles to measure objects in inches

Number Games and Crayon Puzzles

Content

Skills

Number Composition: Composing numbers up to 29 with 2 or more addends

Develop fluency with the 2-addend combinations of 10

Find relationships among different combinations of numbers up to 20

Use 5 + 5 to reason about other combinations of 10

Find as many 2-addend combinations of a number as possible

Try to prove that all the possible 2-addend combinations of a number have been found

Whole-Number Operations: Making sense of and developing strategies to solve adition and subtraction problems with small numbers.

Solve related story problems

Solve a problem in which the total and one part are known

Add 2 or more single-digit numbers

Visualize, retell, and model the action in addition and subtraction (removal) situations

Subtract one number from another, with initial totals of up to 12

Develop strategies for solving addition and subtraction (removal) situations

Develop strategies for solving addition and subtraction story problems

Solve addition and subtraction story problems

Representing Mathematical Thinking: Using manipulatives, drawings, tools, and notation to show strategies and solutions.

Using numbers and standard notation (+, -, =) to record

Develop strategies for recording solutions to story problems

Color, Shape, and Number Patterns

Content

Skills

Repeating Patterns: constructing, describing and extending repeating patterns

Identifying what comes next in a repeating pattern

Using the word pattern to describe some kind of regularity in a sequence

Repeating patterns: Identify the unit of a repeating pattern

Representing a repeating unit in more than one way

Comparing repeating and non-repeating sequences

Describing a repeating pattern as a sequence built from a part that repeats over and over called the unit

Identifying the unit of a repeating pattern

Extending a repeating pattern by adding on units to the pattern

Identifying what comes several steps beyond the visible part of a repeating pattern

Comparing repeating patterns that have the same structure, but different structures

Number Sequence: constructing, describing and extending number sequences with constant increments generated by various contexts

Associating counting numbers with elements of a repeating pattern

Determining the element of a repeating pattern associated with a particular counting number

Determining and describing the number sequence associated with one of the elements in the unit of a repeating pattern

Modeling a constant rate of increase with concrete materials

Describing how a number sequence represents a situation with a constant rate of change

Extending a number sequence associated with a situation with a constant rate of change

Determining how and why the same number sequences can be generated by different contexts

Twos, Fives, and Tens

Content

Skills

Counting and Quantity Developing strategies for accurately counting a set of objects by ones and by groups

Count and keep track of amounts up to 60

Count on from a known quantity

Organize objects to count them more efficiently

Identify and using patterns in the number sequence and on the 100 chart

Identify, read, write, and sequence numbers to 100 and beyond

Count and combine things that come in groups of 1, 2, 4, 5, and 10

Count by 2s, 5s, and 10s

Explore a 2:1 (the number of hands in a group of people) and a 5:1 relationship (the number of fingers and hands in a group)

Count by numbers other than 1

Develop strategies for organizing sets of objects so that they are easy to count and combine

Develop meaning for counting by groups of 10

Whole-Number Operations Using manipulatives, drawings, tools, and notation to show strategies and solutions

Use addition notation (+, =) to record

Record strategies for counting and combining

Consider notation for equivalent expressions (e.g., 7 + 8 = 10 + 5)

Computational Fluency Knowing addition combinations of 10

Develop fluency with the 2-addend combinations of 10

Solve a problem in which the total (10) and one part are known

Mathematical Emphases

Content

Skills

Features of shape: describing and comparing 2-D and 3-D shapes

Developing vocabulary to describe 3-D shapes and their attributes

Comparing size, shape, and orientation of objects

Identifying the characteristics of 3-D objects by touch

Describing a rectangular prism

Comparing a rectangular prism

Observing and describing characteristics of 3-D shapes

Recognizing shapes in the world

Describing 3-D structures

Features of shape: Exploring the relationship between 2-D and 3-D shapes

Matching a 3-D object to a 2-D outline of one of its faces

Matching a 3-D object to a 2-D picture of the object

Making a 3-D objects out of 2-D pieces

Making a 2-D representation of a 3-D object or structure

Building a 3-D construction from a 2-D representation

Bigger, Taller, Heavier, Smaller cont. from May

Content

Skills

Weighing and Balancing

Filling

Measuring Length

Developing a sense of heavier and lighter by feel

Developing language to describe and compare weights

Learning to use a balance

Comparing the weights of objects using a balance

Representing the results of weight comparisons

Developing language to describe and compare capacity

Comparing capacities

Measuring and comparing capacity using nonstandard units

Collecting and keeping track of data

Developing language to describe and compare lengths

Comparing lengths directly

Measuring and comparing length using nonstandard units

Ordering lengths

Representating measurements with numbers, concrete materials, and pictures