This week we reviewed many of the concepts we learned this year and took an assessment.  We are currently working on time and money which we will continue with for the rest of the year. 

This week our focus has been on all aspects of time! We are working hard at telling time using analog clocks.  Watches for 1st and 2nd graders are always great gifts...

We are currently working on counting money and making change.  We are adding some exciting new items (Poke'mon trading cards) to the class store that will motivate a lot of Mustangs to save money (they will be expensive). 

This week we added three digit numbers using Base 10 blocks! 

This week the Black Bats (Kindergarten) shared with us the data they collected about how healthy our lunches are.  Our class did not win their healthy eating contest but we determined that we eat really healthy! 

We have finished our Coins, Coupons and Combinations and will be moving on to Putting Together and Taking Apart. 

Here is a review of concepts we investigated: 

Investigation 1: 10's and Doubles

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  How do students figure out pairs that make 10's and doubles?


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  How do student record their strategies for solving problmes?


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  How do students add two or more numbers?  Do they use materials?


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  Calculator skills

Investigation 2:  Grouping by 2's, 5's and 10's

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  How do students count? Do they keep track of the objects they have counted?


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  How do students group objects?


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  When students are counting by 5's do they recognize any patterns? 


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  How do student record and keep track when counting large groups?


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  How familar are students with coin equivalentcies? 

Investigation 3: Introducing Additon and Subtraction Situations

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  What stategies do students have for modeling + and - situations?


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  Do students solve problems using numerical reasoning?


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  How aware are student s of the relationships between + and -?

Investigation 4: One Hundred

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  How comfortable are students with 100 as a quantity? 


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  Are students able to use the 100 chart as a tool for combining and comparing numbers?


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  What stategies are student using to solve addtion problems? 

"Key Words": A Misleading Strategy

Many of us learned to solve addition and subtraction story problems by using the "key words" technique.  The "key word" technique is when students are taught to recognize words in a problem that provide clues about how to choose which operation to use to solve the problem.  For example, altogether or more signal addition, whereas left or fewer signal subtraction: 

1 have 5 marbles.  Sue gave me 6 more.  How many do I have altogether?

I have 16 mables.  I gave away 8.  How many do I have left?

I have 16 marbles.  Sue has 7 fewer than I do.  How many marbles does Sue have?

There are two serious flaws in the key word approach.  First, these words may be used in many ways.  They might be part of a problem that requires a different operation from the expected one: 

There are 28 students in our class  altogether.  There are 13 boys.  How many girls? 

If we trust in key words, then altogether in this problem should signal addition of the numbers in the problem:  28+13, whereas the problem actually calls for finding the difference between 28 and 13. 

The second reason for avoiding reliance on key words is that we want student sot think through the entire structure of the problem.  They need to read the problem and understand the situation so that they can construct a model of the problem for themselves. 

If student are encourage to use key words, they are likely to pull numbers out of the problem and carry out some operation without developing  a model of the whole problem. 

Making Sense of Addition and Subtraction

Students solve a variety of story problems involving combing and separating, using their own strategies.  Their job is to solve each problem, check their solutions and clearly record their approaches.  As a whole class we discussed the relationship between addition and subtractions situations. Their work focused on: 

• modeling problem situations
• selecting appropriate strategies for different problem structures
• recording strategies
• interpreting standard notation for addition and subtracting
• considering the relationship between addition and subtraction. 

We had some very creative story problems!  We will continue Making Sense of Addition and Subtraction next week.  We are still working with money daily.  Students continue to earn money for their daily jobs and  they have the opportunity to visit the class store once a week.  I can see a huge  amount of growth in the whole class.  We are counting money, understanding how to make change and keeping track of money.  It is exciting to watch how quickly they are learning money concepts by using this real world/ hands on approach vs. worksheets.  Work with money (coins) over spring break! 

We continue to get paid for doing our jobs to the best of our ability each day at school.  This has been an incredibly successful way to introduce and expand on the concept of money.  This week as we work daily with money students are:

• becoming familiar with coin values
• finding all possible combinations of coins to equal different amounts
• matching coin combinations to cents notation 

This week we focused on Basic Addition Fact Rules to help with math fact learning! Next week will be investigating Number Strings. 

Rules we learned: 

Adding Zero:  Once students understand that adding zero truly means adding nother, then they will never get any basci fact about adding zero wrong. 

Adding One or Counting Up:  This involves moving on to the next number.  Children tend to count the first number then the next, making them confused and incorrect.  Make sure they never recount the starting number when demonstrating and correct students immdiately. 

Adding two:  Once students comprehend adding one, well next is adding two!  Do not skip count by two's intially.  This will ensure students understand that they must count up tow times. 

Commutative Poperty:  Students also need to understand that in addition, switching the numbers around does not change the sum.  Order does not matter in additon. 

Adding Ten:  this means students must understand the pattern of increasing numbers in the Tens Place Value chart.  On the hundreds chart we learn that moving directly down a row is adding 10. 

Adding Nine:  Yes this should be next.  Once students understand the strategy of adding ten, then you can ask them to add ten and name the number that comes before. 

Adding Eight:  This can be taught right after adding nine!  It is the same concept, and same strategy.  Except students need to cound down two numbers. 

Our new investigation is called Coins, Coupons and Combinations!  The focus of this unit is on helping students develop a sense of numbers as whole quantities and to begin to look for patterns and relationships that exist in our number system.  We are also working with money daily as students get paid for their jobs.  They have the opportunity to visit our class store every Friday.  Many students are saving their money to buy some of the pricier items in our store!  I love the willpower to save!  We continue with our Math Fact study.  We study our facts throughout the week and take a one minute test on Fridays.  We set individual goals and try to achieve those goals.  We graph our scores and levels. 

We are working with money!  Earning it, counting it, exchanging it, making change, saving it and spending it! The class store is a great success!

What didn't we do in Math this week?!  We were busy focusing on math facts, setting goals and working with money.  I started paying students (with fake money) for their jobs this week.  We will be focusing on coin recognition, counting coins, exchanging and  making change.  We created a class store filled with  real items that they can purchase with the money they earn.  They must do their job to the best of their ability, plan to save or spend their money and keep good records of how much money they have.  The Mustangs will have the opportunity to visit the store each Friday. 

We are gearing up to start our Math Fact Fluency practice and assessing next week.  We have talked about the importance of becoming fluent with our math facts just like we are with our sight words.  We will start with addition and set individual goals.  We will move on to subtraction once each individual student reaches their addtion goal.  We will have a timed math fact test every Friday starting with 0 and moving through the numbers to 10.  Students will keep track of their own progress. 

We are also working on goal setting in all areas of our curriculum. 

The process of setting goals allows students to choose where they want to go in school and what they want to achieve. By knowing what they want to achieve, they know what they have to concentrate on and improve. Goal setting gives students long-term vision and short-term motivation.

Having sharp, clearly defined goals, which students can measure, will allow them to take pride in accomplishing those goals. They can see clear forward progress in what might have seemed a long drawn out process.

By setting goals students can:

1.improve their academic performance

2.increase their motivation to achieve

3.increase pride and satisfaction in performance

4.improve their self-confidence

Now wouldn’t you like to see your students become better believers of their academic abilities? And remember, goal setting is an ongoing process which can (and should) be done all throughout the school year.

We are also starting our Class Store.  We will earn money for our daily classroom jobs. If students put excellent effort in their daily job they will be paid at the end of every day.  They will keep track of their money by recording it.  Twice a month students will be able to spend their money at our very own class store.  This is a real and exciting way to learn about money and making change. 

Math things to do at home over break...

• practice math facts
• practice counting coins
• skip count 2's, 5's and 10's
• write story problems for someone at home to solve
• make a hundred's chart
• measure things in your house
• create a real life story problem using toys, animals, people...

Math this week we solved some more story problems.  At the 1st and 2nd grade level, there are many interrelated objectives that we keep in mind when solving story problems. 

• Understanding the various meanings of the four operations.  It is primarily through story problems that children will gain a full understanding of which operation to use in any given situation. 
• Development of number skills and concepts.  As students solve problems, they are forced to deal with then numbers involved.  Initially, they will use immature counting techniques.  Later these techniques will give rise to more efficient skills and eventually will provide the foundation for mastery of basic facts. 
• Computational fluency.  Related to their number skills are the many different methods that students will develop for computing.  Place-value ideas will be enhanced and utilized as students find new and better ways to break numbers apart and combine them.  The structure of the the problem can significantly influence the way students compute. 

This broad array of goals suggest that there is much more to story problems than simply having students get answers.  We want them to develop number skills and computational techniques as well as to have a rich understanding of the operations. 

In our Math Workshop I believe that most, if not all, important mathematics concepts and procedures can best be taught through problem solving (problem-based tasks).  A problem is defined as any task or activity for which the students have not prescribed or memorized rules or methods, nor it there a perception by students that there is a specific correct solution method.  A problem for learning mathematics also has these features: 

• The problem must begin where the students are. 
• The problematic or engaging aspect of the problem must be due to the mathematics that the students are to learn. 
• The problem must require justifications and explanations for answers and methods. 

We have been problem solving this week.  We are also talking about our learning and soon we hope to be writing about our math learning. 

We had fun this week eploring with math manipulatives, practicing our math facts and skip counting.  We focused on solving word problems.  We are learning to read word problems to find out what we need to do to solve the problem.  We are learning that word problems can be fun! 

How to help at home...

practice skip counting, math facts and coin recognition!

First graders this week have been working on finding combinations of numbers.  We have also focused on how to show our work  using pictures, numbers and words as well as finding more than one solution to a problem.  For second grade Math this week has been part review and part learning how read directions and word problems.  We have been reviewing math facts and learning how to solve problems that are written in different ways.  We also have started talking about the importance of taking the time to read a problem so we know what they are asking us to do. 

  We played number Top it and addition and subtraction Top it!  This is just another way to practice math facts.  Some students are working on number recognition and some are adding and subtracting two and three digit numbers.  We also continue with our Investigations curriculum and worked with Mystery Photos.  With this investigation our work focuses on: 

• identifying places where numbers appear
• counting a set of objects
• combining two groups of objects
• recording a strategy for combining two numbers

Next week we will continue focusing on number combinations. 

Ways to help at home:  

• play card games
• coin identification and counting
• math fact practice (be creative)
• exposure to time and clocks
• make a paper clock to keep at home
• exposure to temperature/themometers
• cooking and measuring in the kitchen
• non standard measurement with items around the house
• cutting numbers out of the newspaper
• counting items around the house (count by 10's, 5's, 2's...)
• sorting/classifying
• playing store
• solving problems written different ways
• take turns telling/make up word problems (keeping it simple)

These are just a few ideas please let me know if you need more. 

We had “Choice time” to explore new and previously learned games.  We played “Turn over Ten”, which is a combination of memory and “10 Go Fish”.  The students were challenged to create combinations of exactly ten by turning over cards in a grid of 12.  If the sum was greater than 10, all cards had to be turned back over.  It brought up the important distinction between putting 2 digits together to make a number and adding two numbers to find a sum.  These games reinforce the important skills of adding in our head and ordering numbers.  Another choice was to explore bar graphs in deciding how to chart student height in the class.

We incorporated “Magic Number Math” in morning meeting.  The magic number was 38 and we did a great job of finding this number through addition, subtraction and multiplication!

We learned a new card game this week to reinforce our understanding of number relationships and basic addition.  "10 Go Fish" challenged students to create various combinations of numbers that add up to 10.  It is played with the same rules and framework as Go Fish.

We also began work on a class height chart so that we can track our growth over the school year.  We started out by investigating units of measurement and deciding the best units for measuring various things around the room.  We decided that to measure ourselves, a combination of feet AND inches would give the most accurate answer.  With the help of partners, each student marked their height on our wall.  Next week, we will record all of the heights on a large chart, which we will keep updated all year long!

We continued with our “magic math” journaling this week.  The “magic number” of any given day is the number of days we’ve been in school.  The mustangs are reinforcing their understanding of number relationships as they look for ways to count up to or subtract to get to the magic number. We track this number each day by adding counting straws to our calendar.  There are pouches for ones, tens and hundreds to help students visualize base 10 number relationships.  As soon as we tally 10 “ones” straws we bundle them up (singing our bundle song!) and exchange them for a tens straw!  This week marked a special benchmark; we have had over 30 days of school!  Our tens pocket is filling up fast!

We are finding great ways to sneak math in to almost everything we do!  The Mustangs love to think about number relationships and have so much fun creating and solving real-world story problems.  For example, in The Trumpet of the Swan, our protagonist Louis starts earning money as a Trumpeter at the Boston Public Garden.  The kids used sneaky tricks like counting by fives and adding zeros to find out how much Louis would earn in total at $500 a week for 10 weeks!  

We learned a fun new game in math called “compare”.  It is a partner game in which each player starts with half a deck of cards.  Each player turns over a card and whoever has the LARGER number says “me!” and collects both cards.  Some students played DOUBLE compare which requires players to turn over two cards and find which SUM is larger.  A couple of brave mathematicians even played triple compare!

We also explored the characteristics of the number 10 by finding out all the ways to build or add up to 10 using the counting blocks.  We were learning a lot of addition patterns.  One student built a staircase and learned that 1+2+3+4 adds up to ten, others used the blocks to investigate grouping numbers to simulate multiplication.  Later in the week, we continued with our number investigations by focusing on a daily "magic number".  The magic number is the number of school days we've had!  For example, we worked on all the ways to build 22.  We found ways to add numbers to reach 22, subtract numbers to get 22, and even multiply to reach 22!

This week, we wrapped up important assessment work in our math class!  I worked with each student to check their recognition of the numbers 1-20 as well as how they write these numbers.  Each student also worked to recognize and answer single digit addition and subtraction problems.  

First grade spent one math class practicing writing our numbers.  We all need plenty of practice writing our numbers to make sure our "3"s, "5"s and "7"s open in the right direction! We also had a chance to explore more of our math manipulatives.  It was great to see students using the manipulatives as tools rather than just as toys.  Everyone in the class had the opportunity to create a story problem featuring either addition or subtraction with the help of some of the manipulatives.  Counting bears, block animals and toy money all brought their story problems to life!  Students were learning about number relationships and the language of numbers.  I heard great discoveries and thinking such as this:

"Counting by 100's is actually easy!  It's just like adding ones but with extra zeros!" (with the help of the play money)

"I made a subtraction problem!  I have 5 animals at my zoo, but three go away.  How many do I have left?  Two!"

This week, we explored the amazing math tools in our classroom through a few math exploration stations.  I was amazed at the insights students came up with after spending time with the manipulatives and fun math books.  Students discovered, for example, that patterns can come in many shapes and sizes.  We could make a repeating pattern using just two colors or more than 15 different colors!  We also learned about the importance of equal measurements and ratios when building.  We learned that we can combine shapes to create new shapes, even replicating the complex shapes of animals, cars or other things in our world.

I conducted a math assessment with all students to get a snapshot of their familiarity with writing and recognizing numbers 1-20 as well as simple addition and subtraction.

In preparation for a big project, we decided to practice thinking and acting like scientists while asking important questions about our local environment.  We decided to answer the question: Is it important to wash your hands?  We decided to test the effects of handwashing on a piece of apple.  We passed around one piece of apple right after snack and recess and then passed around a second piece of apple after washing our hands thoroughly! We placed each piece in it's own labelled jar.

We are tracking the changes in both jars each day.  See above for a YUCKY picture of the two jars.  Can you guess which one was passed around by unwashed hands?  This is helping all of us to remember to wash our hands often each day to prevent the spread of germs!

We spent the week in math creating some illustrative charts and graphs to learn about each other.  These projects help us use numbers to describe the world around us!

We created a "Tooth Chart" to track teeth lost during the school year.  We are also building a "Pet Graph" to help us understand the types of animals in our families.  Dogs and cats, snakes and salamanders, and even goats and pigs are an important part of our lives.  We decided to create a bar graph to count up all of our furry (or not so furry) friends.