The ten tasks in this set are the perfect way to build in your students the “habits of mind” of mathematically proficient thinkers while examining fractional parts of a number. The sequenced tasks in this set will provide you with an entire week’s worth of quality instructional materials – five instructional tasks and five follow-up assessment tasks, complete with administration guides, scoring guides, and other support materials – that will help your students explore with fractional parts of a number while building their reasoning and communication skills.
Please try out this free sample – FREE Mastering the Practices assessment task – to get a sense of what the materials in this set will provide.
I designed these tasks as a way to have students explore an area of mathematical content in a way consistent with the behaviors described by the eight Standards for Mathematical Practices –
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and qualitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
These Standards for Mathematical Practices are not separate from the Common Core Content Standards, but a set of behaviors that students develop and demonstrate as they work with specific content. The content standards identify what the students will learn, but the practice standards describe the way that students should engage with the content. While there are many activities that address the content of the Common Core, not all of those materials also help build students’ expertise with the practices. The tasks in this set were creating with the aim of developing my students’ content knowledge in a way that also develops the “habits of mind” of mathematically proficient students.
Included in this set:
• table of contents
• chart identifying task/mathematical practices match
• 5 instructional tasks (four two-page tasks and one three-page task)
• administration guide for each instructional task
• resource sheets for each instructional task
• 5 one-page assessment tasks
• scoring guides for all 10 tasks
• generic math rubric for scoring written responses
• kid-friendly evaluation checklist
The tasks in this set all relate to finding a fraction of a number. The fractions used are all unit fractions, and the whole numbers are all multiples of the fraction’s denominator, allowing for students to more readily notice the patterns present when finding a fraction of a number. While finding a fraction of a number is not an explicit standard in the Common Core State Standards, the work your students will do as they work through these tasks will lay the foundational skills necessary for thinking about multiplying a fraction by a whole number (5.NF.4) in terms of finding a/b (part) of c (whole).
This set has tasks that are designated as instructional tasks and others that are designated as assessment tasks, though each task can be used for either purpose.
The instructional tasks are slightly longer – most of them being two pages in length – and will take more time to implement. Each of the instructional tasks can be administered in a class period, likely taking less than an entire class period to complete. The tasks are broken into steps that build on each other, and each step will prompt a level of thinking that will help the students better tackle the following step. These tasks are ideally done in a guided manner, with the teacher facilitating a mathematical discussion with the class about the concepts addressed by each part before the students complete the given step. Included with each instructional task is an administration guide that describes one way that the task may be implemented in your class.
Optional resource materials – in the form of cards that can be cut out and manipulated by the students as they work on a particular step of each tasks – are provided for the instructional tasks; while not necessary, as the material on the cards are embedded in the tasks themselves, use of these cards can add a level of physical engagement to the tasks and provide a springboard for discussions that extend beyond the questions posed in each task.
The five instructional tasks are in sequence, with each task building on the work of the previous task. The tasks in this set, for instance, begin with one that focuses on the use of a model for representing the relationship between a part and a whole, and is most suitable for a class that has not done much work with finding a fraction of a number. The final tasks require students to order expressions without solving them, using patterns in the expressions themselves, and use numbers that are larger than the ones in the initial tasks.
The tasks are best completed in order, though you may not need to begin with the first task, depending on your students’ familiarity with the concept. You may also choose to use the tasks to differentiate within your class, having some students complete the beginning tasks, while other students complete the later tasks.
The tasks designated as assessment tasks are shorter – just one-page in length – and are intended to provide a quick snapshot of your students’ understanding of a given concept. Each assessment task matches with one of the instructional task – Assessment Task 1 corresponds to Instructional Task A, Assessment Task 2 to Instructional Task B, and so on. Each one of the assessment tasks focuses on one of the concepts addressed in the corresponding instructional task. They are intended to be administered as assessments, providing an opportunity to see each student’s independent understanding of the target concept. You can use them as formative assessments, administering the tasks before your work with the instructional task, or as summative assessments, giving them after the students have work on the instructional task. You are not limited to using these tasks as assessments, however; they can also be used as any type of follow-up to the instructional: homework, center work, seatwork, or in some other way that suits your classroom routine.
There is an answer key provided for each task. Parts of each task have specific correct answers, and those answers are indicated on the keys. However, a great deal of the tasks involve writing, and students’ answers may vary for any given written response item. The written answers are designed to be scored using the 3-point scale math rubric (included), and each task-specific key identifies specific components you may look for when deciding whether a given answer shows “advanced”, “proficient”, “developing”, or “little or not” understanding of the target concept. Along with the generic math rubric, I have included a kid-friendly resource sheet designed to communicate the expectations of the math rubric in a more accessible manner.
For more practice with fractions, please check out the other related resources I have available –
Name That Equation fraction multiplication task cards + printables set
Fraction Puzzlers - fraction story problems task cards + printables set b
Fraction Attack – simplifying fraction ppt + printables set
Fraction Matchin’ equivalent fractions task cards + printables (set a)
Fraction Matchin’ equivalent fractions task cards + printables (set b)
Monkey Mania & Jumping Giraffes equivalent fractions games + task cards bundle
Flipping for Fractions activity card set
FREE self-checking mixed numeral/improper fraction puzzle set
If you have any questions or comments, please feel free to email me through TPT. I’d appreciate any feedback you are willing to give after you have had a chance to review or try out the resources!
Thanks – Dennis McDonald