## 2nd Grade

18 DecMATH:

1. Students understand the relationship between numbers, quantities, and place value in whole numbers up to 1,000 **( RAIS’s students gained knowledge of these standards in the 1st grade ) **

- Count, read, and write whole numbers to 1,000 and identify the place value for each digit.
- Use words, models, and expanded forms (e.g., 45 = 4 tens + 5) to represent numbers (to 1,000).
- Order and compare whole numbers to 1,000 by using the symbols <, =, >.

2. Students understand the place value of whole numbers: **(3rd grade Math standard as adopted by the California State Board of Education)**

- Count, read, and write whole numbers to 10,000.
- Compare and order whole numbers to 10,000.
- Use expanded notation to represent numbers (e.g., 3,206 = 3,000 + 200 + 6).

3. Students estimate, calculate, and solve problems involving addition and subtraction of two-and three-digit numbers:

- Understand and use the inverse relationship between addition and subtraction (e.g., an opposite number sentence for 8 + 6 = 14 is 14 – 6 = 8) to solve problems and check solutions.
**(RAIS’s students gained knowledge of this standard in the 1st grade)** - Find the sum or difference of two whole numbers up to three digits long.
- Use mental arithmetic to find the sum or difference of two two-digit numbers.
**(RAIS’s students gained knowledge of this standard in the 1st grade)**

4. Students calculate and solve problems involving addition, subtraction, multiplication, and division: **(3rd grade Math standards as adopted by the California State Board of Education)**

- Find the sum or difference of two whole numbers between 0 and 10,000.
- Memorize to automaticity the multiplication table for numbers between 1 and 10.
- Use the inverse relationship of multiplication and division to compute and check results.
- Understand the special properties of 0 and 1 in multiplication and division.

5. Students model and solve simple problems involving multiplication and division:

- Use repeated addition, arrays, and counting by multiples to do multiplication.
- Use repeated subtraction, equal sharing, and forming equal groups with remainders to do division.
- Know the multiplication tables of 2s, 5s, and 10s (to “times 10”) and commit them to memory.

6. Students understand that fractions and decimals may refer to parts of a set and parts of a whole:

- Recognize, name, and compare unit fractions from 1/12 to 1/2.
- Recognize fractions of a whole and parts of a group (e.g., one-fourth of a pie, two-thirds of 15 balls).
- Know that when all fractional parts are included, such as four-fourths, the result is equal to the whole and to one.

7.Students model and solve problems by representing, adding, and subtracting amounts of money:

- Solve problems using combinations of coins and bills.
- Know and use the decimal notation and the dollar and cent symbols for money.

8. Students use estimation strategies in computation and problem solving that involve numbers that use the ones, tens, hundreds, and thousands places:

Recognize when an estimate is reasonable in measurements (e.g., closest inch).

**Algebra and Functions**

1. Students model, represent, and interpret number relationships to create and solve problems involving addition and subtraction:

- Use the commutative and associative rules to simplify mental calculations and to check results.
**(RAIS’s students gained knowledge of this standard in the 1st grade)** - Relate problem situations to number sentences involving addition and subtraction.
- Solve addition and subtraction problems by using data from simple charts, picture graphs, and number sentences.
**(RAIS’s students gained knowledge of this standard in the 1st grade)**

2. Students select appropriate symbols, operations, and properties to represent, describe, simplify, and solve simple number relationships: **( 3rd grade Math standard as adopted by the California State Board of Education )**

- Recognize and use the commutative and associative properties of multiplication
- (e.g., if 5 x 7 = 35, then what is 7 x 5? and if 5 x 7 x 3 = 105, then what is 7 x 3 x 5?).

3. Students represent simple functional relationships: **( 3rd grade Math standards as adopted by the California State Board of Education )**

- Solve simple problems involving a functional relationship between two quantities (e.g., find the total cost of multiple items given the cost per unit).
- Extend and recognize a linear pattern by its rules (e.g., the number of legs on a given number of horses may be calculated by counting by 4s or by multiplying the number of horses by 4).

4. Students know how to manipulate equations: **( 4th grade Math standards as adopted by the California State Board of Education)**

- Know and understand that equals added to equals are equal.
- Know and understand that equals multiplied by equals are equal.

**Measurement and Geometry**

1. Students understand that measurement is accomplished by identifying a unit of measure, iterating (repeating) that unit, and comparing it to the item to be measured:

- Measure the length of objects by iterating (repeating) a nonstandard or standard unit. ( RAIS’s students gained knowledge of this standard in the 1st grade )
- Use different units to measure the same object and predict whether the measure will be greater or smaller when a different unit is used. ( RAIS’s students gained knowledge of this standard in the 1st grade )
- Measure the length of an object to the nearest inch and/ or centimeter. ( RAIS’s students gained knowledge of this standard in the 1st grade )
- Tell time to the nearest quarter hour and know relationships of time (e.g.,minutes in an hour, days in a month, weeks in a year).
- Determine the duration of intervals of time in hours (e.g., 11:00 a.m. to 4:00 p.m.).

2. Students identify and describe the attributes of common figures in the plane and of common objects in space:

- Describe and classify plane and solid geometric shapes (e.g., circle, triangle, square, rectangle, sphere, pyramid, cube, rectangular prism) according to the number and shape of faces, edges, and vertices.
- Put shapes together and take them apart to form other shapes (e.g., two congruent right triangles can be arranged to form a rectangle).

3. Students choose and use appropriate units and measurement tools to quantify the properties of objects: **( 3rd grade Math standards as adopted by the California State Board of Education )**

- Choose the appropriate tools and units (metric and U.S.) and estimate and measure the length, liquid volume, and weight/mass of given objects.
- Find the perimeter of a polygon with integer sides.
- Carry out simple unit conversions within a system of measurement (e.g., centimeters and meters, hours and minutes).

4. Students describe and compare the attributes of plane and solid geometric figures and use their understanding to show relationships and solve problems: **( 3rd grade Math standards as adopted by the California State Board of Education )**

- Identify, describe, and classify polygons (including pentagons, hexagons, and octagons).
- Identify right angles in geometric figures or in appropriate objects and determine whether other angles are greater or less than a right angle.
- Identify, describe, and classify common three-dimensional geometric objects (e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).
- Identify common solid objects that are the components needed to make a more complex solid object.

5. Students understand perimeter and area: **( 4th grade Math standards as adopted by the California State Board of Education )**

- Measure the area of rectangular shapes by using appropriate units, such as square centimeter (cm2), square meter (m2), square kilometer (km2), square inch (in2), square yard (yd2), or square mile (mi2).
- Recognize that rectangles that have the same area can have different perimeters.
- Understand that rectangles that have the same perimeter can have different areas.
- Understand and use formulas to solve problems involving perimeters and areas of rectangles and squares. Use those formulas to find the areas of more complex figures by dividing the figures into basic shapes.

6. Students demonstrate an understanding of plane and solid geometric objects and use this knowledge to show relationships and solve problems: **( 4th grade Math standards as adopted by the California State Board of Education )**

- Identify lines that are parallel and perpendicular.
- Identify congruent figures.

**Statistics, Data Analysis, and Probability**

1. Students collect numerical data and record, organize, display, and interpret the data on bar graphs and other representations:

- Record numerical data in systematic ways, keeping track of what has been counted.
- Represent the same data set in more than one way (e.g., bar graphs and charts with tallies).
- Identify features of data sets (range and mode).
- Ask and answer simple questions related to data representations.

2. Students demonstrate an understanding of patterns and how patterns grow and describe them in general ways: **( RAIS’s students gained knowledge of these standards in the 1st grade )**

- Recognize, describe, and extend patterns and determine a next term in linear patterns (e.g., 4, 8, 12 …; the number of ears on one horse, two horses, three horses, four horses).
- Solve problems involving simple number patterns.

**Mathematical Reasoning**

1. Students make decisions about how to set up a problem:

- Determine the approach, materials, and strategies to be used.
- Use tools, such as manipulatives or sketches, to model problems.

2. Students solve problems and justify their reasoning:

- Defend the reasoning used and justify the procedures selected.
- Make precise calculations and check the validity of the results in the context of the problem.

3. Students note connections between one problem and another.

*s.note: How’s that compared to California’s Common Core Content Standards for Mathematics…*