First Grade
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
1.1.1 Understand numbers, ways of representing numbers, relationships among
numbers, and number systems.
- count by twos, fives, and tens to 100;
- count a group of objects by ones to 100;
- count a group of objects by twos, fives, and tens up to 30;
- count forward or backward by one beginning with any number less than
100;
- recognize the place value of a digit in numbers to 99;
- read and write numerals up to 100;
- count by tens from any number using a hundred chart;
- use manipulatives to model whole numbers to 99 (e.g., base-ten blocks,
sticks, straws);
- identify odd and even whole numbers to 50;
- model halves and fourths of a single object or figure;
- model halves and fourths of a set of objects;
- match the spoken, written, concrete, and pictorial representations of
1/2 and 1/4;
- recognize one whole as two halves or four fourths;
- count the value of a set of coins up to fifty cents;
- order whole numbers less than 100;
- represent numbers in flexible ways using a variety of materials (e.g.,
23 as 23 ones, 1 ten and 13 ones, and/or 2 tens and 3 ones);
- apply the language of ordinal numbers up to twelfth;
- compare two numbers using the appropriate symbol (i.e., <, >, =);
- use a number line or hundred grid to determine one more or one less than
any number to 50.
1.1.2 Understand meanings of operations and how they relate to one another.
- explain the reasonableness of a solution;
- solve simple story problems involving addition and subtraction with numbers
less than 20;
- develop story problems that illustrate basic addition and subtraction
facts.
1.1.3 Solve problems, compute fluently, and make reasonable estimates.
- use words, actions, pictures, and manipulatives to solve problems;
- use pictures or objects, such as ten frames, to show one more or one
less than any number to 99;
- estimate the number of objects in a group and explain the reasoning for
the estimate;
- explain and justify solutions and strategies in problem solving;
- use a variety of strategies to add and subtract two-digit whole numbers
(e.g., counting up or back, taking away, doubles plus one, comparison,
number relationships, modeling);
- use calculators in problem-solving situations.
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
1.2.1 Sort and classify objects by size, number, and other properties.
- sort objects by two attributes;
- describe how objects in a group are alike and how they are different.
1.2.2 Represent and analyze patterns and functions.
- identify and describe growing patterns found in literature, in the environment,
in physical arrangements, and in pictures;
- translate a repeating pattern from one medium to another (e.g., red-blue-blue
to snap-clap-clap);
- create, describe, and extend concrete, visual, auditory, and number patterns;
- identify the unit of a two-part repeating pattern.
1.2.3 Use concrete, pictorial, and verbal representations to develop an understanding
of the language and symbols of mathematics.
- use manipulatives to demonstrate addition and subtraction sentences written
symbolically involving numbers 0-20;
- communicate and use mathematical terms and symbols appropriately;
- interpret and solve simple open addition sentences.
1.2.4 Illustrate general properties of operations.
- apply the commutative property of addition.
1.2.5 Analyze change in various contexts.
[no accomplishments for this learning expectation at the first grade 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
1.3.1 Analyze characteristics and properties of geometric shapes.
- recognize basic properties of and similarities and differences between
simple geometric figures (e.g., number of sides, corners);
- predict and describe the results of putting together and taking apart
two- and three-dimensional geometric figures.
1.3.2 Specify locations and describe spatial relationships.
- uses directional terms in a variety of situations (e.g., over, under,
forward, backward, between, right, left);
- apply spatial sense to create a figure from memory;
- identify the position of a whole number on the number line.
1.3.3 Recognize and apply flips, slides, and turns.
[no accomplishments for this learning expectation at the first grade 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
1.4.1 Demonstrate understanding of units of measure and measurable attributes
of objects.
- compare and order objects according to length, capacity, and weight;
- recognize the need for standard units of measurement.
1.4.2 Apply appropriate techniques and tools to determine measurements.
- demonstrate understanding of the concept of length;
- measure and estimate length using a variety of non-standard units;
- measure to the nearest inch or centimeter;
- measure weight to nearest pound or kilogram;
- recognize a calendar is a way of measuring time;
- describe the relationship between days and months;
- read and write time to the hour and half-hour;
- compare units of time;
- use a thermometer to measure temperature.
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
1.5.1 Develop, select, and use appropriate methods to collect, organize,
display, and analyze data.
- represent and interpret data using concrete objects, pictures, pictographs,
and bar graphs.
1.5.2 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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