Grade 4

Challenging Word Problems

Advanced Model Drawing Virtual Class Homework #6

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

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Challenging Word Problem

Advanced Model Drawing Virtual Class Homework #5

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


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Challenging Word Problem

Advanced Model Drawing Virtual Class Homework #4


Try a model and share in the comment section below.

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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.


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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.

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Why do Students Struggle When Learning Math Facts?

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?

Subtraction mistake when learning math facts

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.

Continue reading

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Conceptual understanding comes first!

How can we help student refocus on understanding versus just an answer?

Too often when we pose a problem and students shout out an answer.  We need to ask ourselves do students understand the concept or are they obtaining the correct answer by fitting the symbols and numbers into a structure they know?

In this example, the anchor task was to subtract 34 from 87.  The teacher wanted to screen the children first wondering, Do students know what it means to subtract one number from another?  To find out more the teacher posted the following problem, removing the numbers.

Do students have the conceptual understanding or just fit the numbers into a given structure?

Students were asked to set up the expression that could represent the situation.  The student A on the far right was the only student in the class that seemed to understand. When asked to explain his thinking, many observing teachers felt he understood the concept and that he gave us a platform to generate a discussion.

Do students understand the part-whole relationship here?

Following this analysis, the numbers were inserted into the problem.  Subtract 34 from 87.  It was interesting to see student A’s work.  Much to our surprise, Student A who seemed to understand the concept had a hard time transferring that knowledge to another situation.  Notice his equation is not correct but he gets the final answer.

Can student A  transfer knowledge from one setting to the next? Look and listen to help guide students to conceptual understanding.  Looking at answers does not tell us the whole story.

Less is more.  Spend more time on conceptual understanding and listening and watching students versus solving more problems.  The answer does not help assess student reasoning or how we can extend or guide the learning process.

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Rounding Using the Number Line

Use of number line to show rounding.  In each case what place is the student rounding to?  How do you know?

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Groundworks are great problems for Anchor Task-Factors

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Anchor Task-Factors

Do you have any ideas for anchor tasks for 4th grade multiple and factor lessons?!

Check out the attached pdf and games on the website.  -Sarah

Factors-Anchor Tasks

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Journal Prompt based on misconception

Who do you agree with? Explain.

Spiky says his number 32 tens + 5 ones is the biggest.
Curly says her number 1 hundred + 3 tens + 2 ones is the biggest because she has the most hundreds.
Buzz says his number 5 ones + 3 hundreds + 2 tens is the biggest because the first digit 5 is bigger than 3 and 1.

I got this!- Student 1

Do we know how to help Student 2?

What can we work on with student 3?

Student 4 needs more concrete experiences. Maybe we have them build these numbers and edit their journal if needed? This students needs to reflect once they can see the mistake on what the error was.

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Sarah Schaefer

 Sarah Schaefer - Student Work

Great Day 1 journal prompt to set up structure of journaling.

What do you like about learning math?
Give 2 examples and an explanation.

Day 2:
What do you not like about learning math?
Give 2 examples and an explanation.

Great way to get to know your students. Share your results!

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 Spiky - Student Work

Ready to work on journal writing together? Share prompts that could be used for a unit on counting, number, and place value.

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Models and Word Problems

Here is an example of a grade 4 bar model/tape diagram.  If you were Sophia’s teacher what more could you ask her to extend her thinking?

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