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Math Resource Websites

What does Mathematics instruction look like at Pittsfield Elementary?

Last year, PES teachers spent time ensuring that all standards are met at each grade level. They have aligned the curriculum so that the same concepts are taught in all classes at a grade level, and that skills are built on in the following grade levels. They also have highlighted the key focal points for learning. Those can be found here.

Teachers group topics together, plan how they will assess those topics and then they plan the daily lessons. Planning backwards like this makes sure the goal of the unit is kept in mind during all of the instruction. Our base curriculum is Everyday Mathematics. When there is need, teachers will pull from other resources to help students meet the instructional goals of the unit.

 

Below you will find a collection of resources parents have found helpful in the past. This will be updated this year, so please email any resources you love to dharvey at pittsfieldnhschools dot org.

 

 

Need help with understanding Everyday Math?

This site is from the creators of Everyday Math. It has animated resources that will demonstrate the some of the different methods that students can use to solve computation problems. Students will be asked to try and practice methods shown in class, but they can use whatever is efficient and accurate for them.

 

This is another site from the creators of Everyday Math. This site has four great aspects. You can access the glossaries, answers to frequently asked questions and all the family letters that are sent home with each unit. (Please keep in mind we use the third edition.) It also has materials that will help you help your child with Homelink and Study Link problems.

 

 

Still have questions? Email Dharvey at Pittsfield.k12.nh.us

Musical Fractions

http://www.philtulga.com/fractionbars.html

 

Looking for fact practice?

THE Place for Educational Games. This site has time, money, addition, subtraction, division, multiplication. You can set up a game and play with your friends.

 

http://jmathpage.com/JIMSBestintermediate.html

 

http://www.thegreatmartinicompany.com/

 

www.khanacademy.org

 

http://freerice.com/

http://www.oswego.org/ocsd-web/games/Mathmagician/maths1.html

http://www.thatquiz.org/

http://www.multiplication.com/

http://teacher.scholastic.com/activities/adventure/math1.htm



This is an interactive site to practice math facts against the clock.


 

This site has math and logic challenges for families to try together.

 

 

This is the National Council of Teachers of Mathematics (NCTM) website. If you click on the activities section, it will bring you to a variety of games and activities that can be searched by grade level.

 

 


Function Robot – This site is an interactive version of the “what’s my rule?” machines we see in Everyday Math. This activity can build number sense and encourage basic skills.

 

 

 

 

This site allows the user to pick a skill to focus on. There is a chance to read about the skill and then if you scroll down there is a place to practice the skill.


This site has a few interactive math skills that focus on addition and subtraction concepts.

 

 

 

 


Trade First Subtraction

In Everyday Mathematics (EDM) students are introduced to many different methods for subtraction. As they get older, they are introduced to subtraction algorithms. Some are easier to learn, but not as efficient as others. EDM picks one algorithm as its focus algorithm. Focus algorithms are powerful, relatively efficient and easy to learn and understand. The focus algorithm for subtraction is trade first subtraction. Students are taught this method and expected to show that they know how to use it, starting in second grade. In problem solving, however, students may use any algorithm they chose. The aim of this approach is to promote flexibility while ensuring students know at least one reliable method for each operation.

The trade first subtraction algorithm resembles the traditional U.S. subtraction algorithm, except all the trading is done before all the subtraction, allowing the user to concentrate on one thing at a time. The steps involved are below.

1. Examine all columns and trade as necessary so that the top number in each place is as large or larger than the bottom number. The trades can be done in any order. Working left to right is perhaps more natural, as with partial sums addition, but working right to left is a bit more effective. (When students first learn this process it is modeled with base-10 blocks.)

2. Check that the top number in each place is at least as large as the bottom number. If necessary, make more trades.

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3. Subtract column by column in any order.

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Trade first subtraction is highly efficient, similar to the traditional algorithm, and relatively easy to learn. It is an effective algorithm for paper and pencil calculation.

Many teachers find that drawing vertical lines between the places is helpful for students when first learning this algorithm. The vertical lines allow for students to focus on one column at a time. They also help students avoid mistakes if unnecessary trades have been made.

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Examples of all of the algorithms are available online. If you go to the PES website (http://pittsfield-nh.com/pes/) find the “Curriculum” dropdown menu, and chose “Everyday Mathematics”. This will bring you to a page with many useful links. The first link will bring you to a page that demonstrates the different algorithms taught to students.

An Alternative Addition Method: Partial Sums Addition

In Everyday Mathematics (EDM) students are introduced to many different methods for addition. As they get older, they are introduced to addition algorithms. EDM introduces different methods for addition since some are well suited for mental arithmetic or larger numbers. Some are easier to learn, but not as efficient as others. EDM picks one algorithm as its focus algorithm. Focus algorithms are powerful, relatively efficient and easy to learn and understand. The focus algorithm for addition is the partial sums method. Students are taught this method and expected to show that they know how to use it, starting in second grade. In problem solving, however, students may use any algorithm they chose. The aim of this approach is to promote flexibility while ensuring students know at least one reliable method for each operation.

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An Example of Partial Sums Addition

As the name suggests, the partial sums method calculates partial sums, working one place value column at a time, and then adds all the partial sums to find a total.

Partial sums can be added in any order, but working from left to right is the usual procedure. This order seems natural since we read from left to right, and it also focuses on the most important digits in the addends first (thousands before hundreds, hundreds before tens, and so on). The partial sums addition method can be readily adapted for mental arithmetic.

It is also the most similar to addition with base- 10 blocks. Finding each partial sum corresponds to combining all of one kind of base-10 block. Adding the partial sums corresponds to exchanging blocks as necessary and then combing blocks. This is a wonderful connection that our second graders work on making when they first are introduced to partial sums.

Examples of all of the algorithms are available online. If you go to the PES website (http://pittsfield-nh.com/pes/) choose the “Curriculum” dropdown menu, and “Everyday Mathematics”. This will bring you to a page with many useful links. The first link will bring you to a page that demonstrates the different algorithms taught to students.

This article was adapted from the Everyday Mathematics Teacher Handbook

Using the Number Grid

In the primary grades at Pittsfield Elementary School, our Everyday Mathematics curriculum includes many counting activities that use number grids. For example, we might have children count by 10s starting at 17 (17, 27, 37, 47, 57) or count backward by 10s starting at 84 (84, 74, 64, 54). Parents can use number grids at home, too.

Number grids can be used to explore number patterns. For example, children can start at zero and count by 2s. If they color each box as they go, they will have colored all the even numbers. If they start at one and count by 2s they will color all the odd numbers. If they count by 5s, starting at zero, they will color numbers with 0 or 5 in the ones place.

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Number grids are also useful for addition and subtraction. For example, to find the difference 84-37 you can:

*Count the tens from 37 to 77 (4 tens) and the count the number of ones for 77 to 84 (7 ones). So 84 – 37 is 4 tens plus 7 ones, or 47. This difference corresponds to the distance between the points 37 and 84 on a number line.

*Start at 84 and count back to 37, noting as before how many numbers have been counted.

* Count back 37 from 84 by tens and ones: 74, 64, 54, 53, 52, 51, 50, 49, 48, 47.

Addition problem can also be solved on the number grid using similar methods. The number line simplifies “double counting”, or counting the numbers of numbers counted, that is required in many addition and subtraction procedures.

By identifying number patterns in grids, younger students build concepts for divisibility rules, prime numbers, and factoring in later grades. Have your child show you how the number grid is used in his or her classroom! Try it out yourself. It may make you think about mathematics differently.

This article was developed from the Everyday Mathematics Teachers Reference Book, Grades 1-3.

A Day in the Life of the Math Lead Teacher

Editors Note: This year The Pittsfield Schools have used federal stimulus money through the American Recovery and Revitalization Act to hire two one-year specialists who are charged with training teachers and supporting students who need extra help. Ms. Harvey, a fifth-grade classroom teacher with a graduate degree in mathematics is our new Math Lead Teacher.

What does a math lead teacher do? When I agreed to leave my classroom and take on that role I wasn’t sure what to expect. And although the job is still evolving, my days are beginning to settle into somewhat of a routine.

Mornings, 8:30-9:30 especially, are a popular time for math instruction. If a teacher has asked me to look in on a particular lesson, I schedule that into my day. If not, I check my log and join a class that I haven’t visited in a while.

Today, I decided to join a second grade classroom. I observed as the lesson’s objective was introduced and then floated around the room to support the students’ work.

At ten o’clock I moved on to a sixth grade classroom where I had been invited to help out with a Differentiated Instruction (DI) day. During a DI day the class splits into different groups and each group works on a particular skill, either with extra practice or enrichment. The groups change as the students’ needs change. I got to work with five students, three of which were my former fifth graders! We worked through methods for finding perimeter, and the different number models that can be used to represent that work.

Next, it was back downstairs to a third grade class. The class was working on probability. We had a great time discussing the probability that it would rain chocolate milk. Afterwards, the teacher and I discussed how the lesson went, and I shared my observations of the students’ understanding.

Later, I took some time to meet with a special education case manager about how to best support a student during math class. Together we brainstormed possibilities for making the curriculum more accessible for this student. I’m looking forward to seeing the outcome.

I spent the rest of the afternoon looking at results from the NWEA testing. The results are being used to help identify students who would benefit from morning math groups. It’s exciting to start organizing these groups. Once the groups start, on October 19th, I’ll be adding that to my routine.

My role is somewhat fluid; I go where the needs of the students lead me. But whether it’s working hands-on in the classroom, collaborating with colleagues, or taking care of administrative pieces, there’s one thing I can say for sure: the job is never dull.

By Danielle Harvey

PES Math Lead Teacher

Math Games, An Easy Way to Help Your Child Learn Facts

Students must master certain skills in order to become flexible problem solvers. The Everyday Math program provides multiple methods that help students practice basic skills and math facts. Many games are designed specifically for this purpose. One of the best ways you can help your child learn math is to play a math game or complete a math activity at home once a week.

The Everyday Math curriculum has a wide variety of fact practice games. Since children find these games much more engaging than standard drill exercises, they are willing and eager to spend more time practicing their basic facts.

Drill exercises aim primarily at building facts and operations skills. Practice through games shares these objectives, but, at the same time, games often reinforce other skills including calculator skills, money exchange, shopping skills, logic, geometric intuition, and intuition about probability and chance (because many games involve numbers that are generated randomly).

This year all PES classroom teachers, in kindergarten though sixth grades, will send home weekly games. Playing games at home with family members reinforces the skills children are learning in class. Playing games also allows parents a chance to see the curriculum in action. We thank you for your support and hope that your family enjoys challenging one another! We would love to hear from you about what you learn while you play.

Some games call for materials such as cards, dice, or coins. We will send home directions on how to modify a regular deck of cards to make it a math deck. We hope your family enjoys the challenge of math games.