I hope everyone has a fun April vacation!  When we get back we will focus on making sure we understand the math content we will need for fifth grade.  Our first math unit following vacation focuses on building understanding and skills of multi-digit multiplication.  We will review and practice multiplying by 10, 100, and 1000.  We will review and practice multiplying by multiples of 10.  We will practice using what we know about area to sketch a multiplication problem, we will use partial products to solve multiplication problems and we will try out the standard algorithm (they method that you and I learned) for multiplication.

We will represent multiplication of two-digit by two-digit numbers using what we know about finding the area of rectangles.  For example:  27 x 23

When using this area model we draw a rectangle and label the length and width with our factors written in expanded form.  We find the area of smaller rectangles within the larger rectangle and add them together.  This method leads very nicely into partial products.

We will move from the visual representation above to the more efficient method of using partial products.  For example:

When using partial products we have to remember place value.  The 2 in 27 represents 20.  Just like in the area model above, when you have a two-digit number multiplied by another two-digit number you will end up with four equations.  In fact, the four equations are exactly the same as the four smaller rectangles in the visual model above.

Both of these initial methods help us to understand place value and magnitude.  We begin to really comprehend just how fast numbers grow when multiplying big numbers.  Adding 50 + 50 brings us to 100.  Multiplying 50 x 50 brings us to 2500.  That is a much greater increase.  The visual model helps us to see the difference.  Partial products help us to focus on the place value and thus the magnitude of the numbers we are multiplying.

We will introduce the standard algorithm (they method that you and I learned) and will show how it connects to the visual model as well as with partial products.  We will also discuss the fact that the standard algorithm is efficient but not always the most efficient method for finding an answer.

By the time we are finished students will have been exposed to the standard algorithm for two-digit by two-digit multiplication.  They will be experts in multiplying using partial products for three-digit by two –digit numbers.  And finally, students will be able to apply multiplication in problem solving situations.  These skills, as well as memorizing multiplication facts, are what we will need to be ready for fifth grade multiplication. 

Inquiry is a very important part of our science curriculum.  When we are practicing our inquiry skills we begin by asking a question, we design an investigation to answer the question, we make a prediction, we collect and analyze data, we make observations and we finish by drawing a conclusion.  Right now we are working on a science unit that has a lot of opportunities for inquiry.

Our current science unit is about forces and motions.  The Vermont grade expectation is that “students will demonstrate their understanding of force by investigating and describing how different amounts of force can change the direction and speed of an object in motion.”  We have 3 ramp investigations during this unit.  The first investigates whether the length of a ramp effects the distance a ball will travel, the second investigates whether the height of a ramp effects the distance a ball will travel and the third investigates whether the mass of the ball effects the distance the ball will travel.  All three require us to control variables, run multiple trials, collect data, and draw conclusions.  It’s also really fun to play with balls and ramps.

This unit also includes a NECAP science practice task.  When we finish a NECAP science test each year we are allowed to keep the materials for the inquiry task.  We are also encouraged to use the materials to prepare for the NECAP science assessment.  Several years ago the fourth grade NECAP science assessment included a task about forces and motion.  We will conclude this unit by doing this task.  We have been practicing all of the steps, it will be our opportunity to show what we are able to do independently.

I will do my best to post pictures soon of one of our investigations. 

In science we have been studying weather.  Last week we made stop motion animation videos to show the results of research projects on weather fronts, air pressure, and clouds using iMotion on our iPads.  Enjoy!

Fractions!  Fractions! Fractions!  We just finished the first of two fraction units.  Fractions are by far the topic in math that people in our society have the most trouble with.  I think it is because when many people learned about fractions they memorized a series of processes without any meaning attached.  I know I learned to use prime factors to find common denominators.  I tossed around teams like LCM and LCD without knowing what they meant in terms of the size or the value of the fraction itself.  Fractions are a very important topic in fifth grade and, trust me, your children will start fifth grade with a solid foundation to build upon!

     In fourth grade we spend a lot of time modeling fractions focusing on the fact that a fraction is part of a whole.  We used egg cartons, rulers, clocks and number lines to illustrate the size and value of proper and improper fractions as well as mixed numbers.  We found the size of the whole if given a fractional part.  I used candy bars to illustrate the point that we don’t know the size of a fraction unless we know how big the whole is.

     In fourth grade one of the things we focus on is equivalent fractions. We use area models and number lines to reason about equivalence.  We see that the process of multiplying the numerator and denominator of a fraction by the same number corresponds physically to dividing each fraction into smaller equal pieces.   For example:

 

States of Matter Video by 4th Graders

My fourth grade students created this video to help a class of first grade students understand three states of matter.  I divided the class into three groups.  Each group created, practiced, and recorded a video.  I directed the introduction using students who recorded the other sections.  It is amazing what fourth graders can do.  Enjoy!

Using Devices

We have been practicing math facts using our netbooks and iPads!

Learning Multiplication

Multiplication is a major topic in fourth grade mathematics and we have been working hard to learn it.  Many parents wonder why we approach multiplication so differently now than when they were learning it.  Multiplicative reasoning is more than being able to multiply and divide.  It is learning to think in groups.  Multiplication and division strategies can be considered as falling within three levels.

Level 1 is making a picture and counting all of the quantities.  If we need to find the total number of wheels on 5 tricycles, we would draw the five tricycles, each having three wheels and count the wheels.  This level is generally used in second grade.  Level 2 is skip counting by a number such as for 3: 3; 6; 9; 12; 15; 18; 21; 24; 27; 30. The count-bys give the running total.  It can be hard to skip count by numbers that are high.  I know I can't count by 8's without already knowing multiplication facts.  At some point I would revert to counting by ones which is a level 1 strategy.  This level is generally used in the beginning of third grade. Between levels 1 and 3 you will find students repeatedly adding quantities to find an answer to a multiplication situation. These two levels have been left behind at this point in fourth grade.  By the end of third grade students are moving from skip counting to thinking of multiplication problems in an array.

Level 3 methods use the associative property or the distributive property to take numbers apart, multiply the parts and put them back together.  This strategy is what we work to solidify in fourth grade.  We do this by relating multiplication to finding the area of a rectangle.  See example below.

We move from using the diagrams like the one above to using partial products.  Our goal is for every fourth grade student to use partial products to multiply multi-digit numbers by the end of the year.  We will introduce the traditional algorithm before the end of the year and they are taught the traditional multiplication algorithm in fifth grade.

It is important that students have a deep understanding multiplication before they learn the traditional algorithm or they won’t learn to think in groups.  If students don’t fully develop multiplicative reasoning abilities they will have trouble understanding fractions and proportional reasoning in middle school, which will then impact their ability to understand algebra.  

For information go to -- http://commoncoretools.me/wp-content/uploads/2011/05/ccss_progression_cc_oa_k5_2011_05_302.pdf

I really enjoyed meeting with parents at our conferences.  Students learn best when they have a strong team of parents and teachers working together for them.  Parents, please feel free to contact Heidi or me any time you have a question or a concern.

We are finishing up our Animal Adaptations unit.  The weeks before and after Thanksgiving will be devoted to our final projects and activities.  Students will be designing their own animal by focusing on adaptations for survival.  This should result in some interesting animals!  Students will work in partners to make a poster and write paragraphs to picture, name and describe their animal and its adaptations.

In math we continue to build understanding and skills for multiplication.  Students should be working on memorizing multiplication facts.  If they have their facts memorized they will have more mental energy for solving more complex problems. 

On a final note, the fourth grades will be performing a skit about a bullying machine at an assembly on November 30th.  They will need a gray hooded sweatshirt.  If your child doesn't have one please let us know and we will provide one for them.  If your child has and extra gray hooded sweatshirt and is willing to share it, please send it in.

Enjoy your holiday!

Linda

Blog Alert!

Welcome to my first blog!  I hope this will help me to keep you informed about our work in math and science in fourth grade this year.

Math and science are my favorite subjects to teach!  I am the math teacher leader for the Hartford School District at the elementary level so you know math is important to me.  We finished our first unit in math which was all about developing a visual model to help understand multiplication and division.  Did you know that the dimensions of a rectangle and the area of a rectangle are the same as the factors and product in a multiplication problem?  We have also begun learning our multiplication facts.  My goal is for everyone to memorize these facts by the December break.  Our next math unit is about place value and multiplication of larger numbers.  We just got started.  Pretty soon your child will be able to show you how we use the area model to help us understand multiplication.

I love math but science is my other favorite!  I especially love the unit we are currently working on.  We began learning the inquiry process through activities using real animals.  We asked the question, "Do crayfish prefer to be alone or together?", made predictions based on our observations of the crayfish, set up a "fair test", gathered evidence and wrote a conclusion.  What do you think the answer is?  You can ask your student what our evidence showed.  Next we worked in small groups to ask a question about an animal that we found at the Dothan Brook.  We followed the inquiry process again with support from our peers.  We will be incorporating inquiry into science whenever possible.  We are currently studying animal adaptations.