Visualizing Rounding with Vertical Number Lines and Midpoints

In third grade, your student used place value understanding to round whole numbers to the nearest 10 or 100.

Fourth graders are expected to round multi-digit numbers from 1-1,000,000 to any place.

Here's how we rounded 399,499 to the nearest thousand using a vertical number line and finding/comparing the number we were rounding to the midpoint:

To use a vertical number line to round our number, first, we thought about how many thousands our number has (399 thousands) since we are rounding to the nearest thousand.   We labeled the endpoint on the bottom.  Then, since we are rounding to the nearest thousand, we thought of the number that is 1 thousand more than 399 thousands, which is 400 thousands and labeled the other endpoint on the number line.  Our number is somewhere between these numbers.

To find the midpoint, some students found it helpful to remember that since we're rounding to the nearest thousand, the difference between how many thousands our number has (399 thousands) and the number that's 1,000 more (400,000) is 1 thousand (or 10 hundreds).  The midpoint splits those 10 hundreds into 5 hundreds and 5 hundreds, so, this means the midpoint would be 399 thousands 5 hundreds, or 399,500.

Next, we placed the number we are rounding (399,499) on the number line.

Since we can see that the number we are rounding is less than half-way, it is closer to 399,000.

So, 399,499 rounded to the nearest thousand is 399,000

This week in class (briefly) and for home learning over the next several weeks, your student will practice rounding four-digit numbers to the nearest thousand, hundred, and ten.  We'll gradually practice rounding five and six-digit numbers to the nearest ten and hundred thousand as well.

Why bother with a vertical number line?  It visually reinforces what is happening when we round numbers--we are looking for the closest number to the number we are rounding, and visualizing greatly helps most learners retain what they are learning.  What students remember they will be able to apply in solving real-life problems!

Adding and Subtracting Fluently Using Standard Algorithms

In third grade, your student added and subtracted within one thousand using strategies based on place value.  This year, we have learned that successful problem-solvers look for shortcuts and are always working toward the most efficient strategy to solve a problem.  Fourth graders are expected to add and subtract fluently (numbers through one million) using standard algorithms.

What are standard algorithms?  They are a processes or steps that when followed correctly in a given situation, will always allow you to arrive at the correct answer.  Translation: it's the way we learned to add and subtract numbers vertically with "borrowing" and "carrying" (which we now call regrouping/renaming).

HOORAY!  Well, at least that would be how I would feel if I was was the parent of a fourth grade Math student.  Finally something you know how to do that isn't taught differently!

Here's the catch--students need to understand what's going on with place value when using these algorithms (as opposed to just crossing out numbers and making them one less, then making the number to the right ten more).  Here's a sample of a think-aloud I will model in class:

Instead of teaching the addition and subtraction algorithms in isolation, I will teach the addition algorithm through using it to check subtraction, as an inverse operation.

So, the think aloud for using the standard addition algorithm to check the subtraction in the example above would sound something like this:

8 ones and 4 ones is 12 ones.  12 ones is 1 ten 2 ones.

8 tens and 4 tens is 12 tens, plus 1 ten from regrouping is 13 tens.  13 tens is 1 hundred 3 tens.

5 hundreds and 5 hundreds is 10 hundreds, plus 1 hundred from regrouping is 11 hundreds.  11 hundreds is 1 thousand 1 hundred.

1 thousand plus 1 thousand from regrouping is 2 thousands.

So, my sum is 2,132, which is the same as the minuend in the subtraction problem, which means I subtracted correctly.

  2,132     minuend
- 1,584     subtrahend
     548     difference (addend when checking with addition)
+1,584     addend
  2,132     sum

We Have the Power to Transform Matter!

Happy Fall!

I firmly believe in making learning enjoyable and connected to the real world, even though we are a "testing grade".  Yesterday, we made "school-made" applesauce in a slow-cooker.  Little did I know that this fun Fall activity would lend itself so well to introducing so many science concepts!

Wednesday was the Autumnal Equinox (first day of Fall), so we discussed Earth's movement (rotation and revolution) in relation to seasons.  Apples are in season during Fall, and I love food, so this lead to a conversation about matter--we observed both qualitative properties (color, form, state, sinks/floats in water, magnetic/not magnetic, reacts to acids [vinegar]) and quantitative properties (I reviewed using a balance to measure mass) of an apple.

Thank you to all the parents who sent in these beautiful, delicious apples!

Then we talked about energy's role in changing the form (shape) of apples when our bodies transfer potential energy from the food we eat to kinetic energy used to cut the apples,

Thank you, Mr. Drugg, for helping cut apples!

and how the transfer of electrical energy to thermal energy changed solid apples to liquid applesauce.

I am even looking forward to future Math connections to this activity, such as when we learn to measure angles later this year and recall that Earth's axis tilts 23 degrees, or when we learn to use multiplication to convert measurement units (pounds to ounces).

8:00 Thursday

9:30 Thursday

11:00 Thursday (right before I made it nice and smooth with my immersion blender)

After chilling the applesauce overnight, we enjoyed it today with a sprinkle of cinnamon.

(I forgot to snap a picture before we devoured our treat today!)

We even integrated Language Arts!  I introduced haiku poetry, and while we lined up for transitions, both classes composed haiku poems about Fall.  Haiku poems originated in Japan and are 3 lines: 5, 7, and 5 syllables per line, and rarely rhyme.

Fall Haiku 

By: Ms. Kirkham's Homeroom

Summer into Fall
Leaves are so cool and awesome
Leaves are red and brown

Fall Haiku

By: Mrs. Remley's Homeroom

Fall is not scary
Fall, Fall, wind, breeze, trees, grass, leaves
(Can you think of a 5-syllable line to finish our poem?  :-))

What do you enjoy most about Fall?  

I love the colors!  I remember the first time we visited my husband's family in Virginia during Fall.  I was amazed at all the colors of the leaves; he was so embarrassed when I asked him to stop the car so I could get out and take pictures of trees in peoples' yards!  He also thought I was crazy for wanting to rake leaves (I did it to be able to jump in the pile of leaves, of course!  :-)).

Calling All Gamers!

Lately we've been learning how to read and write numbers in standard, word, and expanded form.  We've also been comparing numbers.  Do you play video games or games on a phone?  Take a moment to brag comment below--tell your favorite game, your highest score (in standard form) and how you would read that number.  If you're really proud of yourself, compare your score to someone else's using comparison symbols (< = >), then use words to write your comparison statement ho you would read it.  And if you really want to rub it in, you can even tell how many more points your score is than the other person's!

I don't play many games, but I delight in playing beating my brother in Words with Friends.  We haven't played in a while, but it might be time because I just noticed he is one game up on me!  My best score against him was 424 (four hundred twenty-four) to his average game score of 290 (two hundred ninety).  424 > 290 (Four hundred twenty-four is greater than two hundred ninety) or 290 < 424 (Two hundred ninety is less than four hundred twenty-four.).  424 is 134 more than 290, or 290 is 134 less than 424!

How's the Weather?

My 96-year-old oma (grandmother in Dutch, my dad's family is from Holland) lives in California like the rest of my family and checks the weather in Jacksonville in the newspaper every day (She had all boys, who had more boys, and I am her only favorite granddaughter.  :-)).  When I talk to her every other week, the topic of weather always comes up.  Why?  Weather is something that happens all the time, all around us, so we are constantly observing it.

It is only about 4 weeks into the school year, but have you observed any changes in the world around you?  We're just a little over a week away from the Fall Equinox (which is September 23 this year), or the first day of Fall.  To understand the reasons for and effects of seasons in our Science studies this year, first we must be able to make observations and collect data about our climate, which is related to, but different than weather.

Need a refresher about weather and climate?  Have you heard about Study Jams?

Study Jams are terrific Math and Science tutorials that are great for introducing or reviewing concepts.  Watch this Study Jam on Weather & Climate to prepare for upcoming reading, discussions, and activities we'll be doing to explain why we have seasons!

Have you ever lived somewhere other than Florida?  Where?  What is the climate like during the different seasons of the year there?  Post your response below or write it down and bring it to class this week to earn Chief Cash for Always Doing Your Best!

I was born and raised in San Diego, California, but have lived in Jacksonville nearly half of my life.

San Diego's climate is similar to Jacksonville's in that there are not huge differences between seasons.  San Diego's temperatures, like Jacksonville's, are mostly mild throughout the year.  However, in San Diego, the air is much drier, and San Diego receives a lot less precipitation than we do here in Jacksonville.  Summers in San Diego are warm and dry, winters are cooler and dry.  It is strange to think that I never owned a winter coat until I moved to Florida!  :-)

Common Core "Math"

(Thanks to Ms. Kirkham for sharing this with me.  I got a good laugh because if anything, it supports the need for Common Core Math standards, which include understanding place value and not relying on "cute" tricks and shortcuts.)

Sometimes I feel like Math shouldn't be called "Math" anymore because arithmetic (computation) is just one part of the problem-solving process.  The methods for teaching Common Core Math are vastly different than simply teaching arithmetic because the end goal is not just a correct answer, it is genuine understanding of what is happening during the problem-solving process.

Outside school, I'm often asked what I think about Common Core Math.

Is it perfect?  No.

Do I agree with everything?  No.

Is there value in it?  Yes.

Most educators argue that the point of Common Core is to ensure that students are college-ready, but honestly, it goes beyond that.  For many reasons, we live in an intellectually lazy world, and that is a dangerous thing.  Kids will eventually be adults, citizens who will make decisions that affect not only themselves, but others.  We need to raise up a generation of thinkers and communicators who are able to question, analyze, and evaluate what they observe.  Our world needs problem-solvers.  "Math" is just one way to develop and practice these critical life skills.

Making Observations, Collecting Data, & Recording Observations

In Science this week, we learned that we make observations whenever we receive information (data) from our senses.  We can describe our observations qualitatively, with words, or quantitatively, with numbers, measurements, and/or units.

Today we observed, collected data, and recorded data about gummy worms.  We used hand lenses to observe qualitative characteristics and rulers to collect quantitative data (length of gummy worm and stretched gummy worm).  We even tied in some Math (fractions) when we used a number line to practice measuring to the nearest half, quarter, eighth, or sixteenth of an inch.  We also discussed how we can tell equivalent measurements in simplest form using the fewest units possible.