Kindergarten

## Second Grade Common Core Math Standards and Curriculum

In Common Core, 2nd grade math standards are designed to build on previously learned math. Many of the concepts learned in first grade carry over into second grade math, with standards repeating. These fundamentals and basics will provide students with  the framework they need to build new math concepts.

#### Understanding of Base Ten Principles

• The base ten system covers areas of place value and fluency with notation. Students should have already covered place value to 100 in the first grade, focusing on tens and ones. This gives them the ability to work towards exercises involving much greater numbers.

#### Addition and Subtraction with Single Digit Equations

• Fluency with addition and subtraction is vital to working towards more complex equations. The curriculum in second grade math standards ask students to practice with basic addition and subtraction which will have been a large part of your student’s previous year in school. Numbers below 20 were likely focused on, paving the path towards higher value problems.

#### Recognition of Basic Shapes

• By the time students enter second grade, they should be able to recognize and name basic shapes on sight. These include square, circle, rectangle, triangle, rhombus (diamond), ovals, and hearts. Common Core math standards, second grade and higher, will build on this basic shape knowledge. Recognizing the shapes and qualities they possess will aid them in their eventual development of equations and operations involving rules in geometry.
The 2nd grade math Common Core standards are built with step-by-step concept development. As such, falling behind in one area ultimately leads to falling behind in others. To ensure steady and consistent learning habits, encourage your child to practice what they have learned in math over the summer. Games and workbooks, such as the ones available through Argo Prep, will assist in an enjoyable, dynamic, and flexible learning experience while strengthening understanding of 2nd grade Common Core standards for math.

### 2nd Grade Common Core Math Standards: 4 Main Components

In the 2nd grade, math standards hone in on four main mathematical components.

#### Area 1: Base Ten Notation and Operations

In the first, students will develop their skills in the base ten notation system. They will extend their knowledge of this area and recognize place value to higher, more complex numbers. Additionally, they will begin counting in groups, such as in fives and tens, rather than in the typical one-by-one format. This develops a base for multiplication. Place value is an important aspect of common core math standards. Grade 2 students should be able to recognize groups within numbers. For example, your child should be able to break down the number 178. They should recognize that  the number 1 represents a single group of 100, the number 7 represents seven groups of 10, and the number 8 represents eight ones. This ability to interpret groups within a number makes for the basis of division. It will also aid in their understanding of future complex math and larger numbers. Place value to 1,000 will be studied in the second grade.

#### Practice Suggestion for Area 1:

The base ten system can be studied at home with physical examples and base ten notation worksheets. Base ten blocks are excellent tools that allow for physical manipulation and experimentation. Worksheets with illustrations of these blocks are also excellent tools in learning these concepts and meeting grade 2 Common Core math standards. Tutorials may help as well. ArgoPrep provides excellent tutorials on place value and counting in groups. Counting in groups can be practiced with groups of like objects. Lego bricks or other stackable items are excellent choices, as they make creating and maintaining easy-to-recognize groups simple.

#### Area 2: Addition and Subtraction Operations and Algebra

In the second, students will create further fluency with addition and subtraction. Multi-digit numbers will begin appearing in equations, rather than simple single-digit problems. Second graders will develop addition and subtraction fluency with sums and differences of up to 100.  By the end of second grade, students should have all two-addend, one-digit sums memorized. These include 1+1 and so on, all the way up to 9+9. Second grade students should be able to use mental strategies to quickly solve addition and subtraction equations from 1 to 20. From here, addition and subtraction within 100 can begin.  By the end of second grade math, common core standards call for sufficient practice with unknown values as well. This means that in an equation, such as 4+7=11, one of the numbers is represented by a symbol. Rather than adding up the equation outright, students must know how to solve 4+?=11. This develops the flexible algebraic thinking that is necessary for future complex math problems.
##### Practice suggestion for Area 2:
Continue practice with simple, single-digit equations. These must be mastered before other equations can be effectively incorporated. Ten frames and counters are excellent mathematical tools. These gridlike sets of 10, along with the colored counters, make recognizing number groups easy. Other physical examples are encouraged. Worksheets with illustrations are helpful in visualizing the math at hand. ArgoPrep’s workbook selection provides many such illustrations for your student to work with. Coloring pages with a color-by-number design are fun math activities. These worksheets include equations to solve and a key for numbers and their corresponding colors. A fun visual is always a good tool in working math practice into your child’s routine.  Solving equations with unknown values can also be practiced with ten frames and colored counters. Simply write out the equation, place uniform colored counters in the frame to represent the known value, and use another color of counters to count up to (or down to) the given sum or difference. Other physical examples can be used to represent unknown value equations. As long as they are similar in size, shape, and color, they can be used.

#### Area 3:

In the third, students will begin working with standard measurement systems. They will recognize the difference between the typical systems of measurement, as in inches and centimeters. They will begin working with them in real-world examples and with their physical surroundings to develop familiarity and skill with measurement.  Second graders will also work with word problems involving measurement. These are akin to addition and subtraction, but with more concrete examples directly related to measurement. For instance, your child may come across something like this: “Julie needs 9 inches of string to make a necklace. She has 5 inches of string. How much more string does Julie need for her necklace?” While word problems are not new to second graders, those with measurement are.
##### Practice suggestion for Area 3:
Practicing measurement at home can become a fun activity. Using a ruler or measuring tape, measure different things around your home. Measure in both inches and centimeters. Measuring your child’s toys, objects in their room, or even parts of their body, such as their hands and feet, can prove both entertaining and educational. Quiz your child as you measure things around your home. For example, if one of their favorite action figures is 4 inches tall and the other is 9 inches tall, ask your child how many inches taller the second figure is. This will encourage flexible thinking and help them when they face word problems.

#### Area 4:

In the fourth and final area of 2nd grade Common Core standards, math concepts surrounding shapes and their properties will deepen. Students will expand their knowledge in geometry. Students will begin by making observations about the basic shapes that they have become familiar with. Using these observations, they will draw conclusions about the rules and mathematical properties of the shapes and pave the way for complex geometrical operations.
##### Practice Suggestion for Area 4:
Point out shapes in your and your child’s surroundings. Ask them about the shapes. What is the shape called? How many sides does the shape have? How do you know it’s that shape? Which side of the shape is the biggest? Recognizing real-world examples of shapes will aid them when they complete worksheets dealing in geometry. Though perimeter and area aren’t necessarily studied in 2nd grade, developing fluency with shapes and their qualities is a very important part of these math standards. Students in the 2nd grade will need this knowledge to move into higher geometry.

## Operations & Algebraic Thinking

### Represent and solve problems involving addition and subtraction.

#### CCSS.MATH.CONTENT.2.OA.A.1

Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1 Add and subtract within 20.

#### CCSS.MATH.CONTENT.2.OA.B.2

Fluently add and subtract within 20 using mental strategies.2 By end of Grade 2, know from memory all sums of two one-digit numbers.

### Work with equal groups of objects to gain foundations for multiplication.

#### CCSS.MATH.CONTENT.2.OA.C.3

Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.

#### CCSS.MATH.CONTENT.2.OA.C.4

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

## Number & Operations in Base Ten

### Understand place value.

#### CCSS.MATH.CONTENT.2.NBT.A.1

Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases:

#### CCSS.MATH.CONTENT.2.NBT.A.1.A

100 can be thought of as a bundle of ten tens — called a "hundred."

#### CCSS.MATH.CONTENT.2.NBT.A.1.B

The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

#### CCSS.MATH.CONTENT.2.NBT.A.2

Count within 1000; skip-count by 5s, 10s, and 100s.

#### CCSS.MATH.CONTENT.2.NBT.A.3

Read and write numbers to 1000 using base-ten numerals, number names, and expanded form.

#### CCSS.MATH.CONTENT.2.NBT.A.4

Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

### Use place value understanding and properties of operations to add and subtract.

#### CCSS.MATH.CONTENT.2.NBT.B.5

Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

#### CCSS.MATH.CONTENT.2.NBT.B.6

Add up to four two-digit numbers using strategies based on place value and properties of operations.

#### CCSS.MATH.CONTENT.2.NBT.B.7

Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

#### CCSS.MATH.CONTENT.2.NBT.B.8

Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a given number 100-900.

#### CCSS.MATH.CONTENT.2.NBT.B.9

Explain why addition and subtraction strategies work, using place value and the properties of operations.1

## Measurement & Data

### Measure and estimate lengths in standard units.

#### CCSS.MATH.CONTENT.2.MD.A.1

Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

#### CCSS.MATH.CONTENT.2.MD.A.2

Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen.

#### CCSS.MATH.CONTENT.2.MD.A.3

Estimate lengths using units of inches, feet, centimeters, and meters.

#### CCSS.MATH.CONTENT.2.MD.A.4

Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.

### Relate addition and subtraction to length.

#### CCSS.MATH.CONTENT.2.MD.B.5

Use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem.

#### CCSS.MATH.CONTENT.2.MD.B.6

Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram.

### Work with time and money.

#### CCSS.MATH.CONTENT.2.MD.C.7

Tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

#### CCSS.MATH.CONTENT.2.MD.C.8

Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using \$ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

### Represent and interpret data.

#### CCSS.MATH.CONTENT.2.MD.D.9

Generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units.

#### CCSS.MATH.CONTENT.2.MD.D.10

Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.

## Geometry

### Reason with shapes and their attributes.

#### CCSS.MATH.CONTENT.2.G.A.1

Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces.1 Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

#### CCSS.MATH.CONTENT.2.G.A.2

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

#### CCSS.MATH.CONTENT.2.G.A.3

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

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