Math : Critical Thinking : : Analogies : Fun

Math analogies in second grade? Absolutely! We have added a daily math analogy to our Calendar Math routine in the mornings to develop deeper critical thinking skills among our students and to expand their math vocabulary. An analogy is simply a way of looking at items and determining the type of comparison that is being made among them. At the beginning of the year, we start out very simple. Here is the first one we did in class:

one : 1 : : three : _____

When read aloud, a student would say, “One is to 1 as three is to blank.” Students would then look at the first part of the analogy.

How are one and 1 related? One is the word form of the number 1.

After students determine the relationship of the first part of the analogy, they use that information to help them determine what the answer to the analogy is.

Three is the word form of the number 3, which means one : 1 : : three : 3.

As the year progresses, our math analogies will get more difficult. Relationships between the two parts will not always be synonyms. Sometimes the relationships will be antonyms or parts of a whole. Students will have to determine the type of relationship first before being able to solve the analogy.

Here are several more samples for the beginning of the year:

Greater than : > : : Less than : _____

15, 25, 35 : 45 : : 11, 21, 31 : _____

1, 3, 5 : odd : : 2, 4, 6 : _____

Want to do a little more practicing at home? The Critical Thinking Co. has a few great resource books to check out.

Math Resources

Here are a few of my favorite math resources. They are well worth the time if you are interested in learning more about any of the topics we discuss in second grade.

1. Mathematically Sane Website (This website gives a clear picture of why we teach math conceptually. There are many great articles and resources to check out!)

2. Young Mathematicians at Work: Addition and Subtraction by Fosnot (This is the first in a series of three books that show how number sense develops through addition, subtraction, multiplication, division, decimals, and percents.)

3. Teaching Student Centered Mathematics by Van de Walle (This is one of several books by Van de Walle, covering everything from operations, story problems, geometry, measurement, fractions, and algebraic reasoning for primary students.)

Shaping Up!

It is important for our students to not only be able to identify shapes, but to know age-appropriate definitions of those shapes. Students enter the second grade with many misconceptions about shapes. For example:

When asked what shape "A" is, most students in second grade can tell you that it is a triangle. When asked what shape "B" is, some students get very confused. It does not look like shape "A" so it cannot be a triangle. This is when the definitions of the shapes come into play. We teach our students to go through the definition and see if the shape fits the definition, while always using proper terminology.

To practice knowing the definition of several polygons, we play shape games. Check out one of our favorites below.

Shape Practice from Melissa Ross on Vimeo.

Measuring Up

We have moved our focus in class to measurement for the next several weeks. Students are working on developing their understanding of the concept of length. We begin by using nonstandard measurement to determine the length of items in the classroom. Nonstandard units are units that are the same size, but not typically used to measure length. For example paper clips, linking cubes, toothpicks, Popsicle sticks, etc.

Students are working to understand that the length of something is the measurement of how many units it is. We are also working on proper measurement techniques.

The units cannot overlap. The above image shows an inaccurate measurement because the units used to measure (paperclips) have overlapped in several areas and are not all turned the same way.

The units must fill the entire space. The above image shows an inaccurate measurement because the units used to measure (paperclips) have gaps in between each unit. This is not measuring the full length of the pencil.

The units must go from the starting to the ending point. The above measurement is accurate. It shows that the pencil is 4 paperclips long. It is an accurate measurement because the paperclips are lined up end to end, have no gaps in between, and measure the full length of the pencil.

Next, we move into standard measurement. Here, students use a ruler to measure the length of objects. The ruler must start at the beginning of the object. We will look at measuring with a ruler in two different ways. The first way, students will line up the object to the ruler at the zero mark and measure the length of the object. This is the easiest way for students when they are learning to measure, but it is not the only way to use the ruler to measure.


The second way we will look at the ruler is starting with a piece of the ruler and measuring how long an object is. We will not necessarily be starting with the zero, so students will need to be able to count units measured. The ruler below shows that the pencil is 8 inches long. Students will have to line the pencil up with an inch mark and physically count each inch.

Ruler Practice (game)

More Ruler Practice (Put the game on whole or half setting)

Games to Stretch Our Thinking!

We use a variety of games in class to motivate students and get them excited about math. We also use them to refresh concepts we have learned about in class or to give students extra practice. "I Have, Who Has" is one of my favorites. We play this game often and our students love it! Check out the video below for our easiest set of cards, beginning place value.

In the game, each student has his or her own card. The "I have" number is going to be an answer to a question someone asks. The "who has" question is the question that a student gets to ask once an answer has been given. 

In the card above, the student would answer if they heard the question, "Who has 24-10?" The student would then say, "I have 14. Who has 54 + 10?" and wait for a student to say, "I have 64."

Sometimes we time students, sometimes we do it just for fun. Our favorite set of cards are the plus or minus 10 cards. Each card in that deck requires a student to add or subtract 10 from any number 1-99 like the sample above.

Take a look!

How do you add 258 + 392 ?

Yes, this clip is of a second grade student. Thank you for sharing, Miss Russell!