Fantastic Fractions

Well, summer is 7/12 of the way over and soon kids will be back in school and crisp evenings will be here.  Summer is a time my family and I bake and cook a lot.  Extra time allows us to try new recipes and make triple batches of chocolate chips cookies for family gatherings.  Baking and cooking involve measuring ingredients and knowing a thing or two about fractions.  Here's a video I found that explains how to cut a recipe in half. 

I think fractions are important to understand and kids as young as kindergarten can get the basic idea of fractions.  My god-daughter is five and she is so excited to go to kindergarten this fall.  I tricked her with a fraction question yesterday.  We were having cake at a baby shower and I asked her if she wanted 1/2 or 1/3 of a piece of cake.  She said 1/3 and I asked her why, she said because 3 is bigger than 2.  I took a minute to draw her a picture of a cake, divided it into 2 pieces and then I drew another picture of a cake divided into thirds.  Once she saw the picture she giggled and said, "I want that piece" which was the 1/2 piece not the 1/3 piece.   

We all had whole pieces of cake but talking about fractions with a kindergartner was enlightening.  My friends and family are not surprised by my random math tangents anymore.  Taking math classes this summer has provided many teachable moments for me and my family.  Math is all around us and whether it is cooking, shopping, saving, sharing or measuring it is important to have basic math skills.  We could have some funny tasting cookies if the recipe was not tripled or doubled correctly.     

 

Here's a fun fractions jeopardy game to try with a class.  You can have teams and ring in when someone has the answer.

Check out this site for more on fractions.    

How Tall Am I?

Do you have a spot in your house where kids have been measured and their heights recorded for years?  Maybe it is on a special piece of paper, behind a door or on a wall.  Kids love to see how much they have grown and will measure everything in sight when given the opportunity.  Formal and informal measurement are part of every math curriculum.  Informally measuring with arm span, hand span, markers, crayons, paperclips, these are all ways to get kids measuring and thinking about why we have universal units of measurement.

I have worked in classes where first graders measure each other using blocks, string and post-its.  Teachers provide them materials to measure with that they do not normally associate with measurement.  Throughout the year they update and see how much they have grown.  Maybe it is only half a post-it or maybe it is two Lego's.  The learning that takes place through the exploration is beneficial to build their background knowledge.      

The video below shows students using non standard units of measurement to measure themselves.  The teacher asks some great clarifying questions about units of measurement and what they estimated before they began measuring.  I think the video shows the enthusiasm young kids have when they get to explore with math concepts.  Math can be fun and exciting when given the chance to try new ways to measure.   



Climb the Factor Tree

The hot days of summer are still with us for a few more weeks.  Trees offer us some shade from the scorching sun and oppressive heat.  Believe it or not trees are used in school too.  In math class factor trees are helpful to use when teaching students about factors.  I like the clarity of starting with a number and breaking it down branch by branch.  Factor Trees are visual diagrams that allow students to see each factor of a whole number.      

I can see how making a factor tree on a smart board during a lesson would be good, so would practicing with a fun Factor Tree Game.  I thought it was very easy and a quick way to practice finding the prime factors.  I liked how the game gave multiple opportunities to practice with many numbers.   

Songs also teach students many concepts.  I found this song on youtube that was inspiring and explained the concept well.  Thank you Tom Petty for the original song Runnin' Down a Dream.  Rock out to this song about factor trees! 

Who's Counting?

Imagine this:  Students are learning about adding and subtracting positive integers.  A few have prior knowledge working with thermometers or bank accounts that involve positive and negative integers.  The rest of the class looks hungry for a way to learn with their hands and eyes.  Out comes the bucket filled with counters, red and blue disc shaped counters.  Aha... the lesson takes off and students are seeing the negative numbers represented by blue counters and positive numbers represented by red counters. 


The magic of having the red and blue counters in front of each student makes it so much easier to teach the concept of adding and subtracting positive and negative integers.  The students can see how to pair up the counters and figure out easily what the sum or difference is with their counters.  I think using counters is a great way to learn and explore math.  Students that may not jump right into the lesson are suddenly excited to try another problem and use their counters.  Once the concept is understood students will not need counters to figure out problems because they have practiced enough with the counters and it makes sense after all the practice.  Adding positive and negative integers using red and blue counters is taught well by two 7th grade students.

I have worked with students in small groups that noticed how much using counters helped them.  The combination of having something in their hands to work with and seeing math represented by things really helped.  I could see when the concepts clicked for them as they were using the counters.  We had tried paper pencil pictures to represent the same lesson and it was not as clear to some students.  Keep the counters close and use them often! 

Try the game called, Marble Math that uses marbles as counters to add and subtract. 

Area Models of Multiplication

Area Model Video

     What is an area model for multiplication?  I learned this week that the area model for multiplication is a pictorial way of representing multiplication. In the area model, the length and width of a rectangle represent factors, and the area of the rectangle represents their product.  According to Math and Teaching.org "The area model for multiplication establishes the groundwork for helping visual learners in the conceptual understanding of the traditional algebraic skills of polynomial multiplication and factoring."  

Here is an example of the area model for multiplication: 




     I think the area model is a great way to show students that multiplication is nothing more than adding up partial products.  Base 10 blocks are useful manipulatives for teaching kids about multiplication.  The blocks allow students to get their hands on the numbers to see how the numbers add up to the final product.  I can see how cooperative learning groups would be a good way to let kids practice the area model.  Start with groups of 3-4 students and have them use the base 10 blocks together to solve the equations.   
    

Math and Teaching - Area Model




     Websites like Kidspitation have manipulatives that would be fun for students to use while learning the area model for multiplication.  Many classrooms have SmartBoards that students could use to practice on during instruction.  Students would solve a 2 digit multiplication problem by drawing an area model and writing the parital products as they go.  The process of adding the partial products would help students see the step by step process.  I think the area model is a method that will make sense to kids and allow them to see their answers.     

Roman Numerals

XIV June, MMXII

Roman numerals are all around us and I think it is important to teach students Roman Numerals.  For example, many clocks have Roman numerals on the face, book chapters and copyright dates are often marked with Roman numerals.  What if you were in a book club and everyone decided to read to chapter XII and you only read to chapter 7 because you thought X meant 5 instead of 10.  The Olympics and Super Bowl are noted with Roman numerals as well as political leaders such as monarchs and popes.  Imagine taking a history test and you have no idea if King Henry VIII was before or after Henry IV.  Many buildings may also have the year it was built in Roman numerals.  Look around and see what Roman numerals you notice. 

I think back to my schools days and I was the kid thinking “why do we have to know this?”     What I would tell my students now is because Roman Numerals are all around us and learning all types of numeration systems helps your common number sense.  Learning new ways to count gives you a better understanding of numeration systems and broadens your ability to think critically at a higher level.  A class I worked in incorporated Roman numerals into their morning message every day.  The students counted the days of school from I to CLXXII with Roman numerals.  The students became fluent in Roman numerals because they were challenged each day to count how many days they had been in school.       

Numeration systems are fun to learn, it is like learning a new language.  It can be challenging while helping you grow as a learner and thinker.  I found a Roman numeral matching game that helps you practice the numerals against a clock.  Fact Monster also had an easy to read chart to learn the basic numerals.  The last site I enjoyed reading from Nova Roma explained the process and reasoning behind Roman numerals in a more narrative form with detailed explanations.                

Roman Numeral Matching Game

Roman Numeral Chart and Challenge

Roman Numerals