What items will you find on your NUMBER SCAVENGER HUNT?
Yea, parents!!! Due to your overwhelmingly positive (and rapid) response to the parent ideas, I’m posting resources for parents on the FREE RESOURCES page of my web site. Just click on this link and download the first two activities:
https://glennatabor.com/free-resources/
The next blog about number sense will be posted tomorrow. And, of course it will include more free activities to go with it. Stay cool everyone!
âMaking the decision to have a child is momentous. It is to decide forever to have your heart go walking around outside your body.â    -Elizabeth Stone
Summer is a mixed bag of emotions for blended families. As I boarded a flight a few weeks ago, I watched a mother say goodbye to her children as they flew to spend time with their dad. The mother seemed fine until she hugged them at the last moment. All had tears in their eyes.
She repeated several times that they would have lots of fun and that she would see them soon. She went to sit and wait until the plane left the gate. I felt her pain–I’ve been there!
As I took my seat I sighed. A woman sitting next to me asked what the sigh was about. “Having children and goodbyes,” I said. She said, âIt doesnât get any easier as they grow older. I just said goodbye to my 23-year-old daughter.â “Oh, maybe that’s why my dad always dropped me off at the front door of my dorm and never could come to the gate after I’d flown to see them.”
Rats! I really did think it would become easier the older my children were!
This conversation reminded me of several quotes which I have treasured through the years:
âYou don’t really understand human nature unless you know why a child on a merry-go-round will wave at his parents every time around – and why his parents will always wave back.â -William D. Tammeus
âBefore I got married I had six theories about bringing up children; now I have six children, and no theories.â -John Wilmot
âIt’s not only children who grow. Parents do too. As much as we watch to see what our children do with their lives, they are watching us to see what we do with ours. I can’t tell my children to reach for the sun. All I can do is reach for it, myself.â -Joyce Maynard
âThe quickest way for a parent to get a child’s attention is to sit down and look comfortable.â -Lane Olinghouse
âDon’t worry that children never listen to you; worry that they are always watching you.â -Robert Fulghum
I admire the mom who bravely smiled and put her children on a plane that day. I admire all the parents who continue to do what is best for their children. Maybe these quotes will inspire you or at least make you laugh!
Speaking of doing what is best…be sure and check my blog on Wednesday and Friday for more ideas to use at home with your own children. If youâd like to know more about teaching a concept, let me know by posting a question or comment on this blog or sending me an email glenna@taborrotation.com.
To those of you attending CAMT this yearâŚTABOR ROTATION is a featured session in San Antonio on July 15th, 8-9:30am and 3-4:30pm. Canât wait to see you there!
âIf you can’t explain it simply, you don’t understand it well enough.â -Albert Einstein
I recently attended a âMomâs Night Out.â A large group of us decided a few months ago to try and find the best chips and salsa in the area by visiting a restaurant a month. There was much laughter and conversation as we traded mother stories.
Toward the end of the evening one of the moms turned to me and said, âI hear youâre a math guru.â I replied that I may not be a guru, but I’m definitely on a mathematical mission. She went on to explain that she wanted to prepare her children with whatever tools they needed to do well in school. She felt she was doing well with them in reading, but she knew she needed to be doing more in math. Everyone at the table agreed that thereâs not a lot out there to help parents with the development of mathematical skills.
I was thrilled to be able to tell them about the focus of my blogs this summerâsimple, but effective ways of helping your child understand mathematical concepts. I knew then that todayâs blog would begin a series of blogs about my favorite ways to develop number sense with your child.
One way to develop number sense in a preschooler is to use objects that the child uses every day. When my daughter was two we used to have tea parties at her toddler table. We put an animal in every chair. Then we had to give each animal a plate, then a spoon, then a bowl, then a cup. As she went around the table placing each item in front of the animal, we would count up together. We didnât say the number until the item was placed in front of the animal. Then she would go around the table and count again. She liked moving, placing and counting with real objects for a real purpose. Of course she like pouring the âteaâ water into each cup after everyone had their place setting.
This almost daily tea party helped her count up, develop one-to-one correspondence (each animal got each item), and helped her begin to understand relative magnitude (4 represented the number of small spoons and 4 also represented the number of big plates).
What if your child doesnât like to have tea parties? With my son, who had absolutely NO interest in tea parties, we gave each of his trucks and cars an equal number of riders and tools.
With an older child the partitioning of snacks can be a wonderful opportunity to teach fractions, multiplication, and division. Our childrenâs grandfather had a giant chocolate bar he gave to them. They decided to divide it between them. They used the âpaper-rock-scissorsâ method of determining who would do the actual division of the bar into equal groups. Our youngest one won. He looked around the table at his two siblings and said he was going to break it in half.
This comment caused a great disturbance in âthe force.â His two sisters began to loudly argue that he couldnât divide the one candy bar in half when there were 3 people eating it. With the same decibel level as his sisters, their brother said, âI won, so I divide it the way I want.â
I hope all parents reading this are laughing. I stepped in after a few minutes, took the bar and gave everyone a chance to reset. After the girls went outside I asked our son to explain why his sisters were upset. I asked him if we could open up the candy bar and see if there was any other way to divide the bar other than by breaking it into half.
When he opened the wrapper he saw the indentions that divided the candy bar into many smaller rectangles. I asked him what he could do to make sure that each person had an equal amount. He got three plates and put each personâs name on the plate. I asked him to count how many rectangles there were in all. He wrote that number on each of the plates.
He spent the next 5 minutes making sure that he gave each plate one chocolate piece at a time until the bar was gone. Thankfully, the number was divisible by 3. If not, you can divide the last piece or pieces into three parts eachâŚanother blog will have to explore this concept.
When he finished I asked him to count the number of chocolate rectangles each person had. He wrote that number above the total number of parts. I asked him to hold up his fraction bar (his hand horizontal to the floor) and get his terminator voice ready. In a deep voice, that sounds like the terminator, we pointed to below the line and said, âDenominator, the number of parts in all.â
Then we switched to a high-pitched voice, because the number is on the top, and said, âNumerator, the number of parts youâre talking about.âEach sibling received 6/18 of the chocolate bar. We took the total number of parts and divided them into three equal groups.Our 8th grader was asked to simplify the fraction and then all were allowed to eat.
Are you starting to see the connection between our daily lives and mathematical concepts? Do you see a connection between fractions and the simple sharing into equal groups? In the end, Iâm not really sure who made the biggest messâŚthem eating it or me trying to cut the bar evenly!
In a small-group setting in the classroom the discussions and questions would be the same. I try not to use a lot of food for concrete development of a concept, but graham crackers are easy to divide.
For those of you who want to learn more about developing number sense, here are some more ideas. Crewton Ramoneâs House of Math provides pictures and explanations of how children can build walls to understand adding numbers.
http://www.crewtonramoneshouseofmath.com/addends.html
You might want to skim the minilessons authored by Rusty Bresser and Caren Holtzman. These are from their book, Minilessons for Math Practice, Grades K-2. The sample minilesson offers ideas for helping children break apart numbers.
http://www.mathsolutions.com/documents/0-941355-74-8_L.pdf
A page on educationworld.com has an incredible list of games created by Joanne Currah and Jane Felling. Youâll have all the things you need to play these games with your own children and your students if you have dice and playing cards. You may want to take a look at their website for more ideas for your Tabor Rotation Games Station and Manipulative Station. They say they created their company, BOX CARS & ONE-EYED JACKS www.boxcarsandoneeyedjacks.com, for the sole purpose of making math funânot threatening or frustratingâfor children. Theyâre my kind of people!
http://www.educationworld.com/a_lesson/archives/boxcars.shtml
As your children and students increase in their ability to think about numbers, you want to encourage them to use mental computation strategies. Origo Educationâs website contains articles and examples of how to encourage this type of mathematical thinking.
http://www.origoeducation.com/mental-computation-strategies-addition/
âI hear, I know. I see, I remember. I do, I understand.â -Confucius
âPart of the secret of a success in life is to eat what you like and let the food fight it out inside.â -Mark Twain
Yes, Iâm back to blogging on a regular basis again. I wanted to blog. I wrote down lots of great ideas. I even began a few rough drafts of new blogs. However, between the end of school and my website makeover, my blogging has been neglected. Anyone else ever feel this way about things youâd like to do but life gets in the way?
Several fellow educators, who are also parents, made a special request for the summer. They asked if I would make the summer blogs applicable to parents and to teachers. I thought this was a great idea, sooooo…my summer blogs will be based on a mathematical standard or concept, how to integrate the understanding of the concept into your familyâs daily routine, and how to take these same ideas and use them in your classroom.
This first summer blog is about the reading and interpreting of charts and tables. This standard can be found beginning in most stateâs kindergarten curriculum. Variations of this concept continue all the way through high school. It is a life skill that is needed by everyone but is sometimes made quite difficult when we place it into a classroom setting. When it’s learned through a worksheet, most children find it tedious and they almost always find it boring.
How can I do help my child understand charts and tables?
The most convenient place for a parent to work with a child in the reading of data is almost always at the dining table or in the kitchen. Hereâs the scenario in my own house just a few weeks ago. I put out 3 of the cereal boxes from our pantry. Our two youngest children were at the table eating cereal while I drank my morning cup of coffee. I grabbed one of the boxes and challenged them with the statement that my cereal was more nutritious than their box of cereal. The next few seconds consisted of the mad grabbing for the remaining cereal boxes.
After the bartering and trading of boxes (anyone who has more than one child understands the need to trade until you have the ârightâ one), each of us found the nutritional value charts on the sides of the boxes. We looked at each of them and shared at least three things we found interesting about the cerealâs nutritional value. We then shared something that we didnât quite understand from the table and asked everyone else what it meant. We also talked about which box had the most interesting pictures and colors.
We discussed what we saw for at least 5 minutes, then went back to the question of which one was the most nutritious. The children and I took turns calling out an ingredient and the daily requirement percentage that was in the cereal. My middle child, who has an extremely concrete and visual learning style got a sheet of paper to write down the information she thought was important. Her brother, being the youngest and the least likely to want to write in the morning, decided he would look at hers if he needed to.
As we called out the information, I asked the children to make a comparison statement using some of the data they had just shared. One of the most important things to do at this point is to ask questions and give the children âthinkingâ time. I ask a question and then count to 20 before I restate the question. Instead of providing answers to the questions, I keep asking new questions and rephrasing old questions in order to guide them to finding the answers themselves. I also make a habit of asking an equal number of questions I don’t know the answer to either. My children like the fact that I am not “assessing” them, but rather “exploring” with them.
During the process, both of them ended up rereading all three cereal boxes and made complex comparisons. One of the cereals had more minerals and vitamins than the other two. I asked them to make a guess (otherwise known as a hypothesis) as to why this particular cereal might have more of the daily requirements. My eight-year-old smiled smugly and read one of the statements that was already written on the box.
After calling out all the minerals, my daughter suggested that we look at the carbs, the sugars, the protein, and the fat. These comparisons were very interesting. The children both noted that the cereal with the most sugars and the most carbohydrates was also the most popular with children. The also noted that they had seen a bunch of commercials about the cereal.
In defense of the high-carb, high-sugar cereal that had now become âhis,â my son vehemently argued that his cereal had the most protein grams. He was right. It did. Now we had to go back to the original question, âWhich cereal was the most nutritious?â
I love the energy when children are genuinely challenged with a real-world problem. I also love the logic with which they approach their solutions. My daughter said that the most nutritious cereal would depend upon the person who was eating it. When anyone in the family is preparing for an athletic event, they eat lots of good protein. The cereal with the most protein might be the most nutritious for them. When someone is trying to watch their weight, then the most nutritious would be the one with less sugar and carbohydrates.
As we continued our discussion, their older sister came to eat breakfast. She took one look at the three cereals that were available, made a face, and decided that none of them looked goodâno matter how nutritious. Her siblings spent several minutes making strong arguments for their cereals. She listened patiently, but ended up eating a peanut-butter and jelly sandwich. (The rule at our house is, âif you donât like what is being served, you may always have a peanut-butter and jelly sandwich instead.” This rule was instituted when the children began to think our house was a buffet restaurant.)
The closing remark stated as they left the table? âIt doesnât really matter how nutritious the food is if the kid wonât eat it. Maybe we should read the labels on all the junk cereals and buy those instead…lots of giggles at this point…just an idea, Mom!â
What would this look like in a classroom?
The scenario didnât look all that different when I taught the gathering, displaying, comparing, and interpreting of data with my students. I met with the students in a small-group setting in Teacher Time (see the Tabor Rotation Planning Guide ). I put a table cloth on the table where I met with my students. I gave each of them an apron and a place mat. Each student was given a notebook to take notes. I asked them to become a food critic for the local newspaper and determine which food product was the most nutritious. Authenticity or a close simulation was always more engaging.
We used empty food boxes and containers. I guided the students in the exact same way as I guided my children at the breakfast table. The students made statements using data and then showed the comparison statements by writing on an interactive white board. We also created graphs using the interactive white board. I used state public-release questions to model what this type of information looked like on the upcoming state test. They made the connections easily!
The students continued the use of food containers/tables at the Manipulative Station. The students also constructed their own graphs, using interactive white board, in the Technology/Application Station. The Games Station was a perfect place to put a game that required the students to be the first to put information in order and to find information first in a table.
To continue the high level of authenticity and application of real-world concepts, the students wrote recommendation letters to the companies who made the foods they studied. They constructed support for their recommendations by using the data they had collected. The students were making their own real-world connection!
What are some additional resources I can use to teach this concept?
At the elementary level, you may want to look at Gretchen Parrishâs lesson plan for grades 4-5. She created a unit that does a fantastic job of helping students compare the nutritional values of nonperishable foods and use Microsoft Works to create the graphs to explain their finds.
http://www.learnnc.org/lp/pages/3023
At the secondary level I found two great resources. Rachelle Kean offers a unit called, âFast Fats: A Nutritional Analysis of Americaâs Obsession with Fast Foods.â The activities were written for grades 10-12, but could be adapted for younger grades.
http://www.pbs.org/newshour/extra/teachers/lessonplans/health/nutrition.html
âBetter Nutrition by Analyzing Food Labelsâ is the name of the unit written by Lynda Wiest for grades 7 and up. The plans in this unit have students writing formulas, interpreting data, and even creating a triple bar graph.
http://wolfweb.unr.edu/homepage/jerryj/NNN/Nutrition.pdf
Hope this blog helps you begin to think about simple, practical, but meaningful ways you can help your children this summer and your students this fall.
NowâŚif I can just get the children to fix my morning mug of nutritional coffeeâŚ
âIâve been on a constant diet for the last two decades. Iâve lost a total of 789 pounds. By all accounts, I should be hanging from a charm bracelet.â -Erma Bombeck
âMemorization is what we resort to when what we are learning makes no sense.â -Anonymous
âIt’s not what is poured into a student that counts, but what is planted.â -Linda Conway
Our 2nd grader came home with a worksheet a few weeks ago. The worksheet had approximately ten problems about multiplication. As our son started to work on the sheet I observed him trying to solve the problems. The page had pictures and gave an example of how to draw the multiplication problem, but he was still struggling with how to make sense out of the worksheet. The worksheet asked the students to solve the number sentences by drawing marbles in the jars that were under the number sentence.
For each problem the first number represented the number of jars. For the number sentence 8 x 3 there were 3 jars under the number sentence. Anyone out there shuddering at the number of jars? The brain learns by experiencing a concept concretely, then moving to an iconic representation, then moving to the abstract. I knew it was time to put away the abstract and go back to the concrete.
I asked him to just put away the worksheet for now and help me pick out some really cool manipulatives. Our son is our resident âDudley Do Rightâ and immediately responded that he âhad to finish his homework so he wouldnât be late in turning it in.â I told him that we were about to explore multiplication in such a way that his homework would be completed in no time. He was convinced this might be a good idea when I pulled out my box of counters full of insects, cars, boats, and figurines.
We sat on the floor with lots of space around us. I put a stack of ten lids and bags of interesting manipulatives in front of him. I asked him where he would like to go if he could go anywhere in the world. (Money wasnât a factorâa really big deal in a family who lives on a tight budget.) He chose to go to Hawaii.
I asked him how he was going to get there. He chose to go by car. This brought about our quick geography lesson with a map of the world. After learning where Hawaii was, he chose to go by sailboatsâa much better way to cross the ocean! Here is how the next part of our conversation went:
Me:Â Â Â How many boats do you want to take on your first trip to Hawaii?
Him: Â Â Â I think I want to take 5 boats the first time?Okay. Pretend the lids are boats. Put out as many boats as you need. How many bugs do you want to go on each boat?
I put out five boat lids. Can I take people, too, and not just bugs? I think itâd be funny to have them bothering each other?
Sure. Itâs your trip and your imagination. When you pretend you can make it anything you want.
Iâd like to take 2 bugs and 2 people on each boat.
Your choice. Go for it.
Iâm done. There are 4 things on each of the boats.So, tell me about what you see in front of you. As you tell me about it, is it okay if I write what you say on this white board?
Sure. I see 5 boats. I see 2 bugs and 2 people on each boat. I see all the people running around trying to swat all of the bugs because theyâre biting them. Looks like the bugs are winning.
I continued to write down all the statements he made about his cruise to Hawaii. After he had given me 7-8 statements, I asked him to move to another area of the carpet and create another trip to Hawaii that was different than the first. He put out 4 planes with 3 people on each plane.
Again, I scripted the observations he made about his trip.
After 4 scenarios were created with boats and things riding on the boats, I asked him if heâd like to see what his trips looked liked in an abstract/number sentence way. My son is very polite, but he really was genuinely interested in the next step. One of the scenes was 4 boats with 3 people on each boat. Thatâs the one he chose to discuss first.
Me: Do you think thereâs a way for us to draw what the scenes you created?
Him: Sure. Can I draw it any way Iâd like?You bet! Which one would you like to start with?
Letâs do this one with 4 boats and 3 people.
He drew the outline of 4 boats and put 3 heads in each boat. When he finished I asked to tell me about what he drew. He described it and let me know that this trip had 12 people who made it to Hawaii. He drew pictures for each set of concrete objects and told me about each of them. Normally, I donât continue to the abstract level this quickly, but he was determined to finish his homework worksheet.
Me: Is everything starting to make more sense? I think youâre ready to go on to the way the problems were written on that worksheet. Iâm going to write a number sentence. What are some numbers in your observation?
Him: 4 for the number of boats and 3 for the number of people on the boat.
So could I write 4 x 3?
Sure!
If we were to put a label under the number 4, what word should I write?
Boats. Maybe you could write âBâ for short.What about under the number 3?
People, or âPâ for short.Could you go over to your 4 x 3 boats and tell me how many people there were in all of the boats on that trip?
There’s 12.
HmmâŚso how could I finish that number sentence if I wrote an equal sign?
Itâs 12! Itâs 12!
Together, we wrote the abstract number sentence that represented each of the scenes he had created with the lids and the counters. We talked about the pictures he could draw to help him think. He began to truly understand what each number in the number sentence represented. After 30 minutes of concrete exploration, he went back to the worksheet.
As he completed the worksheet he used the lids and bugs so that it would be more fun. After he finished, he asked me if I could give him a really hard problem. I asked him if he could show me between 5 x 0 and 0 x 5. Do you know the difference? He did and left the room with a huge smile and one more tool in his mathematical belt!
âTeaching is the highest form of understanding.â -Aristotle
One of the challenges teachers face when differentiating instruction is how to answer the questions that will arise when you begin to do what is best for all students. Because every student is unique in their understanding of concepts, their level of independence, their interests, and their learning style, what you do for each one must be different.
For some teachers this shift in thinking is very challengingâŚis it OK for me to not be treating my students the same way? You might want to filter your thinking through this quote:
âThere is nothing so unequal as the equal treatment of unequals.â -Aristotle
Here are some scenarios that may occur when you begin to âshake upâ what goes on in your classroom.
Scenario 1: Students Concerns
Youâve overheard several of the students in your classroom talking about the fact that you âlike Brad and Sarah more because they get to do things that no one else does.â What happens next in your room?
Scenario 2: Parental Concerns
During open house night one of the parents makes the following statement. âIâve heard that you donât like to give book work and work sheets.â Just as youâre about to answer someone else starts to mutter in the back about the fact that some students get special treatment and others donât. What happens next?
Scenario 3: Administrative Concerns
Your grade level is starting to differentiate instruction using several different strategies. During the past several grade-level meetings the strategies have been reviewed and are proving to be effective. Your administrator stops in one of your rooms and asks why so many children are doing so many different things. She says it looks rather chaotic. What happens in this meeting?
Scenario 4: More Parental Concerns
During the first month of school the parents of one of the children in your classroom have requested a meeting with you. At the beginning of the meeting they tell you that their child is gifted and they feel she is not being challenged enough. What happens next in this meeting?
Scenario 5: Your Own Concerns
You work hard and try to do your best for students. Everyone is telling you that you have to bring up the level of the lowest students. Now theyâre telling you to challenge the highly able students. Itâs too much!!! What message do you plant inside your mind to encourage you to do what you know is best for all?
I encourage you to read each scenario and visualize what happens next. Send me your comments. In next weekâs DI Blog Iâll post ways I have addressed each.
âThe greatest compliment that was ever paid me was when one asked me what I thought, and attended to my answer.â -Henry David Thoreau
âI’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.â – Maya Angelou
An effectively differentiated lesson clearly indicates that the teacher has anticipated and planned for student diversity (Tomlinson, 1999). Iâve used this fact in a bulleted list almost every time I present on the topic of Differentiated Instruction in Mathematics. But what does it really mean? One of my colleagues once told me that âpeople nod their heads and pretend like they understand even when they donât.â To help you understand Iâd like to use some of my studentâs words.
I was teaching in Prince Georgeâs County, Maryland in a classroom with no walls. (That little tidbit about âno wallsâ is a topic for another set of blogs, so I wonât go into it now.) When student number 37 arrived in January, he was assigned to two of my student hosts to help familiarize him with the routines and expectations of the school and in our class. One of the student ambassadors was Jake. Jake was a hard-working student who reveled in project-based learning. Rasheen, the new student, sat next to him so he could whisper any needed information.
During the first week I called one of my whisper groups back to the Teacher Time Table. After I had called my group I overheard Jake and Rasheenâs conversation. Rasheen asked Jake why I was calling those students back to my table. He thought they must be in trouble.
“Nope,” Jake explained.
“Sometimes she calls us back because we need extra help because weâre doing stuff right.”
“Sometimes she calls us back because we have no idea what weâre doing.”
“Sometimes she calls us back because we like a certain math game.”
“And, sometimes I think she calls us back for no reason at all.”
âDonât try to figure out why. It will just confuse you.â
I couldnât have said it better myself!
“Diversity is not about how we differ.
Diversity is about embracing one another’s uniqueness.” -Ola Joseph
âWe would accomplish many more things if we did not think of them as impossible.â -Vince Lombardi
âGive me a lever long enough and a prop strong enough. I can single-handedly move the world.â -Archimedes
I was working with several students helping them develop greater number sense and algebraic thinking. The students were heterogeneously mixed at this Teacher Time Station (part of the Tabor Rotation structure for simplifying small-group instruction in mathematics) to encourage learning from each other. Having been a believer in constructivism for many years, I began the instructional time by building on their interests.
I knew that two of the students had a birthday in April. One of the birthdays was in four days. I asked them to determine how many hours till that personâs birthday. I told them they had the next 10 minutes to think about it. They could use any method that made sense to them as long as they could explain to others what they had done.
Several students took sheets of paper and began to write out multiplication equations. One student went to the math tool shelf and retrieved a calculator. Another student went to the calendar.
The last student, Matt, just sat there looking down, then up, and then straight at me. Only 1 minute had passed since I had assigned the problem to the group. No one else was even close to the answer.
âItâs 96 hours till her birthday.â
Several of the other students, especially the ones who were writing out the long equations, looked up in disbelief. They couldnât believe he had the answer before anyone else. Maybe I should explain…the student who gave me the answer first was one who, in previous years, was always placed in the âslowâ group. He was usually given extra worksheets to âhelpâ him learn concepts. He was never given higher-order tasks, because he didnât know his multiplication table yet. Instead of problem solving with the highly able group, he had to practice his facts with flashcards.
In fact, his teacher the previous year encouraged me to give him color pages since he “wasn’t really that bright.” That was a poke on my teacher chest. I set out that year to prove her wrong. I KNEW every student in my class was brilliant. It was up to me to figure out how to let them show it!
âThe trick is in what one emphasizes. We either make ourselves miserable, or we make ourselves strong. The amount of work is the same.â -Carlos Castaneda
I encouraged the group to continue thinking throughout the rest of the given time. Then we came back together to explain our thinking. The emphasis during this instructional time was not on the âone right answerâ but on the thinking process they used.
Everyone wanted to hear from Matt first. One student asked him how he figured out the answer so quickly if he didnât even know his multiplication tables (notice how the remediation label is so readily known by all the students in the class).
He replied, âIâm really good at addition, so I just used that. I know thereâs 24 hours in one day. That means thereâs 48 hours in two days. Since itâs 4 days till LaTishaâs birthday, then I just added 48 and 48. I know that 4 tens and 4 tens is 80 and 8 + 8 = 16 and 80 + 16 = 96. That means itâs 96 hours till her birthday.â
“You never know when youâre making a memory.” -Rickie Lee Jones
Thatâs the beauty of memories. I hope this memory stays with Matt* the rest of his life!
(*The names in this post have been changed to protect the innocent. If you’re reading this, Matt, I hope you’re smiling!)
âTrue scholarship consists in knowing not what things exist, but what they mean; it is not memory but judgment.â -James Russell Lowell
Do any of you remember being thrilled about learning how to simplify fractions? I memorized some rules for how to do it and used these rules to complete worksheets filled with fractions. My brain didnât crave memorization of rules. My brain needed something that helped me understand!
I worked with a group of 4th graders a few weeks ago. In Tabor Rotation, this whisper grouping might occur during Teacher Time on Days 2 & 3 or during Readiness Grouping on Days 4 & 5. I was differentiating instruction based upon readiness after I quickly pre-assessed what the students knew about GCF and simplifying fractions. I was differentiating based on learning style by having students manipulate number cards and yarn to create a factor rainbow.
My assigned job was to help them complete a worksheet on simplifying fractions. They told me that their teacher hadnât really explained how to do it, or why they were doing it. They just knew that simplifying fractions was on the state test and theyâd better learn it.
For the two overachievers in the group, the knowledge that it was on the upcoming state test was enough to get and keep their attention. The others in the group needed more. I asked them if they knew what a GCF was. No one did. That gave me a starting point. I opened my rolling case of math tools. This time I was reaching in for hands-on activities for factorization.
As I pulled the hands-on activities out of the case, one of the children commented that I was like Mary Poppins when she opened her suitcase and pulled out so many items. I consider this a great compliment since Iâve admire the way Mary Poppins transformed children. The children learned while having funâjust the way I like it!!!
I told them we were going to make a Factor Rainbow and by doing that we would learn what GCF meant. Each pair of students took pieces of brightly colored yarn and made rainbow in front of them. They then took an envelope with a number on it and the factors of that number inside of the envelope. The first pair to make the factor rainbow correctly would win that round and select the next set of envelopes.
The first set of envelopes had the number 16 on it. The pairs laughed as they placed the number 16 at the top of the rainbow and the factor pairs of 1, 16, 2, 8, and 4 to form the rainbow. In less than a minute, everyone has their factor rainbows made and their hands on their shoulders. Each pair explained how they placed their factors and how they knew that the numbers in the rainbow represented all the factors for 16.
The fastest pair chose the number 12 envelopes for the next round of the game. I asked them to place this new â12â Factor Rainbow next to the â16â Factor Rainbow. As before, the pairs laughed as they placed the factors and gave each other âhigh-fivesâ when they finished. Another discussion of what they were thinking as they created the second factor rainbow followed.
I asked them to look at each of the Factor Rainbows and find the factors that the two numbers had in common. We put buttons next to these common factors. I asked them to find the factor that each had in common that was the greatest and hold it up. Everyone held up the number 4. I asked them if 4 was the greatest common factor of 16 and 12. I wrote greatest common factor on a white board sitting next to me.
Thatâs when the âlightbulbâ moment happened! One of the girls in the group yelled out, âThatâs GCF! We found the GCF! GCF stands for greatest common factor!â
With much enthusiasm and curiosity, the group and I created Factor Rainbows and found the GCF of 3 more pairs of numbers. Now, we were ready to use this information to simplify fractions. The students in that group will never forget what a GCF is. PRICELESS!!!
(What does this have to do with simplifying fractions? Read next Fridayâs Games Blog and find out what happened next!)
âMy life has no purpose, no direction, no aim, no meaning, and yet I’m happy. I can’t figure it out. What am I doing right?â -Charles Schulz, creator of the Peanuts comic strip
âDonât believe what your eyes are telling you. All they show is limitation. Look with your understanding, find out what you already know, and youâll see the way to fly.â -from the poem, Jonathan Livingston Seagull, by Richard Bach
âWhat we call differentiated is not a recipe for teaching. It is not an instructional strategy. It is not what a teacher does when he or she has time. It is a way of thinking about teaching and learning. It is a philosophy.â -Tomlinson
If an educator believes the above quote, then they have a still, small voice that speaks to them every time they walk into a classroom, create lesson plans, or work with a student. It is a guiding force in the strategies used by that educator. It is a belief that every student is unique, special, and deserves the opportunity to be qualitatively engaged in the learning process.
I use some of the words in the previous paragraph when I talk about differentiated instruction, but I don’t always explain what they mean to me. Iâd like to talk about a few in my next few posts about differentiated instruction.
Every student doesnât mean just the ones who are below level and who arenât passing the state test. It doesnât mean just the ones who have been identified as gifted. It doesnât mean just the ones whose parents âsqueakâ the loudest. It doesnât mean just the ones whose parents volunteer the most or are a PTO officer. It means that every single student who walks through the doors of your classroom deserves learning experiences that appeal to her interest and her learning style.
Qualitatively means that the teacher identifies how much the student knows about the content they are studying (their readiness level, not their ability), then provides them with activities that will help them move âa little bit further than they were the day beforeâ on the readiness continuum for that content. It doesnât mean giving them more if they finish. Thatâs quantitatively challenging students with more work.
Engaged means that all students are actively involved in the learning process. If you were to walk in a classroom where all students are engaged, they wouldnât even notice you were there. Engaged students donât watch the clock waiting for the bell to ring or count the minutes till recess. Engaged students are busy as they develop understanding of the concepts they are studying.
I wish my 4th grade math teacher had understood what differentiated instruction was. She explained concepts by working a problem on the board with her back to us. This was of no help to me since Iâm a visual learner and never got to see her face. After working no more than two examples, she assigned the odd numbers from pages in the textbook. I need to feel connected when I learn. Iâve never felt âconnectedâ to a textbook.
When one of us finished the odd problems she had just assigned, then she made us all work the even problems, too. No one wanted to work more problems, so we developed a system of looking busy until the bell rang. We also timed ourselves and used non-verbal signals so that no one finished early.
I have wondered what would have happened if we had spent that creative energy in exploring math in a differentiated way…
âQuality in a product or service is not what the supplier puts in. It is what the customer gets out and is willing to pay for. A product is not quality because it is hard to make and costs a lot of money, as manufacturers typically believe. This is incompetence. Customers pay only for what is of use to them and gives them value. Nothing else constitutes quality.â -Peter F. Drucker
