Happy Monday!

As always, I hope you are healthy, happy, and loved. Last week was tough for me.  I experienced a lot of successes and wins, but I over-focused on the things that were not going so well. I had to remind myself of one of my favorite mantras, “Focus on what you do want to happen, not on what you don’t. Then, magically I received an email from a principal who was sharing pictures of the great work their teachers were doing. Thank you!

I have been working with a few schools that have a weekly assessment they must take that addresses multiple mathematical standards. The teachers decided to give the students similar problems to the ones on the test every day so that by the time they take the assessment, they will be used to seeing those types of problems.
That is one approach.
I tend to believe children will benefit more and retain information better if we identify their areas of weakness and give them repeated opportunities to improve those skills and strategies. What are the underlying skills your students need to develop?

Underlying Skills

When presenting a word problem, diagram, or chart to students, we must consider what students already know and what they need to know to be successful and independent with the problem.

Do they know how to read a chart?
Do they have the academic language needed?
Do they read through each sentence carefully?
Do they have strategies to add, subtract, multiply, and divide?
Can they construct mental representations based on past experiences with manipulatives?

Smarter Balance Assessment 4th grade NBT sample problem.
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I looked at the second lesson for fractions in a fifth-grade textbook.
The problem is below:

Mr. Smith has a one-meter wire he is using to make clocks. Each fourth meter is marked off and divided into five smaller equal lengths. If Mr. Smith bends the wire at 3/4 meter, what fraction of the smaller marks is that?

The above problem is a top-heavy problem. It is what students should be able to do at the end of a unit or year. Not on day 2 of fractions. When we elect to teach top-heavy word problems embedded with multiple academic terms, excess language not necessary for solving, multiple steps, and academically challenging, we must also identify the skills required to solve the problem.  We must provide additional time and resources to ensure all students can make sense of the problems and solve it accurately and independently. Consider all the skills and knowledge required for a student to solve the above problem independently.

Students would need:
Knowledge of meters, fourths, fourth-meter, and lengths.
Ways to divide the fourth meter into five smaller units.
Understand and create equivalent fractions
Read and make number lines using fractions.

Small Group 1:  Comprehension Strategies for making sense of problems
Small Group 2: What is a fourth? What are fifths?
Small Group 3: Equivalent fractions
Small Group 4: Using a number line to represent fractions

The example problem may be the perfect problem to challenge students with the above skills. But, if my students have comprehension challenges, language challenges, and lack familiarity with meters, fourths, and number lines, the above problem may be too overwhelming and create a sense of uncertainty and fear of mathematics. Small group instruction is likely to be needed to address the many different skills the word problem above requires.

Underlying Skills Required

What would a student who is strong in mathematics do to solve the problem below?

The above problem would require students to:
Skip counting by whole numbers and decimals
Decompose numbers using place value
Use the relationship between addition and subtraction to solve
Have an understanding of the difference or distance between two values
Adding whole numbers, tenths, and hundredths

I would ensure that my students had all the above skills or had opportunities to develop those skills. I would need to create at least four small groups or four new individual lessons to ensure my students could solve the above problem independently and confidently.

Small Groups:
Small Group#1: Skip counting by 100’s, 10’s, 1’s, tenths, and hundredths
Small Group #2: Decompose numbers using place value
Small Group #3: Use the relationship between addition and subtraction to solve
Small Group #4: Have an understanding of the difference or distance between

Building Skills Over Time

You might want to consider making your life easier and using the Common Core problem types in Table 1 and Table 2 if:
your students struggle with comprehension of word problems
have limited academic language
are not ready for the end-of-the-year word problems yet
have limited use or understanding of the mathematical properties (commutative, distributive, associative)

The Common Core problem types are the problems used in state testing. They are simple, straightforward, and intended to build students’ reasoning and strategic thinking skills over the course of the year. They are bottom-up problems that introduce a topic. Teachers can build upon students’ comprehension and mathematical skills as they move through the standards.

If you have students who have advanced mathematical strategies and thinking, don’t slow them down. Place them in a small group and use more challenging numbers, present the data on a chart and have students pull from the chart to solve the problems, or have the students create their own problems.

Small group instruction can provide extra support and challenges to help students grow.

What Are The Underlying Skills Required

Analyze your next problem of the day. Do your students have the skills to solve such a problem with fluency, confidence, and independence? If not, creating small groups to practice each of those skills can be one way to develop independent and confident problem solvers.

Ways To Connect

I love to stay in touch.  Please reach out via email, Danielle@TeachingOneMoore.org, or follow me on Instagram @Teaching1Moore is probably the fastest way to connect.

Have you thought about doing a read-aloud with your small groups? How about beginning a new unit with an investigation or exploration? If you are looking for engaging, standards-aligned small group activities  look no further and click on the link below.

If you would like to take a deep dive into students’ thinking consider enrolling in my online Cognitively Guided Instruction (CGI) math course through the University of San Diego.
Enroll anytime, take up to 6 months to complete the course, go at your own pace, and earn up to 3 graduate-level units.

Go to www.pce.sandiego.edu to learn more today.