Math Curriculum
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Measurement We have been working informally with measurement all year... especially when discussing area and perimeter of polygons, but also with fractions (recipes, time intervals, real-world problems, angles)...  but we are now working on our Measurement Unit.   We began by introducing the differences between the US Customary System (inches, feet, yards, miles, ounces, gallons, etc.) versus the Metric System (centimeters, meters, kilometers, liters, etc.)  While we are far more used to our own conversions:   12 inches = 1 foot;   3 feet = 1 yard;  36 inches = 1 yard; 5,280 feet = 1 mile;  we had to agree that working in metrics is much more aligned with our Base 10 system....  10 millimeters = 1 centimeter,  10 centimeters = 1 decimeter,  100 centimeters = 1 meter, 1000 millimeters = 1 meter. We are using rulers and meter sticks to measure widths and lengths of desks, boards, walls, etc. and then discussing how we find perimeter and area of these items.  If a polygon has 4 sides, we need to add the length of the 4 sides to establish perimeter, etc. We are also using critical thinking to understand that 1 inch is a more accurate measurement for a paper clip than 1 yard or 1 mile.   We will continue using measurement and conversions of measurements with temperatures, weights, time, and many other real-world situations.  When the nice weather is finally here to stay, we will use meter sticks and some pre-planning to measure the length and width of our school building and determine the perimeter and area of our own "home away from home!"
Posted by ghawkins  On Apr 26, 2016 at 6:43 PM 746 Comments
Multiplication -  groups of items ...  how many times more something is than something else Multiplication can be shown in different ways: 1. 6 X 4 2. 6 * 4 3. (6)(4) All of these are read as "Six times Four"  or "Six groups of Four" As students get older, the "X" is not commonly used for multiplication, as it also will represent a variable, "X" Why is multiplication and knowing our facts so IMPORTANT? A huge part of the fourth grade math standards is for students to be able to fluently do multi-digit multiplication and long division using different algorithms (methods).  This is necessary as problem solving depends on these calculations, and students will need to know how to manipulate whole numbers and fractions. We have recently made goals for ourselves on our Math Computations... and we have written strategies to use to help us succeed.  Most students said they needed to practice their multiplication facts, as they do not know them fluently as of now.  Please support your student in this.... 5 - 10 minutes a day is all it takes to become masters of multiplication facts. In school, we will use arrays, groups of items, and the area model to assist us in learning our facts, as well as making multiplication books, and flash cards.  To have a set at home, students can make their own flash cards from just paper....have them write the fact on the front, with the answer on the back.  Then each student can practice by him/herself, even when no one is available to practice with him/her.  Look back soon for the strategies we are using to understand multi-digit multiplication!!
Posted by ghawkins  On Nov 01, 2015 at 4:32 PM 1056 Comments
Steps to Rounding Numbers 1. Underline the digit in the place you are rounding. 2. Draw an arrow to the digit in the place to the right of the underlined digit. 3. If the number that the arrow is pointing to is: 0 - 4  -  Leave the underlined digit as it is 5 - 9  -  Add 1 to the underlined digit 4.  All digits to the right of the underlined digit become 0's. 5.   All digits to the left of the underlined digit stay as they are.
Posted by ghawkins  On Sep 29, 2015 at 6:03 PM 1300 Comments
Place Value We can define place value by using the definitions of each word...  place means "where" something is and value means its "worth." Therefore, place value is simply deciding the worth of a digit depending on where it is in a number. If the digit 5 is in the ones place, it is worth 5 ones, or simply 5. If the same digit 5 is in the tens place, it is worth 5 tens, or 50. 5 -  this 5 is worth 5 56 - this 5 is worth 50 In our base ten system, a digit is worth 10 times the same digit one place to the right. In the number 176, 543 the digits are in the following places: 3 - ones place 4 - tens place 5 - hundreds place 6 - thousands place 7 - ten thousands place 1 - hundred thousands place Therefore their place values are as follows: 3 -  3 4 -  40 5 -  500 6 -  6,000 7 -  70,000 1  -  100,000 Number Forms Numbers can be written in different forms, and all still mean the same thing:   Standard Form:  This is the number written in its place value 573,629 Expanded Form:  This is the number written with each place represented individually 500,000 + 70,000 + 3,000 + 600 + 20 + 9 Word Form:  This is the number written in words, just as you would say the number when reading it Five hundred seventy-three thousand, six hundred twenty - nine Posted by ghawkins at 6:42 PM    
Posted by ghawkins  On Sep 20, 2015 at 7:00 PM 1075 Comments
We have started our Dream House projects in class....these projects incorporate using area, perimeter, multiplication, measurement, and money to create a blueprint of a "Dream House" with a budget of $1,000,000 for the materials for the walls, floors, and ceilings.  There is much excitement about this project, and the end result is a fun, real-life application of some very critical 4th grade math standards!  We are also going to be learning about how to use protractors to measure angles, and we will review the basic building blocks of Geometry....points, lines, segments, rays, angles, and both 2-dimensional and 3-dimensional shapes.  None of Geometry makes any sense if we don't understand the basic units of measurement in both the U.S. Customary System (inches, feet, yards, ounces, gallons, etc.) and the Metric System (centimeters, meters, kilometers, litres, etc.)  We have already used these to measure our classroom and items contained within, and will now be dealing with conversions in both systems.  For example:  1 yard = 3 feet, so 5 yards = 15 feet.  Last, but certainly not least, we will be emphasizing a review of all the standards we have learned this year.... applying them to real-world situations and discussing different strategies.  The fourth grade has worked so hard in all the math standards this year... and we are not letting up now!  Fractions, whole numbers, decimals, percents....  and using them with all four operations - adding, subtracting, multiplying, and dividing.  We are ready for whatever comes our way!!!
Posted by ghawkins  On Apr 26, 2015 at 12:34 PM 955 Comments
After much time spent on understanding the value of proper and improper fractions, how to compare them by making equivalent fractions, solving word problems that use fractions, whole numbers, and mixed numbers, and placing them on various number lines, we are ready to begin looking at how fractions, decimals and percentages are the same. We have started looking at decimals in our place value system: 123,456.789 is read as one hundred twenty-three thousand, four hundred fifty-six AND seven hundred eighty-nine thousandths The decimal point separates the whole number from the "part of the whole" or fraction of a whole.  The place value after the decimal is known as the tenths place, the hundredths place, and the thousandths place.  Therefore,  .5 is read as 5 / 10 or five tenths.  We will spend our time learning to use decimals and percentages in real world problems, just as we did with fractions.
Posted by ghawkins  On Apr 05, 2015 at 2:34 PM 1170 Comments
We have begun our work with fractions.  Fractions are equal parts of an equal whole, and are written as a/b,  where a is the numerator and b is the denominator.  The numerator represent the number of equal parts that we have, and the denominator represents the equal number of parts in the whole. So, 6/7 means that we have 6 equal parts out of the 7 equal parts in the whole.  A unit fraction is the smallest part of the whole, or 1 part of the whole.  Therefore, all unit fractions are represented with 1 as the numerator.  1/10 is the unit fraction of tenths, while 1/5 is the unit fraction of fifths. Fractions can be decomposed into their unit fractions, such that: 6/7 = 1/7 + 1/7 + 1/7 + 1/7 + 1/7 +1/7 We can also make "equivalent fractions."  Equivalent fractions are equal to each other, even though they have different wholes.  For example, 1/2 is equivalent to 2/4 because they both take up the same amount of space, or both equal the same amount of their "whole."   1/2 is 1 out of 2 equal parts and 2/4 is 2 out of 4 equal parts.  If one cuts a rectangle into two equal parts, and the same size rectangle into four equal parts, 1 part out of 2 will be the same size as 2 parts out of 4. Fractions are integral in all we do in the real world.  Imagine recipes that only used whole amounts of items.... we would need 1 cup of sugar, even if the recipe only called for 1/3 cup.  Think of building a fence if we could only have it in equal segments of 1 yard. 
Posted by ghawkins  On Feb 22, 2015 at 5:26 PM 776 Comments
Math Updates We are moving ahead with our Unit on solving word problems by writing situation and solution equations. A situation equation is one where you use numbers and letters to represent exactly what the word problem says.... not necessarily the final equation to solve it.   For instance,  if the Word Problem says: Sam started his stamp collection with 150 stamps from his dad.  His brother gave him some more stamps, and now he has 175 stamps in all.  How many stamps did his brother give Sam? The situation equation, using s for the number of stamps his brother gave him, is: 150 + s = 175 Then, we would use this information to create a solution equation, or one that actually can give us the answer we are looking for: s = 175 - 150 s = 25 So, Sam's brother gave him 25 stamps. A family letter that gives examples of what we are doing throughout this unit was sent home in English and Spanish last week.  We will also continue to put example in our Learning Logs, so please make sure that your student shows you his/her Math Learning Log every day!!
Posted by ghawkins  On Jan 11, 2015 at 5:18 PM 3061 Comments
We are well into Unit 3 of our Math Expressions Program and you should have received the Family Letter that modeled the three methods of Long Division that we are learning.... Place Value Sections Model (the inverse of the Area Model of Multiplication), Expanded Notation (or Partial Products) and Digit by Digit (Traditional Algorithm).  Just as in multiplication, we are introducing all three models and the students are welcome to use any of the three to solve the division problems.  There are many, many examples of all three methods in our Math Learning Logs... please ask you student to bring the Learning Log home every day so you can review these methods, as they may be very unfamiliar to you. We are also spending time on Word Problems, especially those reliant on Division and what to do with Remainders.  Remainders can be written as fractions, needed to be rounded up, or dropped off the problem.  Ask your student to show you examples of each.  We will also be continually reviewing Multiplication and Place Value throughout the year, and homework will likely be concerning these concepts and addition/subtraction.  As we move forward, we do not want to forget all that we have mastered!  In our Math centers, students are using Symphony Math (on-line program), working with Mrs. Hawkins or another teacher and/or volunteer, doing vocabulary exercises, reviewing with the Number of the Day, or learning a new Geometry/Measurement skill.  Some students also do word problem practice in these centers! As you can see, we keep very busy in our Math class!!
Posted by ghawkins  On Dec 07, 2014 at 10:21 PM 854 Comments
November 3, 2014 November is beginning with a bang!   We are starting our pilot of an exciting On-line Math Instructional Tool called Symphony Math.  This program, like Lexia in ELA, gives every student a "placement test" when he/she logs in the first time.  Using this information, the program then places the students at their correct level for instruction and practice, which they continue every time they log on to the website.  I will be sending home login information, in case you want your child to spend extra time at home on this program... it is a wonderful way for the students to receive extra instruction and practice at their own level, and since it is fun and engaging, they want to go back for more!  We will be using this as one of our centers every day and I am so excited for everyone to begin!! Word Problems:  It is a bit strange telling families that we are working on "Steps to Word Problems," since every day, we are confronted with "word problems" in every aspect of our lives.  Last week, we used acting out a little skit that I had created so that the students would believe that any problem in the world, not just Math Word Problems, can be solved with four simple steps: 1.  Understand the Problem  (What exactly do we know, what exactly are we trying to solve for?) 2.  Make a Plan:  (Find a Math, it may be drawing a picture, making an equation, creating a graph,      table, chart, or using manipulatives, etc!) 3.  Do the Plan:  Once you have decided what you are going to use.... Use it! 4.  Check your Answer:  Does it make sense?  Does is solve the problem reasonably?  If not, go back to # 2 and     Make a New Plan!! I was so impressed with the homework that was returned and the In-class work on some complex, multi-step word problems.  We definitely have many critical thinkers in Rm. 20 and Rm. 23!!!  I have really enjoyed listening to the various strategies that the students are using...  make sure to ask your student about the steps to solving problems and why they work on any problem in the world :)
Posted by ghawkins  On Nov 02, 2014 at 6:25 PM 1173 Comments
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