Note Passing

Each year is always a little different in respect to the personalities we are responsible for educating for the year. This year happens to be one in which our grade level is experiencing dynamics in our population that are not optimal for the educational environment.
In blunt terms, many are so busy messing with each other in negative terms, that the learning environment is in danger of being lost.
This year has been what I call "The Year of Notes". I have even started a file folder in which to keep them all and have scanned some to send to parents so they are aware that their child is not doing assignments, but involved in a completely different activity during class time.
The children have been very creative in their delivery of the notes, and other children are enlisted through out the class to pass them along.
Some delivery methods:
1. Student asks to throw trash away, and then another student asks to sharpen a pencil (or whatever) and takes the balled up paper (note) from the trash.
Solution: Monitoring of course, but also, I collect trash from a student and put it in the trash next to my desk.
2. Simply throwing a balled up paper or paper airplane through the air.
Solution: This one is difficult as they usually wait until your back is turned or you are helping another student.
3. Student asks to use the restroom. Leaves note. Another student asks to go after, gets note.
Solution: Class bath room breaks, but as we know there will be the child that insists they will have an accident if they do not go, even if you have just taken the class.
4. Other students used to pass the notes across the class, after the great care a teacher has taken to make sure certain personalities are apart.
Solution: Bring it all out. Let the entire class know that if they participate in the passing of notes during instructional time, they will be just as guilty as the note writers and their parents will also be told of their involvement.
If anyone else has experienced any other methods and can let me know, I would appreciate it. This Year the Notes have not only taken from our educational experiences in class, but the effects of their contents have led to fights, bullying, and drama that needs to decrease.

Division of Fractions with Common Denominators

We teach division of fractions using common denominators. The kids have picked up on this easily, but for some reason don't want to change the numerators when they find the common denominator. The don't do this when they add or subtract, just divide. Any ideas on how to remind them to change the numerator as well as the denominator when they are dividing?

Surviving the holidays

I don't know about everyone else, but this week has been an adventure and not the kind that I want to go on again! Trying the keep the kids focused and caring about class discussions have been very challenging. The last two days before our holiday break, I plan to review all I can. I know new material will go in one ear and out the other and if the review is not for a grade, the students will not complete it.

Five of the same...

Something we started last year at King's Fork Middle was beginning each day with five SOL type questions. We use SOL released items, but change the numbers. The five questions come from different SOL's, including some that we have not covered yet. From Monday through Thursday the students see the same five questions with different numbers. I give them about 10-15 minutes to work them out. When they have finished I go over the answers with them on an Interwrite Pad with projector (a transparency can also be used). They must correct their work on their papers which I collect. Student receive a check if they have shown all the work we went over or a check minus if they didn't. On Thursday, they get a classwork grade. Each check minus takes off 10 points.

Friday we do the same 5 again with different numbers, but this time it is a quiz grade. With only 5 questions worth 20 points each they learn pretty quickly the importance of keeping up with this each day.

Last year we started this at the beginning of the second semester. This year we started about 2 weeks ago. It really makes a difference. It's an ongoing review of SOL's covered, plus it gives them some familiarity with upcoming SOL's.

Think Pads & Notebooks

Everyday my students enter the room and work on 5 Math Review problems to continually practice for upcoming tests. I've had problems getting them to organize their work and save it for future use. I started making sure they work by making it a part of their classwork grade and that part worked. However, I would find their papers on the floor, counters, and tables regularly. I just knew they weren't taking my advice on how useful these would be.

A collegue offered some suggestions and I've taken it a little further with this plan. Now when they enter the room they make their "Think Pad" by folding paper to create three columns. One to show their work, one for the solution we come up with as a class, and one for the multiple choice answer. The rows are folded based upon how many problems you have and the front and back can be used. These are easily graded daily by walking around and making sure each block has the appropriate information inside.

In order to encourge the organization of them we've developed the Think Pad Notebook. Inside they are to keep the weekly worksheet that contains all the problems for the week and behind that sheet they are to keep their "Think Pads". These notebooks are to remain in the room for now and they will be graded each nine weeks for completeness. I've made this worth the same as a Test Grade so they realize the importance of it.

I'll keep you posted with the results!

Giving them the answers!

I really try to emphasize in my class that I'm not that worried about the answers. I want to see the process they go through to get the answers. I've tried a couple of things to help them out. One is that I give them a set of problems and just hand them the answers. They have to spend time figuring out how I got the answers. Another is to pair up students. Each person in the pair has a different set of problems, and their partner has the other person's answers. So, one person does a problem, and then the other checks if they are correct. If they aren't, this generates discussion as the students try to figure out how to get the correct answer. The kids really enjoy checking and helping each other.

Reducing Fractions

I find that sixth graders really struggle with reducing fractions, so I have them come up with the 3 characteristics of a reduced fraction themselves. I put 15 to 20 reduced (simplified) fractions on the board. Some of them have 1 in the numerator, some are consecutive like 3/4 or 8/9, and then the rest have a Greatest Common Factor (GCF) of 1. I put the fractions with 1's in the numerator in circles. The consecutively numbered fractions go in squares and then the remaining fractions go in triangles. I then have the students work together to come up with what each shape has in common. Obviously they have no trouble with the first 2 rules, but they tend to struggle with the "GCF is 1" rule. Once they have thought about it awhile, I have them list the factors for each numerator and denominator. From here I have them find the GCF. By this point they are able to give me the three things they need to look for to see if a fraction is reduced: The numerator is 1, consecutive numbers, the GCF is 1. The fact that they came up with the three rules themselves tends to make it stick a little better.

While teaching dividing fractions this year I started with a paper activity to capture their attention. I held up 4 peices of paper and asked what 1/2 of 4 was. I then wrote the step that 1/2 x 4= They reminded me to multiply the numerators and the denominators. And the last step to simplify. They redidly gave me the answer that 1/2 times 4 was 2. The students were then ready to restate that mutiplying by 1/2 and dividing by 2 were the same thing. The point was made that dividing by a fraction was the same thing as multiplying by it's reciprocal.
Ex. 4 divided by 1/2 (four sheets of paper torn in 1/2 gives you 8 sheets of paper) therfore it is the same as 4 times 2 (multiply be the reciprocal!)

I Can Learn

This year, my middle school has invested in a computer software program called I Can Learn. It is highly recommended to be fully integrated into the classroom nearly all day, every day. My school chose, however, to integrate the program partially, at only 2 days a week for 60-90 minutes. This software is well rounded with problems of the day, pretests, warm ups, lesson videos and notes, examples fully explained, tutorials, quizzes, section tests (pre-made and teacher made) as well as almost full SOL correlations. The program has a list of best practice strategies that add to its 20% increase in student test scores such as students wear headphones continually, notes are taken very methodically and thoroughly, a mastery level is to be set so students can not move on to the next lesson until, for example, a 70% quiz score is achieved, students write out all examples and quiz corrections, etc.

This year I have attempted full integration for 4 of my students from each block. There was criterion for selection, but to my amazement, the students are writing notes, focusing on their own computer screen, keeping their headphones on, and passing quizzes with scores I wondered if they could achieve. In speaking to these students about their math experience, more math vocabulary is being used and student engagement is increasing. I encourage everyone to take a look at the link to the website and watch the tutorial. Complete computer teaching is a futuristic sounding concept, but I have found success with it in my class for a select group this year.

http://www.icanlearn.com/default_new.asp

I am concerned about how I have been teaching percents this year. The district I work in no longer wants us to use the cross product method of finding percents. The preferred method is for students to use benchmarks when solving consumer application type problems. I have tried the Singapore method and some of my students really take to it and like it, but many students say they find it tedious and refuse to use it. I currently teach Pre-Algebra at the 8th grade level and from diagnostic testing a large percentage(about 40%) are at a 4th or 5th grade level of math proficiency. During testing we have done at our school, the teachers who have ignored our districts recommendations about how to teach percents have achieved significantly better (30 to 40 percent better)results in student achievement, making students write out the steps necessary to solve percent type questions using the cross products method. My concern, and I would like to hear any input and advice I an get on this, is that perhaps since so many of my students are 3 to 4 grade levels behind where they are supposed to be, does it make more sense to try and drill them using cross products type solutions or should I continue forcing the students to use benchmarks. What have other teachers seen as the learning curve for students using this technique?

12/5/09
by Don Lloyd
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Patty Paper Proofs

I have been using patty paper in my geometry class to help students understand concepts. It has been a huge help especially with students who have a hard time visualizing. I usually have an easy time knowing when to pull out the patty paper in geometry but not so much in pre-algebra. I am sure this method could be helpful in pre-algebra as well in areas other than geometry. I would appreciate any ideas. I also really like using foldables for note taking. They are a great place to store the patty paper.

"Unwrapping" 1-step & 2-step equations

Last year when teaching this I saw that the students were having a hard time solving 1 and 2 step equations so when this was introduced to me I immediately fell in love with it. It has worked marvelously. Attached are two worksheets I made to help the students with solving 1 and 2 step equations. The first is two step equations. (Of course we started with 1-step but I accidently attached 2-step first oops). For example 2x - 4 = 12. The variable always starts in the first triangle (x) (then follow the arrows) then the first bubble you put what happened immediately to x (multiplied by 2) and second bubble you (subtracted 4) and the answer always goes in the star (12) after the star you follow the arrows around. The opposite of subtracting 4 is (adding 4) and the opposite of multiplying by 2 is (dividing by 2). If you have the students start at the star and do the operations they will get their answer in the second triangle. So have them take 12 add 4 and then divide by 2 to get the answer. They should be able to "substitute" the answer they got in the second triangle and for the variable in this case x and perform the operations to get the answer in the star.

It works the exact same way for 1-step equations.

Hope this helps you like it did me.

Word Problems

Word problems are a constant struggle for my students. I have searched for different ways for students to interact and conquer this skill. I found a wonderful activity that our math coach shared with us called "Silent Pass." In this activity there are 6-8 problems that you place on the back of numbered note cards. Students are asked to divide a paper into 8 sections (by folding). They are then asked to solve each problem in the corresponding box. When they are done with one problem they hold the card up and silently pass it to another student and obtain another card to solve the next problem. This continues until they have answered all 8 problems. I was very impressed with the number of students who were actively involved all the students were. Even those who normally find it out difficult to participate or refuse to do the work assigned.
This activity can be modified to accommodate any level and any subject involving problem solving.

Scale Factor

Since I teach Geography as well as Math I incorported practicing map skills when teaching scale factor. The students had to plan a trip from Norfolk to L.A. making three stops along the way. They had to calculate their distance from each stopping point as well as total distance of their trip using the scale on the map. It was a great way to make an interdisciplinary lesson and make it relevant for the students.

APEX LEARNING

My school district is encouraging us, the Math teachers, to use the Apex Learning for Algebra and Geometry courses. Apex Learning is educational software that offers online courses in mathematics, science, English, Social Studies, Romance Languages, and Advanced Placement. The curriculum is organized into semesters, units, lessons, and activities. A typical semester includes 5 to 7 units, each with 3 to 6 lessons. A typical lesson comprises a number of activities including studies, practices, readings, journals, labs, discussions, projects, explorations, reviews, and embedded assessments. Although each Apex Learning online course provides a complete scope and sequence based on national and state standards, it does not align perfectly with the educational framework (SOLs) in the state of Virginia. Therefore, I need to pick and choose lessons on Apex Learning for my Geometry classes.

Overall, my students like the Apex Learning digital curriculum because it has a lot of interactive activities within each unit. For me, as an educator, I like Apex Learning because it changes my role in the classroom. Since I usually have my students work with Apex before I actually teach a concept, it allows my students an opportunity to become a self-learner, which in turn, allows me to be a facilitator/resource for them. Furthermore, I like the fact that students are allowed to use this program at home once a login ID is created for them.

Perfect Squares & Square Roots

I love to use color tiles to teach perfect squares and square roots! I pass out baggies of color tiles and then ask the students to work with a partner to create as many different squares as possible. The students are allowed to create the squares showing the area or the perimeter. I then have each team share one of the squares they created and I put it on the overhead for the class to see. (I always put up the area model so the perfect square is easy to see.) We discuss what makes each of the shapes a square before we discuss the perfect square. We then work backwards to see the square roots. Once the children have seen perfect squares and square roots like this, they usually remember it!

INTEGER CHIPS

Teaching adding/subtracting integers is sometimes a difficult lesson for students to grasp. I have used the integer chips(red/yellow chips) to give the students a pictorial view of the concept for the last few years and the seem to understand better when I demonstrated adding and subtracting using the chips.

I have an overhead set of the red/yellow chips which makes it very easy to demonstrate. Having the pictorial view is very beneficial for students who are visual learners. They are able to see the red chips represent negative and yellow represent positive. This is also great when explaining zero pairs to add or subtract integers. Subtracting integers appears to be harder than adding integers and when using the integer chips it is easier for the students to see that we're actually adding the opposite by showing them how we're doing it and not just telling them this is what is done!

The only down fall in using the chips is when problems consist of large numbers. Who wants to count out 25+ chips? Plus that can be very time consuming! So, just stick with smaller numbers when demonstrating with the integer chips.

If anyone has any other ideas about teaching integers please let me know!

Unifix for Pythagorean Theorem Proof

I had a student come in for tutoring this week because he was having trouble applying the Pythagorean Theorem. In an "aha" moment I pulled out the cubes to walk through the proof again with him (in class the students used the Pythagorean Theorem Model from the state's website). I could see the lights getting brighter as we created Pythagorean triples with the cubes and walked through solving for a missing side with the manipulatives. He had a break-through and did very well on his quiz the next day.

AngLegs

I've made lots of use of the AngLegs lately teaching SOL 7.7 . The are great to show the students how perimeter is like a distance and by pulling the sides apart we merely get a straight line. It helps them to understand keeping the units straight for perimeter vs. area. Also, I made a parallelogram with them, layed it flat on a table, and poured some beans inside....making sure they were flat and not piled. As I adjusted the shape of the parallelogram the students could see how the side lengths stayed the same but the area changed as the beans started to overflow the borders of the AngLegs.

Also used one of the Sir Cumference books and it went well with some students however, others were bored.

Tarsia

Tarsia is a simple computer program that allows you to create puzzles that students solve by matching. I used this during SOL 7.1. The student had to match fractions, decimals, and percents. One of the finished puzzles looks something like the image to the right. There are a number of different options and shapes.

Suffolk Schools will install the program with a tech request. I requested it one afternoon and had it the following morning. It's also available for free to download from the Tarsia website.

Most of the time I had the kids work in pairs and they loved it. They've been bugging me to make one for area & perimeter.

Real World Shocker

As part of an incentive program in my clasroom, my students earn "Pittman Bucks." I have made a money template with my picture on it and I have denominations of $1, $5, $10, and $50. At the beginning of the year I explain to the students that coming to school is their job and therefore they should be paid for it! I give them a weekly "pay check" of $50 and they earn money for various other activities as well. They can also lose the money for breaking rules or not doing all of their assigned work for the week. I have also thrown in a monthly "bill" of rent in the amount of $60. Boy do they love that! At the end of the nine weeks they have the opportunity to buy things in an auction. Well, today I broke the bad news to them. I informed them that as good American citizens it is their duty to pay taxes. As you can imagine, they were not to pleased! (Don't feel too badly for them though, it's only a 10% tax.) They then had to calculate and pay me their tax money. Each student has a money envelope and on the outside they have a basic check registry that they have to use to keep track of what they earn, lose and spend. Shockingly enough, most of them have great difficulty maintaining an accurate balance. All of this falls into SOL 6.8, consumer applications, not to mention the basic life skill of balancing a checkbook.

Quadrilaterals with Anglegs

I taught a lesson to a 4th grade class on quadrilaterals, using the anglegs. The students were in groups of 3-4. At first, each student had four anglegs of the same color, but each person in the group had a different color. We talked about the shapes they could make and what those shapes were called (square and rhombus). The students formulated rules for their squares and rhombi. We also discussed congruent and noncongruent. Then I had each student take their shape apart and pass two of their anglegs clockwise to the next person. Some students constructed parallelograms and some constructed kites. We discussed the similarities and differences. Next, I had the students who had created the kites change theirs to parallelograms. We compared rectangles and parallelograms and the students again formulated their set of rules. The students loved using these manipulatives!

Math Ticket

Hello everyone,

I recently did a math ticket with my students as a review for their nine weeks test. The students really enjoyed it. The were given a 3 by 3 like bingo card with nine topics of choice on it. They were to choose one square from each row and work on each topic. They were given several days to work on it in class. The students really enjoyed it because they had a choice on what to do. It covered topics such as percent, fractions, and decimal conversions, tips, tax, discounts and simple interest, order of operations, interger models, and math properties. The only thing I see myself doing differently the next time it only allowing them to complete it in class. All of the students worked on it, but when it came time to turn it in some were misplaced or lost because they were also allowed to work on it at home.

We recently just finished teaching conversion of decimals to fractions and fractions to decimals. The students really liked the activity which required them to match cards together that showed the equivalency of the two. Repetition of the most common conversions helps it stick to memory as well as having them think decimals and fracitons in relative terms to money ie. one fourth of a dollar is $.25.

Order of Operations Monarchy

This year I took a different approach then the typical PEMDAS or Please Excuse My Dear Aunt Sally to teach order of operations. Teaching it last year, many students still struggled with questions that had both multiplication and division or addition and subtraction. You may have seen it as well with yours. For the problem 7 - 5 + 3, students run down their list and do addition first because A comes before S in PEMDAS.

To combat this I used a monarchy to teach Order of Operations. Each part of the order had a title according to their position in the kingdom.

King G (grouping symbols)

Queen E (exponents)

Princes M & D (multiplication and division)

Princesses A & S (addition and subtraction)

This may seem a little silly, but worked great with students prior knowledge about a monarchy. The concept is simple, who assumes the throne next? The King is always first. If the King is not present, the Queen is on the throne. This continues down the line.

The problem with multiplication/division and addition/subtraction was solved by drawing upon the students knowledge of a monarchy. I posed the question: "If more than one Prince is present, who assumes the throne?" Students shouted out: "The oldest" and "Whoever's first in line." They got it!!!!! There is our left to right. The same question was posed about multiple Princesses; and the same answered received.

I have had much success with SOL 7.2 using the monarchy. If you have students who are struggling with the left to right for multiplication/division and addition/subtraction and are looking for another way to teach it, give this a try. I also created a foldable with pictures of a King, Queen, Princes, and Princesses, notes, and sample problems that the students worked in to reinforce it.

I'll take a picture of a student's foldable and post it. What do you think?

DaVinci Man- Measurement and Multiplying Fractions

One activity I use to help students understand how math is part of nature is the Proportions of a Man activity. It brings art and math together. Students can measure each other, which involves cooperative learning. First start by measuring height and base proportions on this. Students then measure arm span to see that height and arm span match. I open the activity with the measurement of each other to grab their interest.
Then I give them a model of a circle with a 8 inch diameter and have them work the proportions based on this height. They draw an 8 inch circle and draw the Vitruvian Man with the proportions illustrated below (taken from Wikipedia):

• the length of a man's outspread arms (arm span) is equal to his height
• the distance from the hairline to the bottom of the chin is one-tenth of a man's height
• the distance from the top of the head to the bottom of the chin is one-eighth of a man's height
• the distance from the bottom of the neck to the hairline is one-sixth of a man's height
• the maximum width of the shoulders is a quarter of a man's height
• the distance from the middle of the chest to the top of the head is a quarter of a man's height
• the distance from the elbow to the tip of the hand is a quarter of a man's height
• the distance from the elbow to the armpit is one-eighth of a man's height
• the length of the hand is one-tenth of a man's height
• the distance from the bottom of the chin to the nose is one-third of the length of the head
• the distance from the hairline to the eyebrows is one-third of the length of the face
• the length of the ear is one-third of the length of the face
• the length of a man's foot is one-sixth of his height

The activity can be tailored to just the proportions of the face, or the whole human body. Conversion to percentages is also an option. The finished products are quite beautiful, targets the visual/artistic learning style, and is a way to show how math really is used in nature.

Getting the students to talk

A huge goal for me is to get the students talking to each other about math. We all know that with middle schoolers this can be a HUGE challenge. The Kagan Cooperative Learning books have been a huge help in creating activities that get kids to talk. One of my favorites is called Showdown and involves using dry erase boards. Every kid get a board and a marker. In groups of three to five, give students a set of problems to work. It works best if they have the problems on cards in a ziplock bag. One person draws out the card. Each student works the problem on their own board and turns the board face down when they are finished. The "Showdown Master" calls out "SHOWDOWN!" when everyone has their boards flipped over. The students then show their boards to each other and work together to correct any mistakes. This activity really gets the students talk about the math.

If anyone has other activities, I'm always looking for something new. THANKS!

Fractions in Action

I used the fraction transparency squares to help introduce the concept of multiplying fractions. The kids really liked them and it made the concept easier for them to understand. However, I wish I had a class set of them so that the students could see the multiplication process at their desks easily and they could work their problems out faster. I had the kids fold paper to represent the fractions and the multiplying process. However, this took alot of time to model and for the students to complete their problems. Does anyone know where I can get a class set of them cheap?

Fraction Dilemmas

We are getting ready to start our first unit on fractions. I absolutely love the colored transparencies for multiplying fractions. I am running into a problem because of the limited amount of these. I am looking for ideas because extra kits cost $14. The AIMS books have a non color version, but the color is more "impressive."

I have created a SMARTboard activity that includes this and trying to get the colors just right so we can show the colors as a whole group. This will enhance their learning in whole group, but I'm afraid that group work will not workout so well.

I am looking for any help with these ideas. Also, any other ideas to getting the students engaged and REMEMBERING the fractions would be appreciated as well. :)

Promethean Activevotes

I have a Promethean "Smart" board in my room. I have been using it for everything. I was not that familiar with it so I just began using it as an extension of my computer, e.g. flipcharts and powerpoints. Then I found the ActiveVotes - wow! I have a changed class atmosphere - the students everyday come in and ask if we are using the "eggs" as we call them, and that encourages class participation as well as giving me a plethora of ways I can assess their progress, know what their weaknesses are, teach, and just let them learn. Further I do not have to be concerned about a messy chalkboard!

The thing that has been the most useful is when I use it for the daily warm-up. Our daily warm-ups are given to us by the district but I like to remind them of the things we have done in the past - especially topics in which they struggled but pacing has required us to move on. So we do a daily warm-up consisting of 5 to 10 items that address the current topic, their areas of weaknesses, and just review of topics they understand. They are very competitive and love it when they get it right, but when they get it wrong - they immediately know (instant feedback) and if a lot of them get it wrong it is a chance to review. Otherwise a student gets to go up to the board and show how they got their answer and the whole class gets a chance to see where they made their error.

My measure of success is on Friday, mid-class, how many students are still with me and wanting to learn and so far I have been amazed that they will work up to the bell! It is a fantastic tool!

Promethean ActivExpression

I do not have a Promethean ActivBoard in my classroom. However, I have recently incorporated the ActivExpression, one of the many Promethean’s products, into my lesson. This interactive tool is amazing. It definitely increased the participation of all my students during class.

The ActivExpression hardware is like a mobile phone device. It has a keyboard that allows students to vote for multiple-choice format questions, enter yes or no responses, and convey their thoughts by entering full sentences and character texts.

I was creating a lesson to help my students to review for their upcoming benchmark test. I was going to ask my students to complete a review worksheet. However, I understand that it can be boring to students. Students were still required to complete all the review questions individually using the ActivExpression, but all students got to share their answers with the rest of the class by voting or texting. All of my students agreed that it was a much more fun way to review.

To use the ActivExpression devices, all you need is to install the “ActivExpression” software in your computer. You don’t need to have the Promethean ActivBoard in your classroom to use the ActivExpression!

Blog in the Classroom

My Class Blog

This year I began using a blog with my Math 7 Class. I have found much success with using the blog in the room. Students have used it as one of four stations, as extra credit, also as a whole class assignment. I find it is very helpful so I do not have to have the students type in lengthy websites or frequently ask for directions when we transition into the computer lab. Even if used infrequently, when used in class, the students are more engaged and on task. I have not taught them yet how to post comments, so they are mostly disabled. On the downside, some of my students do not have Internet access at home and most parents have yet to check out the blog. I posted this both to share all the links I have found but also to look for comments that might dialogue about best practices when it comes to blogging in the classroom.

Percent and Consumer Applications

Last week we worked on Percent of a Number and introduced Singapore Math in which you use modeling and illustrations. For example: What is 20% of 80. Make 100% 80 and encourage students to use knowledge of benchmarks (50%, 25%, 10%, 5%, and 1%) to get to 20% (10% x 2, 5% x 4, 1% x 20, etc.). You can also use this when you start with proportions.

Currently I am teaching the consumer apps unit involving discount and sales price, tax, tip, mark up and mark down. The most important piece I believe is vocabulary. I was amazed that the students had no idea that discounts save us money and tax adds to our total. We use the same concept of benchmarking and the Singapore math to find discount, etc. Also it helps if students understand that if there is a 30% discount I am only paying 70%. So if they know 10% they can multiply by 7 and get the 70% and still figure out how much they will pay.