Kindergarten
Numbers and Operations
Content Standard 1.0 The student will develop number and operation
sense needed to represent numbers and number relationships verbally, symbolically,
and graphically and to compute fluently and make reasonable estimates in problem
solving.
Learning Expectations:
1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.
1.2 Understand meanings of operations and how they relate to one another.
1.3 Solve problems, compute fluently, and make reasonable estimates.
Accomplishments
K.1.1 Understand numbers, ways of representing numbers, relationships among
numbers, and number systems.
- count sets of objects up to 20;
- count by ones and tens to 50;
- count backward from 10 to 1;
- match quantities up to twenty with numerals;
- recognize equivalent sets of objects;
- write numerals up to twenty;
- represent quantities up to 20 on ten-frames;
- determine whether a figure has been divided in halves;
- name and identify coins and their values;
- order numbers less than 20;
- express the relationship between two numbers less than 20 using the words
less than, more than, or equal to;
- identify the position of a whole number less than 20 on the number line;
- apply the language of ordinal numbers up to tenth.
K.1.2 Understand meanings of operations and how they relate to one another.
- use manipulatives to develop strategies for addition and subtraction
of whole numbers;
- use a variety of strategies to solve simple verbal story problems involving
numbers 0 to 10.
K.1.3 Solve problems, compute fluently, and make reasonable estimates.
- use words, actions, pictures, or manipulatives to solve problems;
- use pictures or objects, such as a ten frame, to show one more or one
less than any number to 20;
- explain the reasonableness of a solution
Third Grade Benchmarks
Performance Indicators State:
As documented through state assessment –
at Level 1, the student is able to
3.1.spi.1. count by 10’s, 100’s, and 1000’s;
3.1.spi.2. identify whole numbers as odd or even;
3.1.spi.3. add and subtract efficiently and accurately with single-digit whole
numbers.
at Level 2, the student is able to
3.1.spi.4. represent whole numbers to 9999 with models;
3.1.spi.5. identify the place value of a given digit up to thousands;
3.1.spi.6. recognize the value of combinations of coins and bills up to $5;
3.1.spi.7. compare and order whole numbers to 9999 using the appropriate
symbol (i.e.,<, >, =);
3.1.spi.8. add two- and/or three-digit whole numbers;
3.1.spi.9. connect written and pictorial representations of fractions with
denominators up to ten;
3.1.spi.10. solve real-world problems using addition or subtraction of whole
numbers;
3.1.spi.11. determine the correct change from a transaction that is less that
$1.00;
3.1.spi.12. use estimation to select a reasonable solution in problem solving
(addition and subtraction only).
at Level 3, the student is able to
3.1.spi.13. represent whole numbers up to 10,000 in expanded form (e.g,
1000’s
+ 100’s + 10’s + 1’s);
3.1.spi.14. compare unit fractions with denominators up to ten;
3.1.spi.15. subtract two- and/or three-digit whole numbers;
3.1.spi.16. use the multiplication facts 0, 1, 2, 5, and 10 efficiently and
accurately.
Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to
3.1.tpi.1. read and represent whole numbers to 9999;
3.1.tpi.2. create number sentences that describe real-world situations involving
addition and subtraction.
at Level 2, the student is able to
3.1.tpi.3. skip count by tens from any whole number less than 1000;
3.1.tpi.4. use concrete materials and pictorial and symbolic representations
to show numbers to 9999;
3.1.tpi.5. connect the spoken, written, concrete, and pictorial representations
of fractions with denominators up to ten;
3.1.tpi.6. relate adding doubles to multiplying by two;
3.1.tpi.7. use calculators in problem-solving situations.
at Level 3, the student is able to
3.1.tpi.8. select an appropriate rounding strategy in problem-solving situations;
3.1.tpi.9. develop and apply a variety of thinking strategies for computation.
Algebra
Content Standard 2.0 The student will understand and generalize patterns as they represent and analyze
quantitative relationships and change in a variety ofcontexts and problems
using graphs, tables, and equations.
Learning Expectations:
2.1 Sort and classify objects by size, number, and other properties.
2.2 Represent and analyze patterns and functions.
2.3 Use concrete, pictorial, and verbal representations to develop
an understanding of the language and symbols of mathematics.
2.4 Illustrate general properties of operations.
2.5 Analyze change in various contexts.
Accomplishments
K.2.1 Sort and classify objects by size, number, and other properties.
- sort objects by color, size, shape, and kind;
- communicate using mathematical terms appropriately.
K.2.2 Represent and analyze patterns and functions.
- identify patterns in the environment, in arrangements of objects, or
in pictures;
- recognize and extend a concrete, visual, or auditory two- or three-part
repeating pattern;
- create and describe a simple repeating pattern.
K.2.3 Use concrete, pictorial, and verbal representations to develop an
understanding of the language and symbols of mathematics.
- use manipulatives or pictures to demonstrate addition and subtraction
sentences written symbolically involving numbers 0 to 5;
- read and explain simple addition and subtraction number sentences written
symbolically.
K.2.4 Illustrate general properties of operations.
[no accomplishments for this learning expectation at the Kindergarten level].
K.2.5 Analyze change in various contexts.
[no accomplishments for this learning expectation at the Kindergarten level].
Third Grade Benchmarks
Performance Indicators State:
As documented through state assessment –
at Level 1, the student is able to
3.2.spi.1. sort objects by two attributes.
at Level 2, the student is able to
3.2.spi.2. extend repeating and growing numerical or geometric patterns;
3.2.spi.3. represent repeating geometric patterns as repeating numerical patterns;
3.2.spi.4. determine the output for a particular input given the one operation
function rule (i.e., addition, subtraction);
3.2.spi.5. solve open sentences that involve addition and subtraction of whole
numbers zero to twenty.
at Level 3, the student is able to
3.2.spi.6. identify the rules by which objects or numbers have been sorted;
3.2.spi.7. connect open sentences to real-world situations.
Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to
3.2.tpi.1. use manipulatives to demonstrate the commutative property of addition;
3.2.tpi.2. demonstrate that subtraction is not commutative.
at Level 2, the student is able to
3.2.tpi.3. describe a growing pattern;
3.2.tpi.4. determine the input for a particular output given the one operation
function rule (i.e., addition, subtraction);
3.2.tpi.5. create a function rule involving one operation;
3.2.tpi.6. use arrays to represent the commutative property of multiplication;
3.2.tpi.7. describe qualitative change (e.g., a student growing taller);
3.2.tpi.8. describe quantitative change (e.g., a student growing two inches
in one year).
at Level 3, the student is able to
3.2.tpi.9. devise, carry out, and explain a sorting scheme for a group of
objects;
3.2.tpi.10. describe, translate, and create patterns;
3.2.tpi.11. demonstrate understanding that an equation is a number sentence
stating that two quantities are equal.
Geometry
Content Standard 3.0 The student will develop an understanding of geometric
concepts and relationships as the basis for geometric modeling and reasoning
to solve problems involving one-, two-, and three-dimensional figures.
Learning Expectations:
3.1 Analyze characteristics and properties of geometric shapes.
3.2 Specify locations and describe spatial relationships.
3.3 Recognize and apply flips, slides, and turns.
Accomplishments
K.3.1 Analyze characteristics and properties of geometric shapes.
- recognize and name circles, squares, triangles, and rectangles when shown
in various positions;
- recognize examples of circles, squares, triangles, and rectangles in
the environment and as faces of three-dimensional objects;
- recognize basic properties of and similarities and differences between
simple geometric figures (e.g., number of sides, corners);
- create circles, squares, rectangles, and triangles;
- create structures using three-dimensional shapes;
- combine two-dimensional shapes to make pictures.
K.3.2 Specify locations and describe spatial relationships.
- use directional terms in a variety of situations (e.g., over, under,
forward, backward, between, right, left).
K.3.3 Recognize and apply flips, slides, and turns.
[no accomplishments for this learning expectation at the Kindergarten level].
Third Grade Benchmarks
Performance Indicators State:
As documented through state assessment –
at Level 1, the student is able to
3.3.spi.1. name two-dimensional geometric figures (i.e., rectangle,
square, triangle, circle).
at Level 2, the student is able to
3.3.spi.2. name three-dimensional geometric figures (i.e., cube, cylinder,
sphere, cone);
3.3.spi.3. recognize geometric figures that are the same size and shape;
3.3.spi.4. use appropriate mathematical language to find a point on a grid
using whole number coordinates.
at Level 3, the student is able to
3.3.spi.5. identify the result of a transformation that has been applied to
a simple two-dimensional geometric shape (i.e., flips or slides);
3.3.spi.6. identify the line of symmetry in a two-dimensional design or shape.
Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to
3.3.tpi.1. draw two-dimensional geometric figures;
3.3.tpi.2. identify and draw horizontal and vertical lines.
at Level 2, the student is able to
3.3.tpi.3. construct three-dimensional geometric figures;
3.3.tpi.4. draw diagonal lines of geometric figures;
3.3.tpi.5. draw two-dimensional shapes showing lines of symmetry;
3.3.tpi.6. compare and contrast two- and three-dimensional geometric figures;
3.3.tpi.7. use a variety of methods to show that two geometric figures are
congruent.
at Level 3, the student is able to
3.3.tpi.8. predict and describe the results of sliding, flipping, and turning
in two-dimensional shapes;
3.3.tpi.9. describe shapes that have more than one line of symmetry.
Measurement
Content Standard 4.0 The student will become familiar with the units
and processes of measurement in order to use a variety of tools, techniques,
and formulas to determine and to estimate measurements in mathematical and
real-world problems.
Learning Expectations:
4.1 Demonstrate understanding of units of measure and measurable attributes
of objects.
4.2 Apply appropriate techniques and tools to determine measurements.
Accomplishments
K.4.1 Demonstrate understanding of units of measure and
measurable attributes of objects.
- demonstrate understanding of the concept of length;
- compare the length, weight, and capacity of two objects;
- use words to describe time (e.g., day, night, morning, afternoon, yesterday,
today, tomorrow);
- use words to describe temperature (e.g., hot, warm, cool, cold).
K.4.2 Apply appropriate techniques and tools to determine measurements.
- measure and estimate length using a variety of non-standard units;
- distinguish between light and heavy objects;
- tell time to the hour;
- recognize a thermometer as a way of measuring temperature;
- recognize a calendar as a way of measuring time.
Third Grade Benchmarks
Performance Indicators State:
As documented through state assessment –
at Level 1, the student is able to
3.4.spi.1. read and write time to the nearest hour, half-hour, and quarter-hour;
3.4.spi.2. measure length to the nearest centimeter and inch;
3.4.spi.3. solve real-world problems using a calendar.
at Level 2, the student is able to
3.4.spi.4. solve real-world problems involving addition and subtraction of
one-or two- digit measurements;
3.4.spi.5. select an appropriate standard unit to measure length;
3.4.spi.6. use estimation to determine if a length measurement is reasonable;
3.4.spi.7. read thermometers with Fahrenheit and Celsius scales (positive
whole number temperatures);
3.4.spi.8. read and write time at five-minute intervals.
at Level 3, the student is able to
3.4.spi.9. find the perimeter of a rectangle on a grid;
3.4.spi.10. solve real-world problems involving elapsed time to the half-hour.
Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to:
3.4.tpi.1. measure length to the nearest foot;
3.4.tpi.2. use a variety of non-standard units to estimate and/or measure
length, area, and capacity.
at Level 2, the student is able to:
3.4.tpi.3. explain when an estimate of a measurement is sufficient;
3.4.tpi.4. estimate the capacity of a container;
3.4.tpi.5. estimate the weight of an object;
3.4.tpi.6. measure the capacity of a container in liters, cups, pints, quarts,
and gallons;
3.4.tpi.7. measure to the nearest ounce, pound, kilogram, and gram.
at Level 3, the student is able to:
3.4.tpi.8. develop the formula for finding the area of a rectangle;
3.4.tpi.9. explain the relationships among inches, feet, and yards.
Data Analysis
Content Standard 5.0 The student will understand and apply basic statistical
and probability concepts in order to organize and analyze data and to make
predictions and conjectures.
Learning Expectations:
5.1 Develop, select, and use appropriate methods to collect, organize, display,
and analyze data.
5.2 Apply basic concepts of probability.
Accomplishments
K.5.1 Develop, select, and use appropriate methods to collect, organize, display,
and analyze data.
- represent and compare data using concrete objects, pictures, and simple
graphs.
K.5.2 Apply the basic concepts of probability.
- describe events related to students’ experiences as likely or unlikely.
Third Grade Benchmarks
Performance Indicators State:
As documented through state assessment –
at Level 1, the student is able to
3.5.spi.1. interpret pictographs.
at Level 2, the student is able to:
3.5.spi.2. interpret bar graphs;
3.5.spi.3. solve real-world problems in which data is represented in tables;
3.5.spi.4. determine whether an event is certain, possible, or impossible.
at Level 3, the student is able to:
3.5.spi.5. determine the most likely, least likely, or equally likely outcomes
in simple experiments (i.e., spinner, number or color cube);
3.5.spi.6. select all possible outcomes of a simple experiment (i.e., spinner,
coin toss, number or color cube).
Performance Indicators Teacher:
As documented through teacher observation –
at Level 1, the student is able to:
3.5.tpi.1. create bar graphs and pictographs;
3.5.tpi.2. create tables using tally marks.
at Level 2, the student is able to:
3.5.tpi.3. pose questions and gather data to answer questions;
3.5.tpi.4. develop an appropriate method to collect data;
3.5.tpi.5. select an appropriate method to display data;
3.5.tpi.6. explain whether an event is certain, possible, or impossible;
3.5.tpi.7. explain whether an event is likely or unlikely.
at Level 3, the student is able to:
3.5.tpi.8. make conjectures based on data gathered and displayed;
3.5.tpi.9. predict outcomes of events based on data gathered and displayed.
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