Second 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

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.

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).

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.

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.

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.