This is a post from my previous blog - I can't believe I've had this freebie out for nearly four years! I'm glad so many people have gotten to use it!This is a Footloose game to help students practice finding areas and perimeters of rectangles. This Footloose game includes 30 question cards that require students to: calculate area and perimeter of rectangles: find missing sides; find perimeter when given the area and a side length; compare areas and perimeters of rectangles. When playing Footloose, students solve every problem and record their answers in the corresponding box on the Footloose grid that they each receive. To get the freebie, click on the Footloose picture and download! I hope you can use it (if you haven't already:-).
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Teaching Percent of NumberWhen teaching students to find the percent of a number (or the part or whole), I introduce two different ways to find the missing number - using proportions and using equations. Since different students often prefer different methods, I teach both, have them practice both, and then let them choose the one they like better. I've given an example of each method below. The Percent of a Number Wheel shown here includes both methods. Each section of the wheel includes an equation and two examples, with room to solve using both methods. There's also a little room on the wheel (or around it) to add extra notes or your own examples, if you'd like. Around the wheel are a few practice problems that can be completed together or individually. Method 1: Proportion1) Substitute the given values into the %/100 = IS/OF proportion. Use a variable for the missing number. 2) Solve the proportion to find the missing value. Example: What is 15% of 70?Method 2: Equation1) When given the percent, change it to a decimal. 2) Substitute the given values into the equation. Use a variable for the missing number. 3) Solve the equation. * If finding the percent, be sure the answer is in percent form (multiply the decimal answer by 100). Example: What is 15% of 70? part = % ∙ whole x = 0.15 ∙ 70 x = 10.5 When we work with the equations, I do manipulate the equations to show students how they are all versions of the same basic equation. For example, if we start with part = % ∙ whole and we're looking for the whole (say the part is 35 and the percent is 25), we end up with35 = 0.25 ∙ x. From solving algebraic equations, students know that tofind x, both sides will be divided by 0.25, which gives them x = 35/0.25(whole = part/%)If you decide to use the wheel, I hope you and your students like it! This is a repost from 2013, transferred from my previous blog:-)Some students finally got to play Fraction War today! We again worked on the group problem solving that we started last week (comparing and ordering fractions), and continued with Footloose...also comparing and ordering fractions (click for description of Footloose game). Students finish Footloose at all different times, so the few that did finish today had the opportunity to play Fraction War with the fraction card decks I've made. I am loving these fraction cards! I made them during the summer, just with the idea of playing "Go Fish," but I also used them for an equivalent fraction sorting activity, and now they are great for playing "War." The kids who played today did a great job deciding which fraction was larger....I asked them to write their work on paper, so I could be sure they weren't guessing, but after a few turns, I could hear them discussing as they found common denominators and made equivalent fraction to compare, or reduced the fractions to compare. They were definitely thinking! I'm finding that the use of these cards is really helping students' mental math abilities as well as the math conversations that they are having. Only a few students got to play today, but several of them asked to play during 9th period today (homework/activity period). I'm looking forward to more students playing tomorrow, as the rest of them finish up their Footloose! This is a post I wrote back in 2013 (now revised), on my other blog, so the observation I refer to was quite a while ago now...how time flies!I was observed by one of my assistant principals today (a Friday). After 20 years, I don't get super-worried when I'm going to be observed, but I still feel a little anxious. Today, I decided to have the students complete a problem solving activity and then start a "Footloose" activity, even though they wouldn't finish....Footloose normally takes about 40 minutes, so I figured they could do about half and then finish on Monday. (I do this fairly often, to give students flexibility in their work time - they can take as long as needed to complete problem solving, but if they get done quickly, they can move on). Things went so well during the observation...AP commented that there was so much going on in the room, and that the kids were so engaged! I was happy:) During the class, students worked on group problem solving, (which they have done previously, with other math skills). These particular problems involved comparing and ordering fractions. Our procedure was as follows: 1) Each group received a different sheet with a problem "situation" and 3-4 questions about that situation. (I have five different sheets so that we can do the problem solving several different days with the same concepts, if needed and if time allows). 2) Each group read their situation and each of the questions together. 3) Each student spent 5-7 minutes, thinking/working individually to solve the questions, writing their work on their own recording sheet. 4) When students completed their individual thinking time, they compared their ideas (and answers if they had them), discussed any differences in thought, and worked to agree on final answers. 5) The final answers (with work) were written onto a group answer sheet to hand in. When we did this type of group problem solving the first time (with decimal problems), we spent about 5 days on the problem solving, with each group working on a different problem sheet each day. The students really like the problem solving, partly because they are able to talk out their answers with each other. It's great to hear their communication about math and how they are able to point out the steps a group member needs to complete or the concepts that they may have missed. Today, it was great to hear them say "Oh, we're doing this again. I like this!" My AP commented that he listened to hear what they were talking about, to see if they were focused, and he could hear one student explain to another how the work that they had done was different from another student. The problem solving took about 15 minutes, and then as each group finished their problem, they moved on to Comparing and Ordering Fractions Footloose. This is a great game for keeping students engaged, but moving! Students start out with one card and a sheet of paper with 30 blank "blocks" in which to write answers to the questions on the cards. Each card has a number on it, and students record the answer to each card in the same number block as the number on the card. After answering the question on the card they start with, students put the card on the chalk ledge and pick up another card with another question to answer. Students continue answering and returning cards until they have answered all 30 questions. Students work so quietly when they are doing this activity! My AP said it was like "night and day" when they switched from the problem solving to Footloose - they were talking about the p.s., but as soon as they started the Footloose, it was sooo quiet.....and I didn't have to say anything for it to be this way - it just happened. As I mentioned, I don't really get worried when an observation comes around, but it was great to hear the positive feedback for these activities that I create for my students! Four Ways That Self-Correcting Math Work
Can Benefit Students
I have been teaching for more than 20 years. If you have been teaching for a long time, then like me, you may have used a certain strategy/instructional tool for a period of time, and then for some reason,
stopped using it....and then after another period of time you came back to it, and wondered WHY (or when!) you stopped in the first place!
That was me today. I had made 20 copies of my Footloose answer key and had the students correct their own papers (they had worked on the Footloose activity for part of yesterday's class and then finished during today's). I was surprised by the thoughts that went through my brain as they were correcting - the main one being - "When did I stop doing this?!"
I do have students check their homework answers with the answers shown on the board (sometimes), but I don't give them each a detailed answer sheet to use, and I rarely have them grade their own classwork.Here are my re-discoveries related to students correcting their own math work. Some of these may be particular to the topic we worked on (writing algebraic expressions from phrases, phrases from expressions, and evaluating expressions given a value for the variable), and the fact that the answer keys were detailed (not just the answer), but I'm sure I'd observe the similar things when studying different topics as well: 1) Students asked me more questions when checking their work with my key. Since they were working at their own pace and checking individually, they seemed to be more comfortable with verifying whether or not their phrases were ok (I didn't have every possible phrasing option on my key). Students who wouldn't normally raise their hands to ask in front of the class did ask me questions during this time. 2) Correct work is modeled on the answer key. Because I had several options for phrases on my answer sheet, they had to read each one to see if theirs was on the sheet, giving them a little more exposure to correct options. I also had the steps for evaluating each expression, so they could go line by line and have those steps reinforced, as they compared the work to their own. 3) Students were finding their OWN mistakes, rather than me finding them. I heard things like, "I copied the problem wrong," "I said 3 x 3 was 6!" "Oh, I put division for product." And I realized, as I did years ago - it makes so much more sense to them when THEY see the difference between the correct work and the mistake they made, rather than ME finding it....do they really know why I circle a mistake that they made on their paper if they don't take the time to ask me? When find the mistake, they know what happened. I don't need to make those types of connections and observations. They do.they4) Students are engaged - they enjoy having the key! It was fun to see them with their pens or colored pencils, pointing at their papers, question by question, making sure they were being accurate in their grading of themselves, and then being sure to write the correct answer accurately (I did make them write the correct answers, using pen or a colored pencil, so the change would stand out).I don't know what prompted me to copy the keys to use today, but I'm so glad I did. It's wonderful to be reminded of forgotten/lost practices that help students to think just a bit more. Have you re-discovered any strategies/practices recently? Use Task Cards in a New Way, to Provide
Self-Differentiation and Promote Discussion
If you're like me (and so many other teachers), you know that task cards can be used in sooo many ways. From centers to Footloose (or Scoot) to exit tickets to entrance tickets to mini-quizzes - the list is long!
However, if you're like me in other ways, you're always looking for something new and different. This year, my "new and different" was to start using task cards to play Truth or Dare in math and language arts classes! To use them this way, some of the task/question cards need to be written as True or False questions, which can make the questions just a little trickier and lead to more in-depth thinking. I allow students to discuss the answers after the "official" answer is given, and depending on the question, students end up having great discussions! The Dare questions are a little harder, require more calculation or perhaps more verbal explanation than the Truth cards, and so they are worth more points. (Truth cards are worth one point while Dare cards are worth 2 or 3 - I've even thrown in a 4-pointer here and there.) What makes this game fun? Well, it's a little different - with the "dare" part in there. Students also don't always know how many points they're going to get to try, so that offers a little excitement. I like the fact that students can choose the type of question they want, so it allows for some self-determined differentiation...the choice gives the more hesitant students the chance to feel a little more confident. After creating several paper and pencil Truth or Dare games, my wonderful friend Leah (Secondary Resources for Social Studies & English) suggested that I make a Google classroom version, and I'm so glad I did! It's so easy to use and there's little to no copying needed! (A little copying if I want students to write their work/answers on paper; no copying if I want to share the Truth or Dare game in Edit mode and have students type their answers.) Check out the 2-minute video below - it shows how the game works in Edit mode (there are one or two "slow to refresh" spots in the video, so please don't think it's not working:-)
Check out this video to learn more about the way the game is played with paper/pencil - in any subject!
I hope you can use this game idea-it can be used in any subject!
If you've used Truth or Dare for Google Classroom, would you complete the survey below? I'd love your feedback!
I'm really liking the math wheel idea, so I created a new wheel for fraction, decimal percent conversions:-)
How to use this resource (this information is also in the free download):Around the outside of the wheel are the different conversion headings – you can use the wheel to introduce the conversions, filling in just the ones you are covering each day. Or, you can use it to review all the conversions at once. In either case, the wheel can be kept in students’ notebooks as a reference/study tool. 1) I like to begin with decimal to percent and percent to decimal. In the arrows in these sections, you’ll see x 100 and ÷ 100. It think it’s important that students understand that these are the operations being used for these conversions before giving them a shortcut, so I let them use calculators to complete the examples. Once the examples are complete, I ask the students to look for the pattern – what happens to the decimal point in each of these cases? We decide on the “shortcut” rules together and then write them at the bottom of those sections. 2) The fraction to percent and fraction to decimal sections have the rules written already, so the examples just need to be completed. I always relate fraction to percent to students grades. By the time we get to this topic during the year, students have been figuring out their grades for months (I never write their percentages on their assessments – they need to calculate them). They know how to find their percentage if their quiz grade was 6/8 or their test was 48/52. However, sometimes they need a reminder that this official fraction to percent “rule” is the same thing they’ve been doing for months! I have them write a little reminder in that section - “just like test grades!” 3) For percent to fraction, students need to remember that percent means “out of 100,” so the percent number will always go over 100. Then they must reduce. 4) I find that decimal to fraction is sometimes tricky for students. When they have trouble, I ask them to read the decimal number according to place value (“How do you say this number, using tenths, hundredths, or thousandths, etc.?”). Once they speak it, they know how to write the fraction – 0.27 is 27 hundredths, which is 27/100. After completing the examples, we discuss the idea that the denominator will be whatever the last decimal place is (10, 100, 1000, etc.) and the numerator will be the digits in the decimal number. We write this rule as simply as possible. 5) Students then complete the 10 problems around the page. Above each number is the conversion to complete (F to P, P to D, etc.) They can then color the rest of the wheel background. I had a great time coloring my answer key! These could make a fun decoration as well:-) I hope you can use it!!
We know that graphic organizers can not only be helpful for organizing information, but they can also be helpful in creating visual cues that help students remember specific information.
This math wheel focuses on the topic of rounding decimals (obviously:-). When I have reviewed rounding decimals with my students in the past, they often remember whatever trick or saying they've been taught, but they often can't explain the math reasoning (therefore, I always save any sayings/tricks until after the math concept is understood, if I use them at all). When using this math wheel, I start with the number lines - looking at the distance between 1 and 2, where 1.5 is, and visually draw attention to the fact that 1.6-1.9 are closer to 2 and 1.1-1.4 are closer to 1. The students write in the labels and then there's space for you, the teacher, to add several examples of your choosing. Then I move to the benchmarks. You'll see on the completed version, I drew a small number line to create the visual of the space between 1 and 1.1, labeling 1.05 as the half-way point. The same thing could be done for the others, or examples of rounding can be added (like the one below 0.0005).
Students can then do the practice problems all around the page.Above each number is a T, H, or TH, to indicate the place to round to (tenth, hundredth, thousandth).
I have the students color their problems/answers according to numbers that rounded up (my example uses green) and numbers that rounded down (pink), which gives a quick, easy visual to see that they knew which way to round. A closer check will then tell me if their answers are actually correct:-) (You can always let them just color the background later, for fun!) Last,(if at all), I'll have them add a rule/saying to help them remember.....one that each student creates him/herself would be best. I hope you're able to use this math wheel! Let me know if you have any questions:-)
Rumors is another great lesson from Mathline! This lesson allows students to explore exponential growth, in the context of spreading a rumor. In addition to the focus on math concepts, this lesson can also help students to understand how quickly rumors can actually spread....an important idea for middle schoolers to consider.
To begin the lesson, students are presented with the following scenario: "Two students who were both born on December 21st, the date of the winter solstice, decide that it would be great not to have to attend school on that day. Therefore, they start a rumor that schools will be closed to celebrate the winter solstice. So, on December 1st, one of the students told two of her friends that school would be closed. On the next day, each of these students tells 2 students and on consecutive days, each of the new students tells 2 more students and so on. If there are 8,000 students in the school district, the question arises as to whether the rumor was started early enough for everyone to have heard it?"Students can act out this scenario by having students form a human triangle, with Student A first, then the two students she told (students B and C), then four students representing the two that Student B told and the two that Student C told, etc (as far as possible, depending on how many students in the class). This will help students visualize the problem and understand how this rumor is being spread. The triangle also help students to understand the growth pattern. The human triangle will only go so far, so students will then need to use their calculators or paper and pencil to find how many days it will take for the rumor to reach 8,000 people. I would recommend providing the students with a blank chart to give some structure to the students' work after they try the human triangle. The chart below includes the first several days (the numbers for the entire chart can be found in the lesson).
In addition to understanding more about exponential growth, students can be asked to determine the algebraic expression to describe the number of new people to hear the rumor each day (2n), as well as the
expression for the total number of people (2n+1-1). To read the full lesson and the possible extensions, check out the lesson here.
Do your middle school math students like to play math games? Mine do, but over the past few years I've noticed that many of them aren't familiar with some of the games I played when I was a kid, like Yahtzee, for example. So, as we started working on converting fractions and decimals, I decided to create a game to make practicing the conversions more fun AND give them some more game experience! I based it on the idea of Yahtzee:-)
Here's how it works:Students roll four dice, and pair the dice up to create "target numbers" that are decimals or whole numbers. For example, a student rolls 1, 2, 4, and 6. From these dice, the student may create any two of the following decimal (or whole) numbers: ½ = 0.5 4/1 = 4 ¼ = 0.25 4/2 = 2 1/6 = 0.1666... 4/6 = 0.666... 2/1 = 2 6/1 = 6 2/4 = 0.5 6/2 = 3 2/6 = 0.333... 6/4 = 1.5 Once a player has chosen two target numbers, he or she finds the score by adding the dice that were used for each decimal. If the player chose to use 1 and 4 to get 0.25, he or she adds 1 + 4 for a sum of 5 to place in the score column. The second decimal choice uses 2 and 6, to equal either 0.333...or 3. The sum of 8 would go in the appropriate column as the score. On the next roll, this student rolls 1, 1, 3, and 5. This student can pair 1 and 1, to get 1, and pair 3 and 5 to get either 0.6 or 1.666... The score for 1 is 2 (1 + 1) and the score for 0.6 is 8 (3 + 5). In many cases, students' scores will be the same, but some of the decimals can be found with different combinations of numbers (1 and 3 = 0.333..., and so do 2 and 6, so students could score either 4 or 8). Some students will notice this sum difference and go for the combination that will give them the higher score. The students have really enjoyed playing this game. They do need a few examples at the start, to understand exactly how the game works, so if you decide to try the game, be prepared to go through a few turns together.
Detailed instructions are included, and a complete answer key of highest and lowest possible scores for each target number are included as well. This is handy to quickly check student score cards as you check in on their games.
If you give it a try, please let me know how it goes! Click to see on TPT |
To find more posts you might like, check the Blog Table of Contents.## AuthorHi, I'm Ellie! I've been an educator for more than 20 years, teaching all subject areas at both the elementary and middle school levels. |