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Even though this is a very complicated mathematical practice idea, your students will love how simple the learning truly is!
Page 1: Cover Page
Page 2: Examples (Tough example; Can you calculate the stars? Check out the PREVIEW.)
Page 3: Graphic Organizer for Part Part Whole Addition and Subtraction word problem structures. These word problems typically involve a joining or subtracting action. Equation included.
Page 4: Graphic Organizer for Part Part Part Whole Addition and Subtraction word problem structures. These word problems typically involve and joining or subtracting action. These types of word problems are similar to the above problem structure. However, they include more parts and thus are slightly more complicated and have more possible equations to solve the word problem.
Page 5. Graphic Organizer for Compare word problem structures. These word problems typically have no action and are far more complicated than the other two word problem structures.
Page 6: Thank you!
These mathematical graphic organizers help students make sense of word problems. I am using these in my 5th grade classroom where students are working on adding and subtracting fractions within word problems. Students first decide if the structure should be Part-Part-Whole or Compare and choose the correct graphic organizer. Then they FILL IN and LABEL the parts of the specific graphic organizer that they are given from the word problem. This will help students make sense of the word problem they are trying to solve. Then they can determine which equation would best help them solve the word problem. We use fractions in 5th grade but these graphic organizers can be used with any grade level to help children make sense of word problems that have fractions, decimals, or whole numbers.
These have really helped my students learn to solve the Engage NY word problems, including the application problems for each lesson.
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Multiple Mathematical Practices Apply:
Related Mathematical Practices from the Common Core Standards:
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.
Common Core Mathematical Practices
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.
Understanding word problems
Making Sense of word problems
Learning all types of word problems
graphic organizer graphic organizers
Part Part Whole Part Part Total Comparison
Bar model Tape diagram