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.

Modeling a Problem

We encourage students to visualize problems or create models for them if they do not understand what a problem is asking. Models are simply tools for thinking. We have problem solving strategy posters hanging in each second grade classroom to remind students of ways they can go about solving a problem if they do not understand it. Some of the posters include: make a chart or table, draw a diagram, guess and check, find a pattern, use logic, make it simpler, use real objects, or make a list. Let's take a look at how we can use some of these ideas to solve the problem below.

Miss Russell is getting ready for the Relay for Life. She needs 36 inches of tape to hang a sign over the Chets Creek booth. She heads to the store to buy the tape and realizes that they sell tape in feet, not inches. How many feet of tape will she need to buy to have the exact amount she needs to hang her sign? (She knows that 1 foot is equal to 12 inches.)

Your child may see problems similar to this one in Calendar Math. Students are discovering the relationship between units of measurement. (We have previously discussed the relationship in centimeters, decimeters, and meters.) As concepts are learned, we try to present them in a real-life context for students.

One thing that would help getting started with this problem would be to make it simpler. Find out what the problem is really asking. 12 inches = 1 foot so 36 inches = ? feet

Once students determine what the problem is asking, they can then use a strategy to help them. For this type of problem, students may want to make a t-chart or table to help show their thinking. Below are three student samples:

This student used three different strategies to model the problem. In strategy A, the student used a ratio table to show the relationship between inches and feet. In strategy B, the student used a t-chart to show the relationship between inches and feet. In strategy C, the student used a number line to hop by feet and write the inches beneath. All three are perfectly acceptable models to use to make sense of the problem.

Getting Familiar with 100

As we approach the 100th day of school, (WOW! Already?) we like to do lots of fun activities in class relating to the number 100. We bring in collections of 100 things (like 100 hair clips in our hair, 100 buttons on our shirt, 100 lollipops to share with our friends) and make it our class goal to do 100 nice things before the day is out. The most important thing we do on the 100th day of school, however is work with the number 100. Here are some great games you can play with your child to help increase number sense and strategies in working with 100:

1. Guess My Number on the 100s Chart. In this game, one person thinks of a number. The other person tries to guess the number by asking yes/no questions to eliminate as many numbers as he or she can. When a number is eliminated, it is crossed off of the 100 chart. (For example, questions to ask might include: Is your number even? Is your number greater than 50?)

2. Get to 100. This game requires a 100s chart, game pieces, and a die or playing cards with face cards removed. (Uno cards also work great for this game.)  Players take turns rolling the die and moving forward that many spaces on the 100s chart. The winner must land exactly on the number 100. 

3. Splat is an interactive, blank 100s chart. Any number of games can be created and played with it. When choosing a square, you can "splat" it with one of several different color choices, making the number appear beneath the splat. 

4. Get to $1.00. Players need a die, coins, and a dollar bill. Players take turns rolling the die and putting that amount of money in their "piggy bank." The object of the game is to always have the least number of coins in the piggy bank and to ultimately reach $1.00. (So if you have 5 pennies, you would want to trade them for 1 nickel, etc.) 

Check out this video clip for samples of students playing Get to $1.00, Spend $1.00, Beat the Calculator,  Get to 100, and Guess My Number on the 100s chart. 

What is your favorite 100 game?

What's the Probability?

Each morning, as part of our math routine, we begin with Every Day Counts Calendar Math. This month, one of our large focuses is probability. We are flipping one quarter and one penny five times each every day. For each flip, we record on our classroom graph how many times the coin has landed on heads and how many times the coin has landed on tails.

American Heritage Dictionary defines probability as the likelihood that a situation, event, or condition will occur. Is the probability higher that the coin will land on heads or tails?

You can complete this probability experiment at home with your child. Use any coin. Flip the coin and record the number of times it lands on heads or tails. Graph the results using two pieces of one inch graph paper found in the "Helpful Math Tools" section of this blog. Bring your results in and share them with our class.

Virtual Coin Toss