Math

February 19, 2017

DIVISION

We are transitioning from our study of multiplication to the inverse operation of division. We are including a continuous look at related facts (previously referred to as "fact families") and problem solving.

There are two situations that may be described in word problems involving division:  sharing equally and grouping.  
  

When sharing, students will divide a number into a certain number of equal parts, determining how many in each group.

When grouping, students will divide a number in groups of a certain number, determining how many groups. 

 

We will continue to relate multiplication to division and use the multiplication facts that we have learned to check our new division skills.  For more practice at home try visiting:  freerice.com  

Story problems will become increasingly more difficult with more than one step. Some may include multiplication and others will include division, as well as addition and subtraction.  We are developing versatile problem solvers! 

For example:  

 Five boys went camping and fishing.  On the first, day the boys caught 15 fish for dinner.  On the second day, the boys caught three times the number of fish from the first day.  How many fish did they catch both days altogether?

First Day:  15 fish

Second Day:  15 x 3 = 45

Altogether:  15 + 45 = 60  

The boys caught 60 fish altogether on both days.  

How Does Your Garden Grow?

When a problem is presented to the students to design a garden based on arrays, then build the garden, here is what one math class designed and created!

 January 17, 2017

Multiplication Begins in January! 

We will start our study of multiplication this week!  All students will participate in concept building activities, as well as learn strategies for multiplication facts 0-12. Multiplication instruction will lead right into Division instruction after a few weeks. Knowing the multiplication and division facts with fluency will lead to the ease of learning division and fractions later.

The Reflex accounts are currently being switched from addition and subtraction to multiplication and division.  Your child's math teacher and/or homeroom teacher will let them know when to begin practicing.  Thank you for supporting your child at home as they continue to build multiplication fluency skills.




 December 9, 2016

We have completed our study of addition and subtraction, using up to 4-digit numbers to practice our skills, which include plenty of re-grouping situations.   

Games such as WIPEOUT help us to recall our basic number facts quickly. During this game, the roll of 2 number cubes indicates the number that can be removed from the board.  The quicker a student can add the digits, the more exciting the game becomes.  

 When we play 150 and OUT, students begin with the number 150, then roll the number cubes  to determine what number to subtract.  Students continue rolling and subtracting until someone reached 0.  This takes a great deal of organization, recording numbers properly, and subtracting properly in order to stay competitive in the game.   

We have also worked on addition and subtraction skills, including word problems and the importance of estimation through this month. It is important to use estimation to determine if an answer is reasonable?  How can you use rounding (before you add or subtract) to determine what a close estimate would be?

We'll also be thinking about how to use our computation skills when adding and subtracting money.

 

The students will develop the concept of making change from $1.00 and $5.00.  This will include working with money, manipulating, sorting, counting money and counting change.  In addition to manipulation of money, students will continue working on computation skills while adding and subtracting money, comparing amounts of money and pretending to spend money.  This would be a great time to talk to your child about saving money, helping with shopping trips to the grocery store, discussing how much items cost, etc…  Make time to take your child to the store and allow them to make a purchase with a $1.00 or $5.00 bill.  They could even compute the difference between the cost of the item and the $5.00 bill.  The difference is the amount of change that will be received. (These are important skills that are not often practiced without your support.  Make it a fun learning experience!)

 

 

COMPUTATION:  Addition and Subtraction

Students should be firming up their addition and subtraction fast facts!  The REFLEX program is a great way to do this.  (Students know their passwords!)  20 minutes per day (or several times each week, throughout the month of December) would greatly support your child's efficiency when working with larger numbers. You could also work on "flash cards" to build math fact fluency where your child needs to strengthen their knowledge.

We have reviewed the skills learned in 2nd grade- adding and subtracting 2 and 3-digit numbers, sometimes when it is necessary to regroup in the tens and hundreds.  From there, we have also introduced new strategies to support the actual concept of adding and subtracting. (For example: using the representational form or expanded form of a number, using a number line, rounding to estimate, and finally, using the "old-fashioned" algorithm with re-grouping.) The ultimate goal will be for students to comprehend and use the most efficient and accurate strategy to add and subtract large numbers.

  REVIEW place value and ordering numbers with this cool website!

http://www.oup.com.au/__data/assets/file/0019/154045/Numberline.swf

Oct. 9, 2016

Place Value and Rounding

We’ve been comparing numbers using the phrases greater than, less than, and equal to.  We’ve also been using the appropriate symbols to represent those phrases in our number comparisons. (<,  >,  =)  Which number is greatest:  4,590  or 4,750?  Which number is least:  1,399 or 1,939?  When comparing 4 digit numbers with the same digit in the thousands place, we might need to look at the value of the tens or hundreds place to determine which number is greatest or least.  We will also be comparing the value of the underlined digit.    When given two numbers such as 123, 560 and 23,561, we notice which underlined digit has the greater value.  Often students are tempted to choose the 6 because the 6, itself, has the greater value at a digit.  But when looking the place value, students with well-developed understanding of number know that the 1 in hundred-thousands place has a much greater value.  The next part of our unit involves estimation and rounding skills.  

  In order to use rounding numbers to become better estimators, we will be working on our rounding skills for the next week or so.  Students need to have the basic understanding that digits 0,1,2,3 and 4 will round down. In turn, digits 5,6,7,8 and 9 will round up. These reminders will help students recall that some numbers are "closer to" others on a number line.  When presented with larger numbers such as 125, students will be able to round to the nearest tens place or the nearest hundreds place. First they need to be able to identify the options for rounding.  125 to the nearest tens place would be 120 or 130 because those are the tens that fall to the left and the right on the number line.  125 would round to 130 because the 5 in the ones place rounds up.  When rounding to the hundreds place the options are 100 or 200.  Students will look to the 2 in the tens place to determine that 125 rounds down to 100.  We will continue to work on rounding to the thousands place as well. How can rounding help us estimate?  

  

An important part of our place value study focuses on the value of each digit in a number.   When understanding that each digit has a different value (or worth) depending on its place, students are able to identify the value of a digit up to the hundred thousands place, and even millions.

Next week we will begin practicing reading and writing up to 6-digit numbers. We will be exploring the different forms of recording numbers.  Standard form is the number written in digits, such as 3,952.  Written form is the number represented in words. For example:  Three thousand, nine hundred fifty-two.  Expanded form is a number represented in a series, including the value of each digit.   For example:  3,000 + 900 + 50 + 2.  Representational form is when a number is represented by base 10 blocks.  There is an example in this week's homework.

 

We will play a fun game called "I have.... Who has?"  This is a great way to practice reading and recognizing numbers in various forms.  For example:  "I have 3, 576.  Who has Ninety-nine thousand, forty-five?"  "I have 99,045.  Who has Seventy thousand, one hundred sixty-seven?"  And so on.... This game doesn't always work out correctly the first time.  But if we listen carefully and we read the numbers carefully, it should work out successfully.

Place Value

We began our place value unit with a pre-assessment to determine prior knowledge and mastery of place value skills from second grade.  During this 3-week unit, students have been reviewing place value through thousands (as represented by base-10 blocks) and increase their understanding of 4-6 digit numbers through the hundred thousands place.  Students are learning to:  represent numbers, identify the value of digits as determined by their place.  Can you rearrange your digits to create a larger number? What is a digit?  What is the difference between a digit and a number? Can you read a 4-digit number?  5-digit? 6-digit?

Saturday, Sept. 3, 2016

Data and Graphing

     In math, we will be creating and interpreting bar graphs and line plots.  Students are learning to study the data collected to interpret a graph. We will also review picture graphs and pictographs.  Some icons found on these graphs will represent more than one.  Students will need to be proficient in counting by 2’s, 5’s, 10’s as they interpret this type of graph. Look around for graphs in your home, in the newspaper, online, etc. Discuss the purpose of a graph in daily life.  Surveys and data collection often accompany graphs. 

     Throughout the first quarter, we will be reviewing time and reading clocks to the hour, half hour, quarter hour and minute. Students have been practicing reading the analog clock in our classroom throughout the school day for an authentic use of clock-reading.  They also match analog clock times to digital clock times.  Another way to develop a sense of time is to vary the language we use when discussing time.  Try including phrases such as "quarter after" and "half past" or "quarter 'til" the hour.  When discussing family events, consider pulling out a calendar and include the children in conversations about days, weeks, months and years.  We will continue working on naming the months of the year in order.  You might check to see if your child has mastered this skill yet.