Second Grade Math

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

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.

2.1.1 Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

1. count a set of objects to 100 using an efficient grouping strategy (e.g., two’s, three's, five’s, ten’s);
2. count forward and backward by one from any number less than 999;
3. read and write numerals to 999;
4. recognize the place value of a digit in numbers to 999;
5. identify odd and even numbers to 100;
6. use concrete models or pictures to show whether a fraction is less than a half, more than a half, or equal to a half;
7. match the spoken, written, concrete, and pictorial representations of halves, thirds, and fourths;
8. compare the unit fractions 1/2, 1/3, and 1/4;
9. count the value of a set of coins up to one dollar;
10. order whole numbers less than 1000;
11. compare two numbers using the appropriate symbol (i.e., <, >, =);
12. represent numbers to 999 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);
13. apply the language of ordinal numbers up to twentieth.

2.1.2 Understand meanings of operations and how they relate to one another.

1. develop a story problem that illustrates a given addition or subtraction number sentence;
2. use the number line to demonstrate addition and subtraction;
3. write and identify number sentences that describe situations involving addition and subtraction;
4. write and explain related addition and subtraction sentence.

2.1.3 Solve problems, compute fluently, and make reasonable estimates.

1. solve story problems involving numbers to 100;
2. check for the reasonableness of solutions;
3. use calculators in problem-solving situations;
4. add and subtract efficiently and accurately with single-digit numbers;
5. use a variety of strategies and representations to add and subtract two-digit whole numbers;
6. explain and justify solution strategies used in problem solving;
7. use estimation to justify the reasonableness of a computation.

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

2.2.1 Sort and classify objects by size, number, and other properties.

1. sort objects by two or more attributes;
2. identify the rules by which objects or numbers have been sorted.

2.2.2 Represent and analyze patterns and functions.

1. extend a growing pattern;
2. identify the unit of a three-part repeating pattern;
3. translate a repeating pattern from one medium to another (e.g., red-blue-blue to snap-clap-clap);
4. determine the output for a particular input given the one-operation function rule involving addition and subtraction.

2.2.3 Use concrete, pictorial, and verbal representations to develop an understanding of the language and symbols of mathematics.

1. interpret and solve open sentences that involve addition or subtraction;
2. use the language and symbols of mathematics appropriately to communicate mathematical thinking;
3. use manipulatives to demonstrate addition and subtraction sentences written symbolically involving numbers 0-20.

2.2.4 Illustrate general properties of operations.

1. apply the commutative property of addition;
2. show that subtraction is not commutative;
3. apply the addition and subtraction properties of zero.

2.2.5 Analyze change in various contexts.

1. describe qualitative change (e.g., a student growing taller);
2. describe quantitative change (e.g., a student growing two inches in one year).

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

2.3.1 Analyze characteristics and properties of geometric shapes.

1. recognize, name, build, draw, and compare two- and three-dimensional geometric figures;
2. describe attributes and parts of two- and three-dimensional geometric figures;
3. recognize shapes that have line symmetry;
4. investigate and predict the results of putting together and taking apart two- and three-dimensional geometric figures.

2.3.2 Specify locations and describe spatial relationships.

1. identify the position of whole numbers on the number line.

2.3.3 Recognize and apply flips, slides, and turns.

1. a. illustrate flips, slides, and turns using concrete and pictorial materials.

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

2.4.1 Demonstrate understanding of units of measure and measurable attributes of objects.

1. compare and order objects according to length, capacity, and weight;
2. demonstrate understanding of the concepts of perimeter and area;
3. identify the measurable attributes of objects in the environment.

2.4.2 Apply appropriate techniques and tools to determine measurements.

1. read and write time to the hour, half-hour, and quarter-hour;
2. relate days, dates, weeks, and months to a calendar;
3. explain the relationship between inches and feet;
4. measure length to the nearest centimeter, foot, half-inch, and inch;
5. use strategies to make estimates of length and time;
6. solve problems involving elapsed time in hour intervals;
7. measure and estimate weight and capacity using a variety of non-standard units;
8. find area and perimeter using non-standard units;
9. read thermometers with Fahrenheit and Celsius scales.

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

2.5.1 Develop, select, and use appropriate methods to collect, organize, display, and analyze data.

1. pose questions and gather data to answer the questions;
2. read, interpret, and create tables using tally marks;
3. create pictographs and bar graphs;
4. read and interpret tables, bar graphs, and pictographs.

2.5.2 Apply the basic concepts of probability.

1. predict outcomes of events based on data gathered and displayed;
2. explain whether an event is 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