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Is The Jump in Fourth Grade Causing the Slump?

As always, I hope this email finds you with an abundance of people, places, and things for which you can be grateful.

 

I am the type of person who will grow an aversion to and avoid activities that do not bring me success early on. Yes, I know this is not one of my better qualities I am working on it. However, I know there are other people out there who also do not like to fail. The thought of skiing down a hill at a fast speed gives me anxiety. Playing video games frustrates me. I do not like reading directions on how to put things together (thanks, Ikea). As I write this down, it is becoming clear that almost all of my first experiences with the above activities, were learned alongside my very competitive, trash-talking older brother and usually ended in frustration and failure.

 

For many people, if their first experiences begin with failure, they may develop an aversion to the activity. However, when engaging with an activity that begins with even mild success, they are willing to tough it out even when challenges arise. The beginning of the fourth-grade math curriculum has math problems that do not make sense or follow the same rules as previous grades. By beginning with place value, students begin the year with one of the most abstract and challenging units of all.  This is the first jump that can lead to a slump in fourth-grade math scores. Read on to discover the hurdles that inhibit success for many fourth-graders and the jumps that can lead to slumps in test scores.

 

Ways to gain points and student confidence.

  1. Bridge the gap from third to fourth-grade by teaching number sense throughout the year and increasing the number of digits when rounding incrementally.
  2. Teach students to identify the power of ten by identifying how many groups of ten are really in a number like 2,765 (it’s not 6).
  3. Try saying, “How many powers of ten did we multiply/divide by to go from 240 to 24?”
  4. Call a decimal by its name.

 

Reason #1
The time elapsed from third grade to fourth grade.

Every school I have ever worked with at this point in my career (there have been hundreds) begins their school year by focusing on place value. Many third-grade classrooms spend the first 20-30 instructional days in August and September focusing on rounding numbers to the hundreds place and adding and subtracting numbers equal to or less than 1,000. For example,

 

1.) 76  rounds to 80

2.) 734 rounds to  700 or 730

3.) 239 + 457 = ___

4.) 783 – 659 = ___

 

Third graders are very familiar with adding and subtracting 3-digit numbers up to a thousand. In fact, this standard is an exact replica of what they learned in second-grade.

However, students are expected to jump from understanding, rounding, and naming 3-digit numbers at the beginning of third-grade (a repeat of second grade) to manipulating 7-digit numbers in fourth grade, almost one full calendar year later, with no bridge in between, no physical tools to build a concrete understanding of such large numbers, and no experience interacting with huge numbers in real-world settings. Most fourth-grade students I talk to have a hard time even saying a number like 3,079,054 aloud. Yet, this is one of the first challenges they face when they enter the fourth-grade.

*Based on the use of the standard algorithm, this fourth-grade student appears to have very little number sense. Ideally, this child could solve this problem mentally, but defaults to a lengthy, and unnecessary standard algorithm.

 

 

Success begets success. If students must reason about, round and complete operations with huge numbers they have little or no experience with the first few days of fourth grade, it may set many of them up to feel like failures, inept, or incompetent. Is it a good idea to begin fourth grade with this type of challenge? How can we better bridge the jump from 3 digit numbers to 7 digit numbers?  Do students have to master the skill of rounding and adding and subtracting in their first 20-30 days of school? Or can this skill be extended upon throughout the year on a weekly or monthly basis?

Third Grade Standards

Use place value understanding and properties of operations to perform multi-digit arithmetic.¹

CCSS.MATH.CONTENT.3.NBT.A.1
Use place value understanding to round whole numbers to the nearest 10 or 100.
CCSS.MATH.CONTENT.3.NBT.A.2
Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

Fourth Grade Standards

CCSS.MATH.CONTENT.4.NBT.A.3
Use place value understanding to round multi-digit whole numbers to any place.
i.e., 987,054 = 1,000,000  or 980,000

 

Reason #2
How Much Is A Million?

We can probably envision hundreds of things in our daily lives that come in groups of 100 or 1,000 like one hundred dollar bills, the number of days in school, the cost of the weekly grocery bill, our monthly rent, or mortgage payment. However, it can be difficult to envision numbers in the hundreds of thousands or millions that we as adults interact with regularly- the price of a home, maybe, but what large numbers do students interact with on the regular basis?

We might hear about millions of people, but can we envision what a million people look like? Have you ever personally experienced millions of people? Have you ever held a million dollars or close to a million in your hands?  Yet, these are the very numbers fourth-grade students must conceive of and manipulate in the first few days of fourth grade.

What does a 10,000,  100,000, 1,000,000 look like in real-life? I am not saying fourth-graders should not grapple with large numbers. They absolutely should. However, students can benefit from the use of context when working with large numbers. Activities like “The 100 Days” of School and representing 100, tend to stop at amounts up to 100 in the first grade. We can continue to build on this idea.
Tapping into the power of our base-ten number system is one way.

If every kindergarten student in Ms. May’s class brings in a “One Hundred Day” poster with 100 Cheerios, how many Cheerios will we have?
If every kindergarten student in the school brought in a “One Hundred Day” poster, how many Cheerios would we have in the school?
If every student, in every grade brought in a “One Hundred Day” poster of Cheerios, how many Cheerios would we have?

 

Reason #3
The Base Ten Number System- Our number System is Missing from the Curriculum

By looking at examples from posters and worksheets I once had plastered all over my classroom walls, how would a student learn about our base-ten number system by looking at them? We are not allowed to put the number 10 in any of the place value columns. It is forbidden. As soon as we make a ten, we must regroup it to the next column by replacing it with a 1. Yet, our whole number system is based on groups of 10. By looking at the charts or using the standard algorithm, how would our students learn that it requires:

 

10 groups of 1 to make a 10 10 x 1 = 10

10 x 10 = 100

10 x 100 = 1,000

10 x 1,000 = 10,000

10 x 10,000 = 100,000

10 x 100,000 = 1,000,000

 

If you look at the above monkey chart, it will falsely lead you to believe that in the number 1386, there are 8 tens, when in fact, there are 138 tens in 1,386 and 1,386 ones. Yet, this is a misconception or a limited understanding of our base-ten number system. This chart can make it difficult to understand how much value is being added to a number as you move to the left or the right on the place value chart. What types of problems can we pose that will help students understand how many tens
are in a number like 3, 907,865 (it’s not 6).
In addition, fourth-grade students are assessed on their ability to make metric conversions from millimeters to centimeters to meters to kilometers. These conversions would be a lot simpler if fourth-grade students understood they were multiplying by 10, by 100, and by 1000. Again, this is another area where students can gain points on assessments and avoid a slump.

 

Reason #4 Many Students Believe They Are Adding Zeros to A Number

This may seem nitpicky, but it is a little thing that matters VERY much. When a zero appears at the end of a number, zeros are not being added. If I add $0 to a $1,000 check I still have $1,000.
Many fourth graders mistakenly believe that to go from 100 to 1,000 you just have to add a zero. If a student solves problems by  “adding a zero” as a rule, how will it affect their ability to answer the following question?

Example Stem:
Select the statement that explains how the values of the numbers 420 and 4200 are different.

A. 4200 is 1000 times as large as 420.
B. 4200 is 100 times as large as 420.
C. 4200 is 10 times as large as 420.
D. 4200 is 1 time as large as 420.

*Excerpted from the Smarter Balance Assessment Consortium
-Grade 4 Mathematics Item Specification C1 TD

What happens to 10, 100, 10,000 when you have ten of them?
What happens to one whole when you divide it by ten?

 

Reason #5
Decimals

When we look at this number “10” it would probably never even occur to us to say one-zero.

But, when we see the number “0.1”, there is probably a fifty-fifty chance you might say zero-point-one instead of one-tenth.

It is very difficult for fourth graders or any student to understand the value of decimals when they cannot name them accurately. It also very difficult for students to make connections between 0.1 and the fraction 1/10 if they cannot say the number. It will save so much time and trouble if we just call a decimal by its name.

In 2004, fewer than 30 percent of high school students were able to translate 0.029 as 29/1000 (Kloosterman, 2010). Knowing and using the proper name for decimals could help students progress more smoothly up the mathematical ladder. Call a decimal by its value: one-tenth (0.1), one-hundredth (0.01), and one-thousandth (0.001).
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