Mr. Rutter’s 6th graders are working on a multiplication unit that focuses on multiples and factors. In this lesson, he will focus on finding greatest common factors to prepare them for the upcoming fractions unit; his students will also learn...
Teach with Tech
Creating an organized list, table, chart, or other graphic organizer is an important problemsolving strategy (see UDL Checkpoint 6.3: Facilitate managing information and resources). Organizing information will help your students to see patterns and learn mathematical concepts more easily. Organizing will also give your students a structure to help them think about what they do and don’t know about a problem. The strategies below provide a strong starting point for differentiating instruction.
Steps:
Step 1: Provide Clear Explanations
 Introduce this strategy by presenting a list, table, chart, or other graphic organizer (using a spreadsheet or concept mapping tool) and point out why each kind of organizer is helpful. The most common reasons are to see patterns, quickly find a particular example or piece of information, and be sure that you aren’t missing any examples.What to look for in lists and tables
 Labels
 Location of items (rows and columns, for example)
 Order of items (repeat for each dimension in a table or list if needed)
 Connections between items (as might be found in a concept map)
 When you present a particular kind of organizer, give students some time to think about how the information is organized before discussing the features that make the organizer helpful.
 Let students suggest their own ways of organizing information about a topic they are studying or a problem they are solving. You can modify their suggestions as needed, but be sure to explain why you are making changes.
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Interventions should include instruction on solving word problems that is based on common underlying structures
Teach number and operations using a developmental progression.
Step 2: Give Students Strategies and Models
 Explain to your students that organized lists are fairly easy to create so long as there aren’t a lot of items. Show them an example of the kind of list that can be created from a problem, and explain how the list is used to organize the information in the problem.Good problems for organized lists
 How many different outfits can be created if you have three pairs of pants and three shirts?
 What’s the probability of flipping exactly two heads on three coins?
 How many different ways can a basketball team score 10 points with onepoint free throws, twopoint field goals, and threepoint shots?

Explain that charts are pictures that organize information. Some charts are called graphs (line charts or line graphs, pie charts or pie graphs) and others are simply diagrams. Students who are particularly visual or creative might respond better to charts than to tables or lists, so when possible, present a chart in addition to a table or list.
 Use technology to greatly increase the organizing options available to students. Have students experiment with computerbased and paperandpencil versions to understand the benefits of each. Computerbased tools, such as spreadsheets and concept mapping tools (e.g., Bubbl.us), can check that data is organized correctly, make information easier to sort, and save time—especially when creating charts.
IES Recommendations
Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.
Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.
Help students understand why procedures for computations with fractions make sense.
Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade
Step 3: Provide Ongoing Formative Assessment

As your students work on problems, watch for the kinds of graphic organizers they use. Knowing which organizers each student prefers may be helpful to you as you introduce new mathematical content. When a student uses a graphic organizer that you think may not be helpful, ask the student to explain the format and why he or she chose it.

Draw upon a twopart strategy to support students who are not being systematic in how they organize information. First, acknowledge whether the organizer they are using is appropriate, and then ask them questions to help them see a more systematic way to organize information.
Sample questions to ask What are you trying to find out? How will this organizer help you? What might be a problem?
 Explain to me the system you’re using to make your list, chart, map, and so on.
 How do you know what to do next?
 Remember how the alphabetical list of names helped us know that no one was missing? How will this help you know that nothing is missing?
 Tap prior knowledge by creating a concept map that links what they’re learning to what they have already learned. During the unit, have them add to and modify the map. You can then use their maps to talk with them about how they understand the concepts, and about any misconceptions you may have noticed.
IES Recommendations
Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review
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