Series Formative Assessment Practices to Support Student Learning: Formative Assessment: Understanding Fractions
Math.Practice.MP1
 Common core State Standards
 Math: Math
 Practice: Mathematical Practice Standards

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.
Math.Practice.MP2
 Common core State Standards
 Math: Math
 Practice: Mathematical Practice Standards

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 decontextualizeto 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 referentsâ€”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.
Math.3.NF.A.1
Common core State Standards
 Math: Math
 3: Grade 3
 NF: Numbers & OperationsFractions
 A: Develop understanding of fractions as numbers

1:
Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, 8.
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Discussion and Supporting Materials
Thought starters
 Why does Ms. Romano decide to assess her fourth graders' understanding of a third grade content standard?
 How does Ms. Romano encourage productive struggle during the lesson?
 What instructional decisions does Ms. Romano make based on her observations during the collaborative work?
School Details
Four Georgians School555 West Custer Avenue
Helena MT 59602
Population: 494
Data Provided By:
Teachers
Melissa Romano
Newest
UNCUT CLASSROOMS
UNCUT CLASSROOMS
UNCUT CLASSROOMS
Lesson Idea
48 Comments
Ms. Romano encourages productive struggle by helping students understand that grappling with struggles is part of learning and a sign to her that the student is truly trying to elicit evidence of their learning. Ms. Romano talks to each student or group and asks them probing questions that require thought not just a simple answer. By helping them learn to think through their struggle Ms. Romano knows what she might need to include in the next lesson and helps students learn to work through their struggles.
1. Why does Ms. Romano decide to assess her fourth graders' understanding of a third grade content standard?
The topic she was teaching was based off of previous learned content and she needed to know they knew it so they could better relate it to the lesson. This helped her see if she should review previous content before moving on to this lesson or if she could tie them all together so they could begin doing more complex problems.
2. How does Ms. Romano encourage productive struggle during the lesson?
She has the struggling students repeat the questions to her outloud which helps them better grasp the question. She also goes around and individually asks students questions to make sure they understand the problems and if a majority of the class ends up struggling she has a class review of the problem to make sure they all are on board.
3. What instructional decisions does Ms. Romano make based on her observations during the collaborative work?
Ms. Romano said that walking around the room she figured out who was struggling and who was excelling at the content because their partners would kind of push them to her. She realized not everyone was completely understanding the material so she decided to change her instruction and she said it helps her know which areas she needed to work on in her lesson planning.
1. Why does Ms. Romano decide to assess her fourth graders' understanding of a third grade content standard?
Ms. Romao assesses the students' understanding of this particular content standard because it tied into the lesson that the students were going to be doing and she believe that by applying prior kowledge they could relate the lesson to it to make the connections more explicit and to get them to recall.
2. How does Ms. Romano encourage productive struggle during the lesson?
Ms. Romano encourages productive struggle during the lesson by not jumping in. Instead, she ask more questions, allowing the students to talk it through until they come up with the answers.
3. What instructional decisions does Ms. Romano make based on her observations during the collaborative work?
Based on her observations, Ms. Romano decided to change her instruction. She also worked one of the problems together with the class aas a whole and decided to let them work more problems like those so that they could gain more knoledge of the concept.