Staying with the Problem

Monday, November 3, 2014

Day 43: Division of Fractions Practice

Here is a sketch of Lincoln's road to the White House:

1816 His family was forced out of their home. He had to work to support them
1818 His mother died.
1831 Failed in business.
1832 Ran for state legislature - lost.
l832 Also lost his job - wanted to go to law school but couldn't get in.
1833 Borrowed some money from a friend to begin a business and by the end of the year he was bankrupt. He spent the next 17 years of his life paying off this debt.
1834 Ran for state legislature again - won.
1835 Was engaged to be married, sweetheart died and his heart was broken.
1836 Had a total nervous breakdown and was in bed for six months.
1838 Sought to become speaker of the state legislature - defeated.
1840 Sought to become elector - defeated.
1843 Ran for Congress - lost.
1846 Ran for Congress again - this time he won - went to Washington and did a good job.
1848 Ran for re-election to Congress - lost.
1849 Sought the job of land officer in his home state - rejected.
1854 Ran for Senate of the United States - lost.
1856 Sought the Vice-Presidential nomination at his party's national convention - got less than 100 votes.
1858 Ran for U.S. Senate again - again he lost.
1860 Elected president of the United States.

Agenda:

Return weekly quizzes and distribute weekly quizzes as students do 4 word problems on dividing fractions
Review the jumpstart and make corrections to Weekly Quiz #7
Do this 3-act math activity of dividing fractions with my nieces. The key point is getting students to recognize the milk needs to be divided by two
Distribute homework on dividing fractions and let students do it in class. Most students finished more than half of the assignment and a few students were able to finish.

The Assessment: I let two of the classes work in partners and one class I had work independently (they were too fussy when I told them what partner they were with - I have to set limits and they got the message). As they worked I would call back partners to the back of the classroom to work with me on the homework. As soon as I saw they had the concepts, I let them go back to their seats. I differentiated within this assessment. Some students I gave the basic steps (keep the first fraction the same, change division to multiplication and take the reciprocal of the second fraction) and had them go back and give the basic steps back to me in a different problem. For other students I asked them to find out if I ate 3/4 cups of ice cream and they ate 1/2 cups of ice cream how many times more cups of ice cream I ate than them. Almost all students guessed that we did 3/4 divided by 1/2 or 1/2 divided by 3/4 but it was difficult for these students to explain why it was one and not the other. We discussed how the answer should come to more than one since I ate more than they had. We also discussed using analogous numbers in lieu of the fractions that I had chosen to understand what is divided by what. For some students, they were fine with fractions divided by fractions, but were struggling with mixed numbers because they took the reciprocal too soon so we worked on that. For other students I wanted them not just to memorize a process (they were getting that already) but to understand why the answer was coming out the way it was. We discussed estimation and using common denominators as alternative strategies to make sense of problems.

In addition to this assessment, I did have students weekly quizzes graded from the prior week.

Homework: Division of fractions worksheet

My Glass Half-Full Take: I really enjoyed hearing the logic students were applying to the problem where I ran out of Bisquick. I followed up and asked them why I didn't subtract one of every ingredient (since I used one less cup of Bisquick than the recipe required). It was clear to students that we would then not use any eggs or vegetable oil. It was a great example of why equivalent ratios need to be divided or multiplied by the same number - not added or subtracted.

One Thing to Do Differently: I should have pre-warned students that the word problems were significantly more difficult than the problems that did not involve word problems. They always get more motivated by forewarning of challenges and increase focus. Two of the word problems were very difficult.

Link of the Day: Is this a future warm up problem? Almost certainly. Whinnie the Pooh stay home.

Sunday, November 2, 2014

Day 42: Dividing Fractions

I collected Weekly Quiz #6 from all students
Jumpstart question: The ratio of carved to uncarved pumpkins at the Harvest Fest is 11:8. There are 95 total pumpkins. The ratio of carved to uncarved pumpkins at the Haunted House is 11:8. There are 130 total pumpkins. What is the ratio of carved to uncarved pumpkins at both events? See picture below.
As the students worked on the jumpstart I assessed the homework which we went over.
After going over the homework, I gave the students the Powerpoint on eating pizza. It was very appropriate on this day (Halloween) that I was dressed as Rafael.
Students explained to me how each person in a group of 4 would get two slices.
Then I took once slice away and asked students how each of the 4 people would get an equal amount of pizza now.
We did notes on dividing fractions including what a reciprocal is.
The students tried five division problems including the class activator problem about the pizza.

The Assessment: As students tried reciprocal and division problems on their own I went around to assess them. On the whole, most students had the process down, although it was clear to me that there was rote memory - not mastery of how division works.

Another assessment came from the jumpstart. I promised no homework if anyone correctly answered the jumpstart. Many students knew to draw tape diagrams, but did not know they needed to do two separate tape diagrams. Not a single student solved this.

Likewise not a single student could determine that 7/8 of a pizza divided by 4 was 7/32 before they were instructed on that problem (many could afterwards). That being said I had one student who put 1.75 over 8 which was an answer I had never seen before and could be correct depending on the teacher you ask. The student below did 4 divided by 7/8.

I also assessed the homework. In one class it was apparent that six students did not know how to multiply mixed fractions still and it could have been more than that because a few students were missing the homework. I had to reassess this topic again after going over the homework with these students to make sure that they knew how to multiply before I taught them how to multiply the reciprocal.

Homework: Weekly Quiz #7 was made available online over the weekend.

My Glass Half-Full Take: The enthusiasm with trying to solve the pizza problem was great and the students could not argue the relevancy of being able to divide fractions. I enjoy creating a story off of the word problem rather than simply starting the class by telling students, when you multiply by the reciprocal it's the same thing as dividing. We also attempted to discover this pattern rather than having me directly show the students. Two out of three classes recognized a pattern and used the word reciprocal to describe it when I compared problems of division and multiplication of the reciprocal without telling them what I was doing.

One Thing to Do Differently: We shortened each class by ten minutes today in order to give the students an assembly about making positive choices (it was the end of Red Ribbon Week). If those ten minutes were given back to each class, I think I'd give students five more problems on division and ask that they use common denominators to solve one of them just to expose them more to this way of doing the problem.

My prep block was last today, and even though I had plenty of things to do (including write this post) I decided to take up the offer of one of my colleagues to observe his class. He loves using whiteboards and in my time in his class it was easy to see why. He would ask the class to hold up their whiteboards after they were done a problem and he would individually assess each student much faster than I ever could when the students used their notebooks. I'd like to use marker boards myself and get away from notebooks just a little bit in my room.

Link of the Day: This Washington Post article discusses the relevance of common core instruction as it is perceived by adults. I hear adults say to me all the time, "It isn't solved like I was taught." I know how they feel because I can say the same. My feeling is that first of all I am going to teach the standards that are required of the students.

Secondly, I don't have much issue with trying to teach a "simple" problem with area models, number lines, etc. even if Arne Duncan walked into my classroom tomorrow and said you can teach whatever you want so long as it's math. The reason being is that eventually students having an idea of how number lines and area models work allows them to solve problems that aren't as basic as 326-197.

Thursday, October 30, 2014

Day 41: Exposing Students to Limits

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and
V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.

The Learning Objective: Apply multiplication of fractions in order to find a limit.

Quote of the Day: “Spend time with people who constantly drain you, pull you in the wrong direction, or try to knock you down, and it will be almost impossible for your talent to take flight.” - John Maxwell

Agenda:

Jumpstart reviewing like denominators, unlike denominators, and multiplying fractions.
Review the homework. The most interesting problems asked students to find 1/4 of 154 and 1/3 of 120 in a word problem and then compare the amounts.
Physical example of a limit using our classroom.
Limits using a 64-square grid and continuously coloring half of the remaining unshaded grids and the questions which corresponded to this.
Starting the homework in class.

The Assessment: I was consistently circumventing the room during number four in the agenda and also checked homework during step one in the agenda. Overall I was encouraged by the homework results.

Homework: Tonight's homework was page 284 #4-11 and page 285 #14-16

My Glass Half-Full Take: I yelled onions twice today. The first time I got excited was when a student got a common denominator for 4, 10, and 7 compared the fractions and determined which fraction was greatest. Everyone else in the room that could solve it (including myself) multiplied one-fourth, three- tenths and, two-sevenths by 152, 160, and 147 respectively to see how many people were in each group. Then we determined that three-tenths of 160 was the biggest group. By finding a common denominator and changing the numerator, we'd get the same answer. It's always nice to have students sharing alternative ways for solving the problem - especially ways I never would have thought.

Another student eventually recognized that if a person continually walks half-way across a room they will mathematically never reach the wall.

One Thing to Do Differently: The activity we did today was done in partners. One of my colleagues did it in groups of six. I believe that would have worked much better. It would have been easier to facilitate giving colored pencils, and it also would have put the learning on the students instead of on me. I ended up being at the board for most of the block as it were and I believe students did not think as much as they should have. I also believe that perhaps ditching time to start on homework is better because the activity is deeper on Bloom's Taxonomy than our homework. Perhaps a simple assessment of three problems for homework will be a more appropriate way to give out homework in the future on this lesson.

Link of the Day: If you're looking for a hot button issue to talk about with Halloween in educational way, perhaps discussing the appropriateness of costumes would suit you.

Wednesday, October 29, 2014

Day 40: Multiplying Fractions

6th Grade Math Standards: 6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction model to show the quotient; use the relationship between multiplication and division to explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc .) How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as
would be found by multiplying the edge lengths of the prism. Apply the formulas V = lwh and
V = bh to find volumes of right rectangular prisms with fractional edge lengths in the context of
solving real-world and mathematical problems.

The Learning Objective: Multiply fractions to find a product.

Quote of the Day: “You can have the courage to be positive as you get up in the morning to face the day. You can have the courage to be gracious in defeat. You can have the courage to apologize when you hurt someone or make a mistake. You can have the courage to try something new - any small thing. Each time you display bravery of any kind, you make an investment in your courage. Do that long enough, and you will begin to live a lifestyle of courage. And when the bigger risks come, they will seem much smaller to you because you will have become much larger.” - John Maxwell

Agenda:

Jumpstart on converting mixed numbers to improper fractions
Review the homework on unlike fractions by having students do the problems on the board (4 at a time)
My favorite no 3/5 x 1/2
Multiplication Fractions Notes
Multiplication ticket to leave
Multiplication HW started

The Assessment: My favorite no and the ticket to leave. Keep in mind the problem was 1/2 times 3/5. While the most popular was 3/10. The three pictures listed below appeared more than once today during the pre-assessment. The post-assessment in the last picture appears great in that picture, but it too was far from perfect - although students demonstrated gains in fractions times fraction (mixed numbers was harder).

Homework: Page 269-270 all problems.

My Glass Half-Full Take: I really enjoyed having students come to the board and do the problems from the homework. This sounds like it's teaching 101, but I almost never have students go to the board. It was great because I did it essentially by cold calling and by picking students that I knew had the wrong answer or no clue how to do a problem. The answers we got were very telling. It provoked questions like what difference does it make when the denominators are 6 and 9, and the common denominator is 36 instead of 18? Things I would have never gotten to thinking on my own.

One Thing to Do Differently: I would change the my favorite no to include mixed numbers instead of regular fractions. The majority of students could do the my favorite no, so in a sense it led to over-confidence during the notes. When I did the ticket to leave most students couldn't actually do a mixed number times a mixed number, and that's after I did a problem with a mixed number in the notes.

I would also change the notes so that the third problem was a mixed number times a mixed number instead of a mixed number times a fraction. As part of this, it's important to let students try to solve it on their own first so they have more interest and are invested when I review it at the board.

I also wish that I had done a jumpstart on something as simple as what two whole numbers is 3 and 2/5 between. In doing an estimate of these problems it's amazing how many students have no idea what to say when I ask them what's a whole number that's too low and too high for 3 and 2/5. They all want to go way too low or way too high. Some say numbers that are both too high.

Link of the Day: Inspiration for working hard and seeing things through courtesy of one of my colleagues.

Tuesday, October 28, 2014

Day 39: Adding and Subtracting Fractions

6th Grade Math Standards: 4.NF.3d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem.

5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or
difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12 .
(In general, a/b + c/d = (ad + bc)

5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to
represent the problem. Use benchmark fractions and number sense of fractions to estimate
mentally and assess the reasonableness of answers. For example, recognize an incorrect result
2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2 .

The Learning Objective: Add and subtract fractions.

Quote of the Day: “It starts with control of your emotions, but it also extends to having the resolve to resist the easy choice, the expedient solution, and, at times, temptation in its various and alluring forms...Self-Control in little things leads to control of bigger things. For example, the reason I prohibited profanity - a small issue - during practices was because it was usually caused by frustration or anger. A player that can’t control her language when she got upset during a drill or scrimmage would be more likely to lose control in more damaging ways during the heart of a competition - fouling, fighting or making other poor decisions that would almost certainly hurt the team.” - John Wooden

Agenda:

Jumpstart: Stop & Shop sells Coca Cola in packs of 9 cans for $7 and Richdale sells Coca Cola in packs of 12 cans for $10. Which store offers the better deal? Show your work at least two ways.
Weekly Quiz passed back to all students while they worked on the jumpstart
We reviewed the jumpstart
Like denominators notes
Like denominator practice and tickets to leave
Unlike denominators notes
Unlike denominators practice

The Assessment: I collected the students work on like denominators at the end of the first class and had time to grade and return to one of my classes a few hours later. I did not have the opportunity to return it to another class as I ran out of time, but will give it back tomorrow. The main concern I had for students in terms of the feedback I gave them had nothing to do with the fractions. It was their lack of circling the key parts in a word problem. In my six years of teaching, this as much as any calculation issue has proven problematic again and again. The student below did not execute in the second biggest mistake I saw. She tried to mentally subtract 3 and 2/4 from 8. She got 5 and 1/2. Even for students that wrote 8 minus 3 and 2/4 (or 3 and 1/2), they still struggled to arrive at the difference. I think part of the reason for the struggle is what I would call "problem fatigue." In other words, they had to add (do one step) before getting to the next step.

Another assessment I did was check off students as they worked on the homework. In one class I had much more time to do this than another (more on that in things I'd do differently).

A third assessment was reviewing again the rates issue that we are having as a class. I am confident that we are now turning the corner on this type of problem, but the students will see a similar problem in the near future. The students that are successful seem to be gravitating more and more toward making a chart and finding the least common multiple.

Homework: Students did eight problems finding the sum or difference for of unlike fractions and also two to three word problems. They were given time to start this in class.

My Glass Half-Full Take: One thing that I don't plan for (although in a perfect world I really should) is having students get out of their seats. Today as we were doing the notes, I was constantly asking students to get out of their seats and explain to someone in the class how to do the work or simply to check the problem. It's amazing how beneficial this is for everyone in the class. It shrinks the ratio of student to teacher for me and also gives the students who "get it" a more developed idea of how to solve the problems as they view their classmates who might solve it correctly in a different way or are solving it incorrectly and they try to search for the mistake.

One Thing to Do Differently: Everyday there are many more than one. It's just a matter of whether I share it or not. Here's what comes to mind:

The reason my notes aren't linked here are because I ditched them after the first class. I instead handed out a worksheet and just picked out problems I sensed we could struggle with. It worked much better. I then used the word problems from that sheet as the ticket to leave.
These are fourth grade standards and I'm a sixth grade teacher. Just five years ago these exact standards were sixth grade standards, so guess if the students struggled? "The idea that 4 is 32/8 is crazy. It doesn't make any sense." - Student. I wish I knew that before teaching this lesson. I also noticed that more students got 8 minus (1 and 3/8 + 1 and 1/8) wrong than those that did not get it correct. Fractions are tough. It doesn't matter that "they were already taught this." I probably assumed too much going in and could have relied on a pre-assessment better to guide the lesson.
There is a small pack of students that are struggling converting a mixed number to an improper fraction. Since we are moving toward the sixth grade standards in the coming days (multiplying and dividing fractions), I think it's going to be essential to continue to hammer this skill home perhaps in a formative nature.
Notes practice, notes practice. I tried my best with my energy to liven things up, but I feel like there's something that can be done differently here. I am doing a kinesthetic/visual/notes/partner activity in two days so that will be a nice change for everyone.
I gave out two sheets that are essentially the same sheet, but one says unlike fractions and one says like fractions. The one that says unlike fractions is homework. What are the odds that everyone does that assignment tonight and nobody does the other one?

Link of the Day: What works better? Drilling a concept repeatedly in a day or trying to several different concepts in the same day - for several days? According to research, spreading out the concepts works better. The technical term is interleaving. Only the youngest of children benefit more by drilling initially.

Monday, October 27, 2014

Day 38: Fractions Introduction

4.NF.3c Add and subtract fractions mixed numbers with like denominators, e.g. by replacing each mixed number with an equivalent fraction and/or by using properties of operations and the relationship between addition and subtraction.

The Learning Objective:Differentiate between two rates. Turn a mixed fraction into an improper fraction. Turn an improper fraction into a mixed number.

Quote of the Day: “Out of all the applicants from all over the world, my department at Columbia admitted six new graduate students a year. They all had amazing test scores, nearly perfect grades, and rave recommendations from eminent scholars. Moreover, they’d been courted by the top grad schools. It took one day for some of they to feel like compelte imposters. Yesterday they were hotshots; today they’re failures. Here’s what happens. They look at the faculty with our long list of publications. ‘Oh my God, I can’t do that.’ They look at the advanced students who are submitting articles for publication and writing grant proposals. ‘Oh my God, I can’t do that.’ They know how to take tests and get A’s but they don’t how to do this - yet. They forget the yet.” - Carol Dweck

Agenda:

Passed back the ratios quiz and weekly quiz
Students wrote in their journals, graphed their results, and wrote in their journals
I reviewed Problem #9 in detail with the students
Students were given this paper Hershey bar and answered these questions with us as a class
Students took notes using this template and filling in this information
Since the topic should be reviewed based on 4th and 5th grade standards, I had students start the homework in their spiral notebooks without me doing any examples. As students had issues, I had student helpers assist these students in teaching the process.

The Assessment: Circumventing the room as students began homework. Student journals were also used.

Homework: Like denominators practice. Four problems with proper fractions, four problems with whole numbers and a fraction, four problems with mixed numbers, and four word problems.

My Glass Half-Full Take: It took a full block to go over the quiz. Not because I was going over every problem, but because the students were asking me to go over different problems. It's nice that they were not insecure about worrying if their classmates cared that they did not know how to do something. It's also nice that they were willing to learn even though the grade had already been recorded. I think this is one of the advantages to giving retakes for everything that we do in class. Students never want to stop learning.

One Thing to Do Differently: I did better with the Hershey Bar activity without giving the students a worksheet. The activity was truly meant to be an experience with manipulatives and I think the students relished the opportunity to not be writing something for a change in math class. I would probably keep the worksheet for myself as a place to ask students questions, but the students could do without it.

Link of the Day: With fractions the topic of discussion, I thought this was a clever way to introduce fraction division.

Saturday, October 25, 2014

Day 37: Ratios Quiz

6th Grade Math Standards: 6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
a. Make tables of equivalent ratios relating quantities with whole-number measurements, find
missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables
to compare ratios.
b. Solve unit rate problems, including those involving unit pricing and constant speed. For
example, if it took 7 hours to mow 4 lawns, then, at that rate, how many lawns could be
mowed in 35 hours? At what rate were lawns being mowed?
c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the
quantity); solve problems involving finding the whole, given a part and the percent.
d. Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities
The Learning Objective: Write a ratio three ways. Calculate the unit rate. Find equivalent rates. Complete a ratio table. Find the equivalent rate. Determine the best rate between two options. Create a ratio table and list the coordinate pairs. Graph ratios on a coordinate plane. List ratios in a double number line.

Quote of the Day: “Students with the growth mindset continued to show the same high level of interest even when they found the work very challenging. ‘It’s a lot more difficult for me than I thought it would be, but it’s what I want to do, so that only makes me more determined. When they tell me I can’t, it really gets me going. Children with the growth mindset can’t tear themselves away from the hard problems.” - Carol Dweck, Mindset

Agenda:

Collect the Weekly Quiz #5
Complete the Ratios Quiz
Students got to work on Weekly Quiz #6

The Assessment: The ratios quiz and weekly quizzes were collected, graded, and will be returned to the students.

Homework: Students are going to finish Weekly Quiz #6 for Monday. When they do, I will return it to them the following day and let them know what needs to be fixed.

My Glass Half-Full Take: The quiz covered many of the ratio standards and was fairly rigorous. Only two problems were not connected to word problems. I had built in enough time for students to do the quiz and work on their weekly quiz, but could not teach another lesson after the quiz, which was the intention a week ago. My colleagues and I had an inkling after this quiz was put together that this was a possibility, so it wasn't a big deal. In correcting the quizzes, the most encouraging thing for me was seeing that two of my students chose to solve number nine by finding the least common multiple.

One Thing to Do Differently: Many of the quizzes had the same mistakes. The first problem of the quiz students incorrectly ordered the units. Instead of 3:5 they said 5:3. I wish that I had forced students to circle these terms from the beginning of the unit. It's really something that I push all of the time, but I don't think I push it hard enough.

Another mistake was the rate problem of Stop & Shop versus Costco. We had this exact problem (technically I changed two numbers) in class just days before, but it was still the most popular wrong answer on the quiz. Interestingly the preceding question about recipes which measured students ability to tell if rates were equivalent went very well. This question on Costco and Stop & Shot used harder numbers though, and more specifically tougher units. Perhaps I could have devoted a full class to understanding the insight of this idea in lieu of just half of a class, but then I would have compromised actually teaching the lesson on unit rates (notes included). Students actually did quite well on question eight which tested the objective of seeing whether or not two rates were equivalent. I always believe that students who put the units of what they are dividing, multiplying, etc. have a better chance of getting a deeper understanding. In this particular problem, that could not have been more apparent. I need to do a better job of calling students out on not writing the units down. Perhaps some annoying buzz sound whenever they don't put units will serve as a reminder.

Link of the Day: Some worksheets from Mathfunbook on each and every standard with a little differentiation worked in as well. That said, I don't think it's the most engaging thing a student has seen. Still I see this as a cheap alternative to a textbook for any district out there that's looking to transition away from texts.