# Teacher Forum

## Mallory

Hi There!

We are currently working on adding and subtracting fractions with unlike denominators. I want to effectively visually model this for my kids, but I’m not quite sure how to do it. Should we use paper folding? For instance, how would we show adding 1/2 and 1/3 with paper folding?

Thanks!
Mallory

## Took the Challenge and Aced It!

I knew that each girl’s original amount of jellybean less the 1/7 for Martha and the 24 for Mary had to be equal.
Used guess and check to find that 1/7 was 27.

# Advanced Model Drawing Virtual Class Homework #6

Try a bar model and post in the comment section below.

# Advanced Model Drawing Virtual Class Homework #5

Try a bar model and post in the comment section below.

# Advanced Model Drawing Virtual Class Homework #4

Try a model and share in the comment section below.

## Frustrasted with Fractions

Dear Sarah,

I am dying with my 5th grade…they are struggling with fractions (the chapter is hard) and with not a strong Singapore foundation from last year…well…we are on our 4th week! Should I do the 4th grade fractions chapter?? I honestly am at a loss.

Thanks

## Do students need to draw the bars when solving word problems?

Dear Sarah,

I am currently in the unit of Parts to Whole, teaching bar modeling.  Looking ahead, it seems to me that bar modeling is a big part of not only this unit but upcoming units as well.

My wondering and question: I have students who are looking at the problems and can figure them out by stacking numbers then using the renaming strategy which was what they learned in lessons before bar modeling.  Should I be encouraging all of my students to draw the bar model before stacking the numbers to solve the problem? How critical is it for them to bar model? Please know that I am not saying that I don’t want to teach it at all, but I don’t know how much I should be “pushing” those that either don’t understand it or those that feel like they can work the problems using other strategies.

# Learning Math Facts

Math facts are simply the basics: addition, subtraction; multiplication; division. They are basic number combinations and calculations we do every day.  So why is it that learning math facts  creates such huge problems for teachers and students in our classrooms?

Common subtraction mistake when children are learning math facts.

Is it that some of us are just naturally better at math than others?  Perhaps.  The good news is you as a teacher can help anyone improve their math skills.  You might be wondering how.  Well, rote memorization alone won’t get us there.

# Meaning of Equality

Often we teach the meaning of equality as the equal sign indicating “put the answer.”  To prepare students for future mathematics, we need to rethink the way we communicate this representation to students.  The equal sign is too important to attach such a limited meaning, especially when students are moving to abstraction.  When moving to abstraction, it is important to use this symbol as a “reader” versus a “speller.”  What do I mean by that? Let me explain.  First, a speller sounds foreign because the student is trying to make sense of abstract symbols that they don’t fully understand. A reader connects meaning that they can comprehend while connecting the story to the symbol.

For example, when teachers record the following equation,

A speller would say, “Four plus five equals nine”.

A reader would say, “Four apples and five apples is the same as saying ‘I have nine apples’” .

In the journal prompt below, we want students to see the statement as 5 and 4 is the same as 2 less than 11. If we focus too much as a speller, students see symbols as performing actions rather than relating ideas, which leads to misconceptions of the equal sign.

Less is more. Hesitate in thinking math becomes harder by creating larger numbers, rather provide depth early on using children’s intuitive understanding of basic number operations.   A simple journal entry can help assess what students understand about operations and the meaning of equality.  Once you find that a student understands the meaning of addition and subtraction, it is time to create tasks that dive deeper in understanding equality.  These task can be as simple as asking questions such as, 4 + 5 = ____ + 6.  Additional equality tasks can be found in the Algebraic Thinking and Reasoning with Numbers books (Groundwork Series) by Greenes, Carole, et al., (https://www.mheducation.com/prek-12/program/MKTSP-O8302M06.html).

In the book, “Thinking Mathematically,” Carpenter, Thomas P., et al. suggest some benchmarks to keep in mind while moving towards the conceptual understanding of equality.

1. Establish a starting point.  What are students’ initial ideas regarding the equal sign?
2. Mix it up.  Don’t always write equations in the form a + b = c, rather c = b + a.
3. See the equal sign as a relational symbol. Emphasize students proving that each side is the same as the other.
4. Compare sides without calculations. Encourage students to look for relationships without performing calculations.

Listen to students and be aware of where they are in the process. Encourage them to question if it is true.   If so, why is it true?  By listening and looking we may be pleasantly surprised at what we find out.

Below is student work demonstrating various levels of understanding within the concept of equality.

Spiky says that 5 + 4 = 11 – 2 is false.

Curly says that it is true.

Who do you agree with and why?

This student understands how to simplify expressions but lacks applying the meaning of equality.

This student is confused in understanding what it means to have expressions on each side of the equal sign.

This student understands the meaning of equality. What can we ask next?

This student demonstrates a shallow understanding of equality. What can we do next?

This student can solve for an answer but needs practicing in mixing up the form of an equation.

## Communicating Home

Often we share our students progress by sending home “Monday” folders with worksheets that were completed, test or quizzes taken the previous week, or maybe we have a site where parents can go and see the current grade in your class.  Are we informing parents on their child’s progress?  Does the grade or worksheet give an accurate picture of student growth?

I often challenge teachers to give feedback on an ongoing basis.  We should not only assess from the papers turned in but from what we are seeing, hearing and collecting on a daily basis.  Use journal entries or a table with your objectives (I can statements) to allow for a more productive discussion at a parent conference.  The following guidelines can help your conversation whether it be in the form of report card comments, parent conferences or the chat in the pick-up line.

-What area is the child is doing well? (Have pieces of work that demonstrate growth.)
-What area does the child struggle? (Show specific concepts not just a broad topic.)
-What are you doing in the classroom to help?(The learning does not stop after a chapter test. It is your responsibility to help the child learn it!)
-What can they do at home to support you and their child? (Parents want guidance on how to help.)

Attached is an article from the Wall Street Journal – 10.18.17 addressing the idea of a student-run conference.  This conference helps children communicate their progress while building the metacognitive process.  Would love to see this happening more in our schools.

Communicating Home