## Monday, October 29, 2012

### Teaching Students to Count Objects Up to 20

Try these fun counting games with whichever numbers you are teaching. Start with 0 or 1 and continue through 20 or higher. Hold up 10 pencils, paper clips, pieces of colored paper, crayons, drinking straws, or other objects in your classroom. Ask the students how many you are holding. Check by having the class count the items aloud as a child takes them from you and places them on a table. Draw the number 10 on the board.

Count the objects again as a student points to them from left to right on the table. Choose a new volunteer to point to the objects from right to left as the class counts the objects once more.

Copy this number chart and bring 20 beans, paper clips bottle caps, or other counters for each student. For younger students, just copy the first two to four rows of the chart. Click here to download a PDF file of this chart:
Give each student 10 counters. Let each student place a counter on the chart as you count aloud numbers 1 through 10.

With Excel Math, students develop a strong foundation in math beginning in Kindergarten. Used in classrooms for over 30 years, Excel Math curriculum carefully presents math in a spiraling fashion. Students learn and review different concepts throughout the year while developing a solid foundation of math skills. Using strategically placed spaced repetition, Excel Math gives educators a proven approach to teach math concepts to students from Kindergarten through sixth grade for long-term retention. Read more here.

To help your students visualize counting, duplicate the number line below on the board. Have a student point to each number as the class says it aloud. Then have the student circle the numbers as they are counted.

If you have time, enlarge the number line so it can span across the floor of your classroom or hallway (with the numbers spaced about 5 inches apart).

You may also like these articles:

## Thursday, October 25, 2012

### Base Ten Learning Tools

In Excel Math, we help students learn to add and subtract numbers using everyday objects, hands-on experiences, number cards, reproducible manipulatives and even mental math. We've created some Pumpkin Base Ten Cards you can print for the fall season. Here are some ideas you can use in your classroom.
 Pumpkin Base Ten Cards
Make a set of cards for each student to help them identify and add numbers. Or use them as flash cards. Cut apart the cards. Hold up a card and have students tell you the number. Then have them write the number. Remind them to write neatly. Place several cards on your whiteboard pen tray or tape them to a wall and let students put them in order from least to greatest. (Use removable tape.) Do the same with students holding the cards while another student arranges them in order. Have the students mix up, and let another student put them in order. Mix them up again and have another student arrange them in order from greatest to least.

For addition practice, give students counters (beans, pumpkin seeds, beads, paper clips, etc.). Let students add a counter to each empty space and then write the combination for the equation:
3 + 7 = 10 or 10 = 3 + 7

Show a card and have your students tell you how many more pumpkins would be needed to make ten. Check the answer by having a student count the empty boxes. (It would take 7 more.) Then have a student tell you the corresponding number sentence:
3 plus 7 make 10, or 3 + 7 = 10 or 10 = 3 + 7

Have students shuffle their cards. Let each student take one card from her pile. Have the students add the pumpkins to find the total. Then have them create a word problem for that number sentence.

To help your students understand the visual patterns of numbers and their relationships, here is a blank base 10 chart you can download and use with your class. Give each child a chart plus 10 counters. You can use beads, paper clips, raisins, dried beans, small blocks, paper shapes or counters of your choice. Draw a number on the board. Let students place counters in the boxes to equal the numbers you show them. Point out that one full row equals 5.

For addition practice, write the number 3 on the board. Have your students place three counters on the chart. Ask them how many more counters they would need to add to the chart to make 10. Let them say a number sentence to describe that equation (3 + 7 = 10 or 10 = 3 + 7). Do this for various equations. When your students are comfortable with addition, try subtraction.

For your Kindergarten students, give each child a set of number cards from the Excel Math Student Lesson Sheets or from the Manipulatives in the Teacher Edition. Hold up a Pumpkin Card and let the student find the matching number card. Older students can match the Pumpkin Cards with their appropriate number words.
 Excel Math Kindergarten Number Cards from Lesson 15
Use the pumpkin base ten cards for subtraction. Let your students create story problems to go with each card. For this equation: 10 - 7 = 3 you could create the following story:
Jamie had 10 pumpkins. He gave 7 to his friends and neighbors. Now he has three left.

 Excel Math Pumpkin Card from the PDF link above
Use the cards with white and orange pumpkins for additional addition and subtraction practice. Combine cards to add larger numbers. Have children work in pairs to add and subtract using the cards and a timer. See how many cards each student can add in one minute. Play again and see how many students can beat their original time.

Play a card game having children turn over two cards at a time. The person with the highest card gets all four cards (a variation of the card game "War", in which opponents each turn over one card, and the one with the higher card keeps both). For addition practice, have children turn over two cards at a time, and the person with the highest sum gets all four cards. Repeat until someone gets all the cards, or the students get tired of playing.  For multiplication practice, have the students multiply the two cards they turn over. The winner has the pair that when multiplied together forms the highest product.

Visit our web store to order Student Lesson Sheets (155 lesson sheets plus tests) and a Teacher Edition set of 155 Lessons with brainteasers, teaching suggestions, the answer key, activities, and reproducible manipulatives for each grade level. Excel Math is available for Kindergarten through Grade 6.

Since an entire year of Excel Math curriculum is as low as \$11.00 per student, many schools use it as their core curriculum. Other schools find it's a powerful supplement to their adopted curriculum. In both situations, students gain confidence in mathematics as test scores soar.

Because Excel Math uses a unique spiraling strategy, the lessons build upon each other and need to be taught sequentially within each grade level in order to get the concepts into your students' long-term memory. Try out some sample lessons but then use it for a full year in your classroom to see the amazing results.

Interested in finding out more about Excel Math? Take a quick tour here.

## Monday, October 22, 2012

### Celebrate Mole Day in the Classroom

Know the math behind chemistry? Then you’ve likely heard of Avagadro’s number (6.023 × 1023) that’s used as a basic unit of measure in chemistry. This number is more commonly referred to as a mole.

As you might guess, Mole Day is observed on October 23rd from 6:02 am to 6:02 pm, and can include anything mole related from eating molé sauce to playing a game of Whack-a-Mole. The punnier, the better.

In  Excel Math, we help students apply math to everyday life. For over 30 years, Excel Math has produced excellent results, including improved test scores and high student engagement with elementary mathematics—all while giving students a solid foundation of math skills. Take a quick tour of Excel Math here. Now fix yourself some mole sauce using either of the recipes below. Enjoy a snack break with some guaca-mole while you read more about moles, mole day and Excel Math.

Molé sauce (pronounced MO-lay) is a mexican tradition, and often includes chiles, oregano, cumin, garlic, chocolate and cinnamon, among other spices. With countless regional variations, this sauce can be green, yellow or red. It's usually served over smoked beef, chicken or enchiladas. Your class can try this easy recipe for Mole Sauce and then taste it as a dipping sauce for tortillas. Use the recipe as a math problem by having your students triple the recipe or divide it in half. Calculate how many tortillas you'll need if each student in the class gets a half. Then find out how many you would need for 3 classes with 25, 26 and 30 students in each class. If you're looking for a more authentic molé sauce recipe, try this one.

One teacher created this cute fabric mole pattern as a way for students to earn extra credit. You can download the PDF file here: Make-a-Mole-pattern:
Using the fabric of their choice, students can make a small stuffed toy mole to help them remember that a mole in chemistry is actually 6.023 × 1023. The photo below was taken after Ms. Kristy Gilmore's General Chemisty class at Hillcrest High School in Missouri made moles last year. Read more about their creations here.

To study mole-cules and density, use this activity from Excel Math Grade 6 to give your students a hands-on lesson. Bring two clear glass beakers labeled A and B, two ice cubes, 200 ml of water and 200 ml of isopropyl alcohol. Explain that density is a measure of the amount of molecules in a given object or volume. Draw two empty squares on the the board. Draw five large dots in one square and 10 large dots in the other. Ask the students if they can tell which box has a higher density. Help them understand that an object with a lot of molecules has a high density while an object with fewer molecules has a lower density.

Ask the students what would happen if you dropped an ice cube into a glass of water. Would it float or sink? Explain that fluids like water also have densities. Ask them if density might play a role in this question. If so, how? (Ice has a lower density than water. Objects with lower densities than water float to the top.) Ask the students what would happen if you put the ice cube into another liquid that has a different density than water? Fill Beaker A with 200 ml of water and fill Beaker B will 200 ml of alcohol. Do not let the students know which liquid is in which beaker.
Hand out the lesson sheet below. Have the students write their observations about the two beakers on the lines provided. (Do not let the students smell the liquids.) Write a few of their observations on the board. Show them the two ice cubes. Explain that they are exactly alike. Ask them what they predict will happen when you drop the ice cubes in the beakers. Have the students write their predictions on the lines provided. Write a few of their observations on the board.

Drop the ice cubes in the beakers. Show the students how one ice cube floats to the top while the other sinks. Help the students understand that the liquids must be different. Based on your previous discussion, ask them which beaker contains water. Then ask them to explain the relationship between the densities of the ice cube and the liquid in Beaker B. Have them write their answer to question C on their papers. Then talk about the answer, explaining that the ice cube has a lower density than water but a higher density than alcohol.

## Wednesday, October 17, 2012

### A Tribute to Martin Gardner & Brainteasers

Martin Gardner was born on October 21, 1914 and died in May 2010 at the age of 95. Read more about him in this interesting profile by Philip Yam. Mr. Gardner was a fan of mathematics, puzzles, magic tricks, gag gifts, and feral cats. In his honor, October 21 (his birthday) is set aside as Celebration of Mind Day. Since it falls on a weekend this year, you may want to celebrate all week long. As you might expect, this celebration encourages a fun and playful approach to math. Students can mark the day by doing fun math puzzles, performing illusions, and even sharing math stories.  Read our previous post about Math Storytelling Day for additional math story ideas for the classroom.

Martin Gardner was fascinated by mathematics, magic and Alice in Wonderland. He was a prolific American writer who had interests in music, philosophy, scientific skepticism, religion and literature. Mr. Gardner enjoyed creating mathematics and logic puzzles and writing about them. You can find some of those puzzles in his ebook, Fractal Music, Hypercards and more . . . Mathematical Recreations from Scientific American Magazine at scribd.com. This book is an anthology of Gardner's Mathematical Games columns from the 1978 and 1979 issues of Scientific American Magazine (the 14th in his series of such collections). Try some of Martin Gardner's brainteasers and play some puzzle games online or download them for your students at Puzzles.com.

One of Mr. Gardner's most famous puzzlers was the onion (sometimes changed to a cherry) in the glass. This was originally demonstrated using matchsticks. For the classroom, you could use a bead or counter for the cherry (or whichever food your students prefer in their lemonade or soda—lime, orange slice, raspberry, etc.) with 4 toothpicks for the glass. Some of your students may have played the ball in the cup tossing game. If so, you could change the puzzle from a cherry in a glass to a ball in a cup. The object then would be to try to toss the ball out of the cup by rearranging two toothpicks. Here's how to arrange the toothpicks and the ball or bead:
The problem is to move just two toothpicks so the cherry (or ball) ends up outside the glass (or cup). The finished glass may be turned left, right or upside down as long as the cherry is outside it. Try it yourself before looking at the solution below.

The Excel Math Teacher Editions for Grades 2-6 include a variety of math brainteasers and logic puzzles called Stretches. Stretches teach students various kinds of thinking skills and, like the rest of Excel Math, carefully spiral through math concepts. Here's a Stretch from the third grade Teacher Edition in the style of Martin Gardner:
Draw the figure below on the board or have your students use 13 toothpicks to create it. Ask the students if they can remove 1 toothpick (or one line) so it forms 3 squares instead of 4. The answer appears below.

Stretches can be used as math warm-ups or bell work to get the students focused on solving problems before they begin the daily lesson. Read more ideas for math class warm-up activities in our July 23 blog post.

This is the answer to Mr. Gardner's cherry in the glass puzzle. We've color coded the toothpicks so it's easier to see how they move. If you slide the green toothpick right instead of left, the cherry ends up on the outside left of the glass. To see some of the incorrect moves your students might try, read Philip Yam's blog.

Here's the answer to the Excel Math puzzle from above. Simply remove the top center toothpick (or line):

Because Excel Math uses a unique spiraling strategy, the lessons build upon each other and need to be taught sequentially within each grade level (including Guided Practice, stretches, and interactive activities) in order to get the concepts into your students' long-term memory. Try out some sample lessons but then use it for a full year in your classroom to see the amazing results.

Since an entire year of Excel Math curriculum is as low as \$11.00 per student, many schools use it as their core curriculum. Other schools find it's a powerful supplement to their adopted curriculum. In both situations, students gain confidence in mathematics as test scores soar.

Visit our web store to order Student Lesson Sheets (155 lesson sheets plus tests) and a Teacher Edition set of 155 Lessons with brainteasers, teaching suggestions, the answer key, activities, and reproducible manipulatives for each grade level. Excel Math is available for Kindergarten through Grade 6.

Interested in finding out more about Excel Math? Take a quick tour here.

## Monday, October 15, 2012

### 7 Steps to Successful Math Students (& Parents)

1. Overcome math anxiety

## Wednesday, October 10, 2012

### Five Steps to Giving Students Effective Feedback

Students today are bombarded with information, images, music, noise, and soundbites. So how do we get through the communication barriers and provide them with effective feedback in the math classroom? Let's take a look at five characteristics of effective feedback: Immediate, Targeted, Concrete, Action Oriented, and Confidence Building.

Immediate
After students turn in an assignment, they often have to wait a day or two to find out whether they were on track. In that brief amount of time, they can easily forget why they made the mistakes they did. And since they haven't yet discovered where or why those mistakes occurred, they keep making them again and again. As a result, the mistakes continue and bad habits are beginning to form.

When students get immediate feedback, they can switch gears and start tackling math problems correctly. Dr. Janice Raymond, the author of Excel Math lessons, created a natural feedback loop with the unique CheckAnswer system. The Excel Math CheckAnswer lets students see immediately if they've made mistakes and gives them a chance to correct those errors on their own. It is used throughout Excel Math lessons for Grades 2-6.

This CheckAnswer system enables students to check their own work and verify for themselves that they understand the concepts in the daily Guided Practice and Homework. As a result, students are encouraged to solve the problems, show their work, check their answers, and then go back and fix any errors they've made. At the same time, students are given an immediate feedback loop so they don't have wait until the next day to find out which problems they've missed. Read more in our previous post.

Targeted
Feedback is most helpful when it is targeted and applied to a student's specific needs. This can be difficult, if not impossible, with a class of 30+ students. Fortunately, Excel Math tests have built in some feedback tools teachers can use to identify students who need more help on certain concepts.

Regular assessments are included in each Excel Math grade level. In the Teacher Edition, on every test page is key to the concepts each test problem covers. When a student misses a problem on the test, you can see at a glance which concept was addressed in that problem and where that concept was first introduced. In the example test below, the first question asks students to add 4-digit numbers:

The test table in the Grade 3 Teacher Edition shows that the concept covered in test question #1 was first introduced in Lesson 67. So students who missed this question can be given a recap of Lesson 67 or solve a few problems from the Guided Practice for additional review:

Concrete
Concrete, specific, individualized feedback can help students pinpoint the problems they are dealing with so they can address those problems head on.  Since some students are visual learners, providing a visual explanation of math concepts can sometimes help them grasp the concept more easily. In addition to looking at the example on the Student Lesson Sheets, projecting the lesson on a screen or interactive whiteboard gives the teacher a chance to explain the problem-solving technique to many students at once. With Excel Math Projectable Lessons, slides of the problems are followed by slides showing the answers and the steps needed to complete the problems. It can be helpful to leave these examples on the screen while students move on to the Guided Practice as a visual reminder of how to solve the problems.

According to Grant Wiggins in his Educational Leadership article for ASCD, "Research shows that less teaching plus more feedback is the key to achieving greater learning. And there are numerous ways—through technology, peers, and other teachers—that students can get the feedback they need." Read more at ascd.org.

For the most part, the lesson of the day for math class needs to take only 15-20 minutes (or less), allowing plenty of time for students to practice solving the problems on their own. During Guided Practice, students find out where their understanding is weak, and the teacher is available to help students who need it, while allowing them to progress independently through problems they understand. In this way, the teacher can give specific, individualized feedback and students can catch and correct any errors before they are repeated at home.

Action Oriented
Instead of simply pointing out errors when students make mistakes, it's more helpful to students when we give them the tools to continue the problem-solving process independently. As students solve problems on their own, they start to succeed at mathematics. Building on that success, the student begins to relax. We've eliminated any reason for the student to be defensive. Instead, the student gains confidence and realizes "I can do it!" and "it's not that hard."

When students take an assignment home, there obviously is no teacher to help them. It is assumed that if a teacher gives help in class, the student is therefore 'ready' for independent practice. The problem however, is that in many mathematics curriculums, students are asked to complete homework on concepts to which they have just that morning been introduced. It should be no surprise that kids come back to school the next day and say, "I didn't understand this, so I couldn't do it." Here's where Excel Math's true spiraling process with spaced repetition and a built-in feedback loop help close the achievement gap and make homework more of an independent study and review process.

When a concept has been practiced by the student and guided by the teacher for at least a week, by the time it goes home for independent instruction (homework), the student is able to complete the homework successfully most of the time.

Confidence Building
Being able to complete homework independently (for the most part) is a huge confidence builder for students who have struggled with math. Confident students are much less likely to become discouraged when faced with more difficult problems. Instead, they are better equipped to tackle new challenges when they come up in the future.

During Guided Practice, students work on math problems that reinforce the concepts just taught. The teacher is free to move around the classroom, helping those students who get stuck. Students are can work independently but still ask for help when they need it. This system allows students to check their own work and gives them a chance to actually get the answer correct!

Parent/teacher conferences can also be confidence-building tools. Teachers can point out areas where the student is improving and may suggest additional resources for skill building such as paper or electronic flashcards, Timed Basic Math Fact Practice, math games, cooking (measuring, doubling a recipe), menu planning on a budget, measuring with a ruler or tape measure, etc. Many parents feel ill-prepared to tutor their students in math. Some simply aren't available after school when students do their homework. You may want to provide parents with a list of resources such as your own office hours and availability, free tutoring groups, students available to be "math buddies," homework clubs, online helps, and homework chat lines.

Here's a feedback form you can customize and use at your next parent-teacher conference to give parents feedback about their students. Once you download the form, you can fill it in on your computer or print it out, copy it and fill it in by hand. Click here to download the customizable Word document or here for the printable PDF file. TIP: If you print out the form, sign and date one form. You may want to add your class expectations on the back. Then print a signed form for each student in the class and fill them out individually. Keep one copy of each student's form for your records.

What feedback methods have you found work best in your classroom? Share your ideas using the Comments section below.

You may also like these articles:

## Monday, October 8, 2012

### Excel Math: Fully Correlated to Common Core Standards (CCS)

If you're looking for math lessons that teach to the new Common Core Standards, Excel Math is for you. Excel Math is also an excellent tool for transitioning to the Common Core and getting students up to speed and prepared for the upcoming math assessments..

Excel Math provides students and teachers with powerful support, in-depth practice, and frequent assessment for Common Core. Plus, Excel Math is fully correlated to the Common Core math standards. We were pleased, but not really surprised, to find out how well our Excel Math lessons correlate to the new Common Core Standards.  You can download our correlations by grade level and print them out for your own reference as well as for your colleagues.

See samples of our Common Core Teacher Editions for Kindergarten through Grade 6 as well as a Scope & Sequence for each grade level.

If your state has not moved to the Common Core, visit our correlations page here. Find your state and click on the state correlations by grade level. Our Standard Teacher Editions are available for non Common Core states.

Recently, we added some Common Core Lesson pages and Projectable Lesson slides to expand on those concepts already included in the Excel Math materials. Click here for our Tools for Teachers and these revised lesson pages (available for download as PDF files). If you have a Teacher Edition, simply insert these revised pages into your book. If you order a new Common Core Teacher Edition, it will now include these revised pages plus additional Activities, manipulatives, discussion suggestions, and Common Core vocabulary.

New to Excel Math? Find out more and take a quick tour of the program here.

## Wednesday, October 3, 2012

### The Hottest Place on Earth

Scientists have recently re-examined the data and have concluded that the hottest place on earth is actually Death Valley National Park with a record-breaking high temperature of 134º. Previously, El Azizia in Libya was considered to be the hottest place in the world. Heat waves across the United States this year have broken previous records. Read more about Death Valley and see some amazing photos at NationalGeographic.com.

Excel Math lessons teach students to calculate temperature and understand the relationship between positive and negative numbers. Show your students the following thermometer (or have students make a large one for your classroom) and ask them what the temperature is:

Point out that the thermometer shows -10º below zero. Explain that below zero is colder than above zero. Ask your students if it is warmer when the temperature is -20º or 10º. Tell them that the positive sign is usually not written, because a number without the negative sign is assumed to be positive. Help students understand that even though 20 is greater than 10, the negative sign before 20 makes it smaller than zero and also smaller than positive (or negative) 10. Let them practice greater than and less than (or warmer and colder) with additional numbers on the thermometer.

The temperature problem shows just one way Excel Math lessons encourage students to apply math skills to real life. Excel Math Create A Problem exercises are designed to do the same. In this story problem from Excel Math Grade 6, students learn about Mt. Whitney, Mt. Everest and Death Valley as they practice calculating elevations and estimating: