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Second Grade Math Curriculum (Sample Problems, Songs, and Games)

This page is all about how to master 2nd Grade math and getting ready for 3rd grade math curriculum. Parents can boost their kids’ education and keep up with the classroom using this article. We emphasize that having fun is the key to success, so remember to keep the practice fun and challenging!

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    Introduction To Math Education

    At TutorOcean we stand for helping students thrive. In Math, one thrives by always building on prior knowledge. Math education always works on this principle. Elementary school math is the foundation for high school math. High school math is the foundation for Undergrad math. Undergrad Math is the foundation for PhD math. A poor foundation could affect the whole education system. That is why it is important to master the basics of math. 80% on your math test may sound good, but what if the foundation of your house was only 80% complete? You can’t ignore foundation problems. It is with this perspective that we should look at our child’s education.

    A diagram showing 2 pyramids. They represent educational learning with the foundation being Elementary School Math. The Pinnacle being a pHD. A knowledge gap at the base cuts through to the top.
    A diagram showing 2 pyramids. They represent educational learning with the foundation being Elementary School Math. The Pinnacle being a pHD. A knowledge gap at the base cuts through to the top.

    2nd Grade Math Curriculum

    Check your local education website for grade 2 math standards. Sometimes they use the word “standard” instead of “curriculum”. It all means the same thing. The content of this blog post is an approximation of the grade 2 math curriculum. Your school district’s curriculum may differ.


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    2nd Grade Math Curriculum Examples

    Addition And Subtraction Within 40

    Numbers let us say what we see. They are my friends and I hope they can be yours too. Cavemen only had two numbers: 1 and 2.

    The number 1 represents one-ness. If there is only one of something, anything.

    • One apple
    • One rock
    • One Mom
    • One family
    • First day

    The number two represents two-ness. If there are only two of something.

    • Two cherries
    • Two wheels (a bike)
    • Two parents
    • A couple dogs
    • Second day

    After 2 of something, the cavemen didn’t have numbers to express how many. They only said “Many”, But “Many” is not a number. Human Civilization continued to evolve, and we invented a whole number system! Numbers can represent anything. They can be big or small. The number of leaves on a tree. 10,000. The number of gold bricks in my basement. 0.

    Numbers can bunch together. That means “added” together. If we want to know the number of apples and cherries, then we can add the number of apples to the number of cherries.

    A whiteboard showing addition of apples. two apples plus one apple is three apples.
    The TutorOcean whiteboard shows addition of apples. two apples plus one apple is three apples.
    A whiteboard shows subtraction of 1 apple from 2 apples
    The TutorOcean whiteboard shows subtraction of 1 apple from 2 apples.

    Got the idea? Good now try on your own to practice. Adding things around your house. Got Apples?

    Addition And Subtraction Word Problems

    • If you’ve got a basket of 7 apples and you pick 7 more apples, how many apples do you have?
    • If you’ve got a basket of 7 cherries and you eat 3 of them, how many cherries do you have?
    • If you’ve got 20 cherries and 20 apples, how many cherries and apples (together) do you have?

    Place Value

    Place value lets us talk about bigger numbers. Hold your hand out and count your fingers. I hope you’ve got ten! If two people hold out their hands you can say that there are two counts of ten, or twenty fingers. From 10 to 20, the 10-place value increased by 1.

    The “place” shows how big the number is. There is a one’s place for counting one-by-one, and there’s a ten’s place for counting ten-by-ten.

    A whiteboard showing addition of two tens by showing two pairs of hands with all fingers extended
    A TutorOcean whiteboard shows addition of two tens by showing two pairs of hands. With all fingers extended each pair of hands represents 10.

    Place Value Word Problems

    • If you’ve got two ten’s, eight one’s, how many do you have?
    • If you’ve got four ten dollar bills, how much money do you have?
    • If you’ve got forty dollars and you spend ten dollars on lunch, how much money do you have left over?

    Money

    A whiteboard shows a quarter and a nickel added up equals 35 cents.
    A TutorOcean whiteboard shows a quarter and a nickel added up equals 35 cents.

    Money Word Problems

    • If you’ve got a quarter and a dime, how much money do you have?
    • If you’ve got a dollar and you buy an apple for a quarter, how much money do you have left?
    • If you’ve got a dollar, a quarter, a dime, a nickel, and a penny, how much money do you have?

     Time

    • How to tell time
    • How to tell time on a number line EX: 7:30
    A line drawn with 12 ticks each representing one hour. A blue dot is halfway between 7 and 8. This represent s the time 7:30
    A line drawn with 12 ticks each representing one hour. A blue dot is halfway between 7 and 8. This shows the time as 7:30.
    • How to tell time on a clock
    A clock with two hands, The hour hand points to halfway between 7 and 8 and the minutes hand points to 6.
    A clock with two hands. The hour hand points to halfway between 7 and 8 and the minutes hand points to 6. This reads 7:30.
    • Pro Tip: In a pinch, if you need to know the times tables for 5s, look at the clock. Most exam rooms have a clock and it’s not cheating to look at it!
    A diagram shows the meaning of the ticks on a clock.
    In a pinch, you can use the clock to remember the 5's on the times table.

    Measurement

    When we want to say what we see with numbers, the numbers represent something. Sometimes what it represents is the length of something. The length of your arms or your height for example. We have different kinds of measurements to make measuring easier. It’s easier to measure a small thing with a small measurement. Also, it’s easier to measure a large thing with a large measurement. Think about the different sizes of things. A Tree against. A mouse. A Cell or a City.

    What measurement would you use to measure:

    • A mouse’s tail
    • An elephant’s trunk
    • A chocolate bar
    • The distance to the nearest shopping mall
    • The length of a cell

    Using these (metric system) measurements:

    Metric System

    • Kilometer (Cities)
    • Meter (Height)
    • Centimeter (Finger)
    • Millimeter (Finger nail)
    • Micrometer (Bacteria)

    Imperial System

    • Mile (Cities)
    • Yard (Tree)
    • Feet (Height)
    • Inch (Thumb)

    It’s possible to measure something big with something small. What would happen though? The numbers will get too big! That makes it hard. Pick the right measure and it will be more simple. What are you measuring? What “measure” makes sense to use?

    How To Measure With A Ruler

    Using a 6-inch ruler a flower is measured by width to be 3 inches
    You can measure small stuff in inches with a 6-inch ruler.

    Estimating

    If you cannot measure, you can estimate. The way it works is by looking at and understanding the difference between what we know and what we don’t know. For example here we see a 40 cm sunflower beside a sunflower that is about half the height. So, we can say that the shorter sunflower is about 20 cm because 20 + 20 = 40.

    A picture shows the comparison of two sunflowers. One has a known height of 40 cm, while the other one is unknown. We can estimate that the smaller one is about 20cm because by inspection we see that it is about half the height.
    A picture shows the comparison of two sunflowers. One has a known height of 40 cm, while the other one is unknown. We can estimate that the smaller one is about 20cm because by inspection we see that it is about half the height.

    Rounding To The Nearest 10

    Another way to estimate is to round to the nearest place value. You can round to any place value. The the 1’s place, the 10’s place, the 100’s place. 

    Measuring Word Problems

    • You are 4 kilometers away from from school. You run half way to school, how many kilometers did you run?
    • You have 100mL of fruit juice. You drink 20 mL in one sip. How many mL of fruit juice is there after 2 sips of 20mL?
    • You have 12 inches of fruit roll up, you eat 10 inches of it. How many inches of fruit roll up do you have left?
    a picture of a 6 inch ruler measuring a fruit roll up
    You can measure a fruit roll up in inches with a ruler.
    A diagram showing a beaker of juice with 200 ml before and after two sips have been taken.
    Juice in a small container is best measured in millilitres.

    Data

    A Pictograph is a way to show quantity of different things and compare them. Quantity means the number of something. The number of tons of wheat produced by a country is in the pictograph below:

    A pictograph shows the top 5 wheat producing countries in the world
    A pictograph shows the top 5 wheat producing countries in the world. Created by TutorOcean virtual classroom.

    Geometry

    There are three types of ovals. Some ovals have two axes of symmetry, meaning they look the same on both sides of a line, like a speed skating rink. Some ovals only have one axes of symmetry, like an egg. The last type of oval is a circle, and it has endless axes of symmetry!

    This is a diagram with two kinds of ovals pictured. On the left is a perfect oval which has two axes of symmetry like a skating rink. On the right if a lopsided oval like an egg. It has one axis of symmetry.

    Ovals have:

      • No sides (or infinite sides?)
      • Can have one axis of symmetry or two
      • Comes from Latin word for egg “Ovum”

    There is only one kind of circle. A circle is a special oval with infinite axes of symmetry. That means any line that passes through the center of the circle is an axes of symmetry. That means that the circle looks the same on both sides of the line.

    A picture shows a comparison of a circle and an oval. A ciricle is an oval but its height and width are the same. Ovals are lopsided.
    A picture shows a comparison of a circle and an oval. A circle is an oval but its height and width are the same.
    • A circle is also an oval
    • Like an oval it has no sides (or infinite sides?)
    • It has an infinite number of axis of symmetry

    Rectangles:

    • A rectangle  always has right angles (90 degrees).
    • A square is a special kind of rectangle with equal sides.

     

    A picture shows the comparison of two rectangles. The one on the left is a square. The one on the right is a flat rectangle.
    A picture shows the comparison of two rectangles. The one on the left is a square. The one on the right is a flat rectangle.

    Triangles:

    There are many kinds of triangles. Three main ones are equilateral, Isosceles, and Right-Angled Triangles. Triangles are special because any polygon is actually a bunch of triangles. Even circles are triangles in computer graphics.

    Three types of triangles are shown in this picture. Equilateral triangle is the one where all sides are equal. Isosceles is the one where two sides are equal. The right-angle triangle is the one where on angle is 90 degrees.

    There are three types of triangles are in this picture. Equilateral Triangle is the one where all sides are equal. Isosceles Triangle is the one where two sides are equal. The Right-Angle Triangle is the one where on angle is 90 degrees.

    • All triangles has acute angles. That means every triangle has an angle less than 90 degrees. 
    • Some triangles have an obtuse angle. That means one of the angles of the triangle is greater than 90 degrees.
    • Trapezoid
      • Obtuse angle
      • Acute angle
    • Rhombus
      • A square is a rhombus, but rhombus not a square

    Grade 2 Math TEKS (Texas Essential Knowledge and Skills)

    • It’s a process for teachers to follow to improve a student’s understanding of complex content.
    • The process is about defining content standards.
    • In the State of Texas there is an assessment of academic readiness called STAAR. 
    • In Mathematics, the STAAR assessment starts looking at students starting in Grade 3.
    • More information is available about the STAAR assessments here. 

    Grade 2 Math Songs

    Learn How To Read The Clock Song

    Days Of The Week (Seven Days)

    2nd Grade Math Games

    Your second grader will love learning math from these games.

    Save The Cat (Addition, Subtraction Under 40 Game) Coming Soon!

    Second Grade Math Problem Worksheets

    Are you looking for something you can hand to your second grader to start learning? Check out our free 2nd grade math worksheets which you can download or try out our math problem generator to learn online.  You can make a copy, download, and print these problems. Make it an exciting game and start learning Grade 2 math today! If you don’t have a printer, open it with the iPad and play online. 

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    Did you master Grade 2 Math? Continue to our Grade 3 Math Curriculum resource page!

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