Category: Teaching Algebra

Adding and Subtracting Polynomials

Rocket Llacey April 2015Ever launched a Rocket and wanted to determine how High it goes? Polynomials can come in handy when trying to model the flight path of a Rocket.  Did You Know that  when shooting a rocket straight up in the air, the rocket’s path can be modeled using the polynomial equation: y = -16t2 + vt + ho? Yes, it is True. Using this Equation you can easily Determine when the Rocket will hit the ground and even how far the Rocket will shoot into the sky. The Height the Rocket will reach is dependent on the initial velocity of the rocket and the initial height.  (Rocket Photo:

Notice that the Rocket Equation does not involve the weight of the Rocket. As a Rocket is launched the initial Velocity allows it to overcome Gravity. However, eventually, that initial force from the launch dissipates and Gravity takes hold. A Rocket reaches its Maximum Height shortly before Gravity forces it back toward the ground.

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Learn More!  Let’s try an example, using the Polynomial Equation: d = -16t2 + vt + ho. If a Rocket is launched with an initial Velocity of 50 meters per second off of the ground, how high will the Rocket be after 3 seconds?  Solution:  So, the Rocket will be 6 Meters off the ground. The Rocket is likely on its way back down toward the ground.

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Problem Solving Activity

Too often, we rely on worksheets to help our students learn. Students need to be active participants in their learning. They need to explore, communicate and problem solve. Here is a fun activity appropriate for second and third graders to complete during your measurement unit. Not only does it help them practice measurement skills (weighing items and counting money), but it also facilitates math process skills such as communication and problem solving.

Materials: scales, envelopes, coins, student directions and recording sheets (attached). Note – you will have to weigh the envelopes you choose to use (the ones I used weighed 3 grams).

Overview: Students work together to determine the amount of money contained in an envelope through problem solving and application of math concepts. If students can successfully determine the amount of money within the envelopes, they are given “credit” to shop for items (erasers, pens, colored pencils, etc.) in their class store.

Class Store

It is your lucky day! Your teacher said she will give you money to shop in the class store. However, there is a catch. She will not tell you how much money you will receive. Instead you need to figure it out. You will be given four different envelopes. Each envelope holds a different type of coin (quarters, dimes, nickels or pennies) which is written on the envelope. No envelopes hold a combination of coins. You must figure out how many coins are in each envelope, how much those coins are worth, and determine how much money you have altogether. Hints are given below.

Fill in the chart completely. If you determine the right amount, your group will be able to spend it in the school store.


1 envelope = 3 grams

4 quarters = 23 grams

5 dimes = 11 grams

4 nickels = 20 grams

4 pennies = 10 grams

Complete the chart:





Work Space:

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Patterning for Algebra

Algebra used to be viewed as a class for high school students. We know realize the importance of introducing algebraic thinking early in education. Identifying and studying patterns is a significant concept to help the youngest learners develop and enhance algebraic thinking. Creating, completing, identifying and describing patterns help students expand their mathematical mind. Here are some fun patterning activities for your students.

 1)    Allow students to create patterns in a variety of ways – Have students create patterns for one another. One student acts out the pattern and chooses a classmate to complete it. If the classmate can correctly continue the pattern, she makes a new one for someone else to continue. Encourage students to be creative using different instruments, movements, etc.

2)    Manipulatives – Pattern Blocks, Attribute Blocks and Color Cubes are all wonderful math manipulatives to use to practice patterning. But don’t limit yourself to these products. Use everyday items such as buttons, crayons, pencils, erasers, stickers and anything else you can imagine.

3)    Problem Solving Activities – One problem solving strategy young students often use involves determining patterns. Here are some examples that can be solved by using patterns.

A)   In a video game, the first score was worth 10 points. The second score was worth 20 points. The third score was worth 30 points. How much was the sixth score worth? Show and describe the pattern that helped you solve this problem.

B)   At the carnival, there was a prize wheel. Each student got to spin one time to see if he or she won a prize. Spinning a “1” won a prize. Spinning a “2” or a “3” did not win a prize. Spinning a “4” won a prize. Spinning a “5” or a “6” did not win a prize. Rita spun a “12.” Did she win a prize? Show and describe the pattern that helped you solve this problem.

C)   Katie’s gym teacher was trying to get them in shape. On the first day, the kids ran 1 lap. On the second day, they ran 3 laps. On the third day, they ran 5 laps. On the fourth day, they ran 7 laps. How many laps did they run on the tenth day? Show and describe the pattern.

D)   The students in the class were lining up for the music concert. The teacher lined them up 1girl, 2 boys, 1 girl, 2 boys. If the teacher continued with this pattern, would the 10th child in line be a boy or a girl? Show and describe the pattern that helped you figure out the problem.

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