Teaching students to add fractions that have unlike denominators can be a challenge. It starts with teaching how to find a common denominator. Far too often, this can lead to a purely procedural account of the how, but not the why behind the math. Using LEGO bricks to teach this concept brings new understanding of the term “common denominator” by providing a visual and tactile link.
A key piece of knowledge when comparing fractions concerns understanding same-sized wholes. Students often make errors when trying to add or subtract fractions because they don’t grasp the concept that fractions can only be compared if the whole (the denominator) for both fractions is the same size.
Let’s add the fractions 1/4 and 1/3 together to show how the process works. First, build models of the two fractions on a baseplate using LEGO bricks. Model the fraction 1/4 with a 1x1 brick and a 1x4 brick, placing the 1x1 brick above the 1x4 brick. Model the fraction 1/3 with a 1x1 brick and a 1x3 brick in the same way. Build the 1/3 fraction model next to the 1/4 fraction model, leaving a little space between them, as shown.
In algebra, we use the phrase, “What you do to the left you must do to the right,” to help remember how to approach equations. Here we say, “What you do to the bottom you must do to the top,” to remember that the way you treat the denominator defines the way you treat the numerator. The fraction train shows the multiplication that takes place as you build the common denominator model. Note: As you build the fraction train, you distinguish between counting bricks and counting studs.
To build the fraction train, find another 1x4 brick and place it on the baseplate below the two fraction models. Then find another 1x3 brick and place it just underneath the 1x4 brick.
This begins the fraction train and represents the two fractions in the order they appear in the equation: 1/4 + 1/3 = ____. Add another 1x4 brick to the train, and then another 1x3 brick to its train. Continue adding 1x4 bricks to that train and 1x3 bricks to the other train until both fraction trains of bricks are the same length. Ask students to count the number of studs in each line when they are equal in length. (Answer: 12.)
This is the common denominator. Place a 1x12 brick at the bottom of the baseplate to represent the common denominator of 12. This is part of the solution model.
Now it’s time to determine the numerators, based on the common denominator. Start with the 1/4 fraction. Look at the fraction train built by the 1x4 bricks and ask: “How many 1x4 bricks are in the train?” (Answer: there are 3.) Now look at the model of the fraction 1/4 and ask: “What brick represents the numerator of the fraction 1/4? (Answer: the 1x1 brick.) Remind students that what you do to the bottom you must do to the top. Since there are three 1x4 bricks in the denominator, there must be three 1x1 bricks in the numerator of the solution. Place three 1x1 bricks above the 1x12 brick that represents the common denominator in the solution.
Repeat the process for the fraction 1/3 by counting the number of 1x3 bricks in the fraction train. (Answer: there are 4.) Since there are four bricks, place four 1x1 bricks in the solution model next to the three 1x1 bricks you just added.
Count the number of studs in the numerator: 7
Count the number of studs in the denominator: 12
The solution: 1/4 + 1/3 = 3/12 + 4/12 = 7/12
When you take students through the modeling of the solutions, you give them a powerful way to visualize what common denominators look like. Creating and modeling same-sized wholes (the fraction train that shows the common denominator) with LEGO bricks is key to understanding how to add unlike fractions. For both visual and tactile learners, this method helps students understand the multiplication process utilized with fractions, as well as the relationship of same-sized wholes and common denominators.
If you want to learn more about how to teach using LEGO bricks, check the website for the Brick Math program, www.brickmath.com.
Below is the text of Dr. Shirley Disseler's guest column wrote for The High Point Enterprise, High Point, N.C. The guest column was originally published on Jan. 29, 2018
Research shows that the creativity level of Americans is on the decline, affecting areas like problem solving, ideation, and entrepreneurial endeavors from those who finish high school and college as they enter the workplace. Many workplaces, such as Google, LEGO, and Disney, are choosing to put play into the workday to enhance communication, reduce stress in the workplace and create a greater sense that out-of-the-box critical problem solving is accepted in adult work environments.
That’s why International LEGO Building Day occurred on Sunday as a way to celebrate the patent of one of the most creative toys in the world. People across the world joined in the idea that play is not just for children.
According to experts in the field of play and creativity such as Stuart Brown, Sir Ken Robinson, and American Association for Play Therapy, the phrase “Playing with Purpose”is important to all people in terms of health, critical thinking and problem-solving, and communication. Building things with one’s hands provides the brain with a release that decreases stress, and promotes active thinking, which is key to positive decision making. A child’s imagination forms the building blocks of lifelong creativity, which is why it’s not such an outlandish notion that “Play”can help adults unlock a more creative side of themselves.
According to the famous artist, Henri Matisse, “Creative people are curious, flexible, persistent, and independent with a tremendous spirit of adventure and a love of play.” In our schools, we need to pay attention to the degree to which we allow for creative flow to occur within our classroom if we want curiosity, flexibility, persistence, and independence in our graduates.
According to research of Fortune 500 companies, 60 percent of them seek employees that demonstrate creative abilities, yet America ranks No. 11 in comparison of all nations in the numbers of employees that actually demonstrate creativity in the workplace. A recent survey conducted by the Families and Work Institute revealed that 41 percent of Americans feel extreme levels of workplace stress. Surveys conducted at locations where creative play was interwoven into the day showed much less stress, less absenteeism and a happy disposition towards their job. Being allowed to be creative in college courses also creates graduates that are better at solution finding, critical thinking and ideation.
The future of our country depends on the ideas of people, not on memorized facts; therefore, all educators, employers, and parents should embrace creativity, promote play and allow for the building of thought with hands-on materials such as LEGO Bricks. Stanford Professor James March, founder of Organization Theory, points to four domains (Called the 4Cs) in which play is crucial. First, he states that play is essential to the development of the cognitive capacity whereby neural pathways are formed through role-play, experimentation and risk-taking. Secondly, he points to creativity as a crucial factor in abolishing rules for creative endeavors. Thirdly, he discusses the connections formed through diverse working teams that offer out-of-the-box approaches to problem solving; and the fourth “C,” courage, offers workers and leaders the opportunity to change things and feel comfortable going out of the norm in their thinking and producing of ideas.
Companies interested in integrating play into the workplace need to first lighten the mood through silliness in small chunks; Secondly, advocate for change by allowing a sharing of ideas amongst groups of employees; thirdly, keep a stash of play materials in the office and put them out on Mondays to get the week rolling; and lastly, be open-minded and prepared to play yourself.
As the world celebrates the patent of the LEGO Brick, let’s build minds, build thoughts, and build dreams. As people, we were born to build! On this day, grab some LEGO Bricks and design the future.
Shirley Disseler, Ph.D., is Chair Elementary and Middle Grades at High Point University;
LEGO Ambassador; LEGO Education Trainer; Curriculum Developer; and Author of “Brick Math Series: Using LEGO Bricks to Teach Math.”
by Dr. Shirley Disseler
If I had a dollar for every time I’ve heard from teachers, ”Students just need to learn the math! They need to learn the procedures so they can ace the test”. . . well, I’d have a big pile of cash, that’s for sure!
I know that data is key in schools today, but we are not educating students to be test takers—we are educating them to use math in their daily lives and to know why it works the way it works. We want them to have good number sense, problem solving strategies, and mental math frameworks.
Using manipulatives is central to this process as students move through learning trajectories in math that include conceptual, representational, and abstract levels of understanding. If we try to skip the conceptual or representational learning and go straight to the more abstract level of procedures, we will create a gap in learning that will hurt the student later on.
Too many classrooms omit the concrete application that creates conceptual understanding. By sixth grade you can easily tell whether students have been exposed to manipulative processes or not. Students who have not used manipulatives in the learning process often have gaps in their ability to think through a problem logically or to show their work.
The LEGO brick allows for the concrete math to be discovered, which helps students understand the “why” behind the math. Posing questions in context while building models with the bricks encourages a sense of inquiry. Students ask questions about the math, discover invented strategies, and “play” with numbers. The LEGO bricks offer opportunities for students to build, draw, and write about possible solutions. This opens the door for discourse about math and number theory.
So when teachers ask me, “Is all this building with bricks really necessary?” my answer is always, “It is not only necessary, it is imperative if you are teaching for more than the test.”
Congratulations to Jane O'Dell, Cindy Beacham, and Tami Broomall, winners of our Brick Math brick set giveaway! Each won a 2-person brick set that works with any of the books in Brick Math. Keep checking our Facebook page, Teaching Math Using LEGO Bricks, for the next giveaway!
Charity Preston of the website Organized Classroom just reviewed Teaching Fractions Using LEGO Bricks, and says it's "super fun!" On her very popular website, Charity notes that she thinks learning fractions always requires some concrete materials to help introduce the concepts, and that's why she was excited to try the activities in the book.
Charity adds an extra tip for teachers when they start using the Brick Math program: she suggests letting students play with the bricks for two minutes before starting the lessons, just so they get the "playing" aspect of LEGO bricks out of their systems and are ready to use them as learning tools. Great idea!
Pat Hensley of the blog Successful Teaching just reviewed one of the Brick Math books, Teaching Multiplication Using LEGO Bricks. Glad to say that Pat loved it! Read her whole review here: https://successfulteaching.blogspot.com/2017/08/teaching-multiplication-using-lego.html
Pat found the lessons easy to follow and great for classroom teachers or a homeschool situation. We're supplying a free book for one lucky reader of Successful Teaching, so go to Pat's blog and sign up to win the book before September 4!
by Dr. Shirley Disseler
According to 2017 research by the LEGO Foundation, using LEGO bricks ignites four key types of processing and 24 key skills in the brain that lead to great retention of information. The four types of processing are:
Modeling and building with bricks to learn math helps with children’s self-regulation skills. These enhance the skills of emotional regulation and attachment to content, long-term memory, attention, mental imagery, and system thinking. During the process of self-regulation, the brain places a “file folder” for that model in the long-term memory of the brain.
Using bricks when learning math helps develop the child’s executive function, which is tied to the skills of visual perception, initiation, adaptive social functioning (collaboration), and one’s ability to self-assess. Being able to actually see the steps in a math problem by modeling it with bricks is a great way to visualize what the math means and why it works.
Learning math using bricks also develops the process of symbolic representation, which directly leads to the skills of kinesthetic awareness, spatial visualization, sensory-motor abilities, mental rotation, and working memory. When you learn math, you identify numbers and spaces by visualizing what they represent or by using mental math. The process of building with bricks places the focus on the eyes and the hands, which lead to cognitive understanding and the ability to visual a number or a space.
The last of the four processes enhanced by building with bricks is spatial ability. This process provides a greater short-term memory, fine motor skills, and increased cognitive flexibility. In math, the ability to utilize invented strategies, think logically, and use reason to determine solutions is all part of cognitive flexibility. Building brick models enhances fine motor skills by providing a tactile experience.
It looks like the brick is the brain’s new best friend! It helps kids attend, engage, and focus on learning through building brick models with their hands.
by Dr. Shirley Disseler
Teachers of gifted students need to encourage them to think, create, and problem-solve. Sounds like a perfect use for Brick Math, with its hands-on modeling with LEGO® bricks! But I’ve found that using Brick Math with gifted students can be an interesting challenge.
Teaching Brick Math with gifted students has opened my eyes. Gifted students often want to get right to the answer and check the problem off the list as “completed.” They do not want to show work, write about it, or discuss with others how they got their solutions. I have found that many of these students don’t really know math. They know how to do math procedurally. They can tell you how, but they can’t tell you why! Standardized scores of US gifted students continue to remain stagnant over time because we are not challenging them to think. We are only challenging them to produce.
I served as a teacher of gifted for math at the middle grades level. I often recognized in my students their need to be perfect. When such students were forced to explain how a math problem worked, they worried about being wrong and were afraid to take risks. I began to have them write out everything to explain it clearly. It was difficult for them at first, because they weren’t always earning 100 on every test, and their parents got worried. But over time, their test scores grew tremendously as they became more comfortable explaining the process behind the math, because they were developing a deep understanding.
We can boost test scores and increase 21st-century skill sets if we encourage explanation, justification, and collaboration among our students. Creative play with content helps our brains explore new ideas and solutions. Using methods that are engaging to the mind create a lot of energy in young people. And energy creates a passion for the subject.
So…encourage your gifted students to play with math! When they see that it’s not always about just getting the right answer, they’ll start to develop the true understanding that is the foundation for math fluency and excellence.
The fourth book in the Brick Math Series has just been published: Teaching Counting and Cardinality Using LEGO® Bricks, plus its companion Student Edition, Learning Counting and Cardinality Using LEGO® Bricks!
Congratulations to author Shirley Disseler for bringing the series to the K - 2 crowd. It's such a natural to teach the concepts of counting and cardinal numbers using the well-known LEGO® bricks. Young students practice one-to-one correspondence by touching the studs on the bricks and compare "more than" and "less than" by building brick models. The hands-on learning with the bricks, together with Dr. Disseler's step-by-step approach, creates a teaching and learning resource that introduces students to the first mathematical concepts.
Next up will be Addition and Subtraction Teaching and Learning books to complete the K - 2 math curriculum, available in June!