What is Applied Mathematics?

What is Applied Mathematics?

Overview

Applied Mathematics problem-solving activities are intellectual challenges that enhance mathematical development. There are 43 activities at each grade for grades 1-8 and 27 activities for kindergarten. These activities are a powerful vehicle for developing conceptual understanding, reasoning skills, and mathematical communication during whole class or small group standards-based instruction. These problem sets are designed with teacher modeling and direct instruction in mind.  All activities can be completed on line or printed and completed as worksheets by students.

These math activities are offered in addition to Classworks other math instruction. They can be found under the preset instruction tab within Classworks or by selecting Applied Mathematics instruction when searching for content.

What is Applied Math?

Details: 

  • Kindergarten: 27 Activities

  • Grades 1-8: 43 Activities per grade

  • 4 problems per activity (3 differentiated, 1 investigative)
    **Exception: Level K lessons have either 3 differentiated problems OR 1 investigative problem**

  • All problems within an activity are related through a common purpose setting statement and all cover the same grade-level standard. 

Within Applied Mathematics, two problem types exist. 

Type 1: Differentiated Problems 

  • Three levels of questions: progressing, meeting, and expanding 

  • Differentiated by the magnitude of the numbers, the number of required steps to solve, and/or the amount of support provided. 

  • Each progressively increases in the necessary understanding and level of communication required. 

Type 2: Investigative Problems 

  • Students are presented with a problem and two sample student responses. 

  • Students evaluate the sample student work for accuracy and understanding. Then they must either defend the correct answer or provide an error analysis for the incorrect solution. 

  • This requires students to critique, reason, and communicate giving you insight into their level of conceptual understanding. 

Planning 

Classworks provides support in planning, implementing, facilitating, and grading Applied Mathematics. Determine what students are expected to learn, master, and demonstrate.

Support provided by Classworks:

  • Primary skill & mathematical practices addressed by the activity* 

  • List of recommended manipulatives 

  • Suggested responses to identify one way students may solve the problem 

  • Common misconceptions to address early on and/or provide the appropriate resources to support student learning 

Determine how students will be expected to communicate and demonstrate their thought processes, work, and understanding.

Whether this is student choice or teacher directed, Classworks provides a variety of tools:

  • Canvas: Students can illustrate and/or write on the canvas. 

  • Recording Tool: Students can record themselves verbally explaining their thinking. 

  • Digital Tools: Students can show their work using one of our digital tools (Hundreds Grid, Number Line, Calculator).  

Primary & secondary standards as well as prerequisite standards are available in the Classworks Resource Center.

Implementing 

The activities were developed with flexibility in mind so they can be easily integrated into your current math instruction. There are several ways to use these activities within the classroom. Below is a list of ideas for implementing the activities:

Differentiated Problems: Use the Progressing, Meeting, and/or Expanding problems to build understanding and work towards student proficiency of the concept/standard.

Investigative Problems: Use to develop students' mathematical communication skills and to assess students' conceptual understanding.

Differentiation 

Content (This applies to only the differentiated problems): 

  • Direct students to complete one of the three differentiated problems based on their current level of understanding and mastery of the concept. Students who are still progressing, proficient, or advanced can complete a problem appropriate with their level of competency, while still addressing the same on-grade level standard. 

OR

  • Use the meeting problem to help teach a concept whole class. Based on how well students grasp a concept, assign students to either work on the progressing or expanding problem in small groups. Work with the progressing group on any common misconceptions they may have. 


Process: 

  • Homogeneous small groups or in pairs: Students can work together to solve the problem with the teacher as a facilitator.

  • Heterogeneous small groups or in pairs: Students can learn different strategies from each other. 

  • Independent work: Students complete the problem independently and then share how they solved it with their classmates that completed the same problem. 

  • Product: Students can show their understanding and mastery of the mathematical concept in a variety of ways. They can illustrate, write, and/or record their thinking and demonstrate their knowledge. 


Facilitating Utilize for whole-class or small group instruction while you facilitate.


Classworks provides the: 

  • Ability to view student work in real time to monitor student progress and redirect as needed. 

  • Ability to view the statuses of the problems to determine which problems are not started, are still in progress, are ready for review, or are ready to be graded. 

  • Talking points to support you in guiding students as they navigate through the solving process. 

  • Ability to provide feedback directly on the student's canvas and/or by pinning a note. 

  • Ability to print resources for offline use. This includes printable activities for students and a Teacher Resource page. 


Grading assesses student's conceptual understanding and knowledge of the concept and process.

Classworks provides: 

  • Auto-scoring for the multiple choice problems 

  • Suggested responses for the open-ended portions 

  • Ability to give the student credit for his/her mathematical thinking


FAQs

Q: Is student work saved in the activities? 

A: Yes! All student work is automatically saved in Applied Mathematics so students can work on problems over time. 

Q: Do my students have to complete all of the problems? 

A: No. We developed the activities with flexibility in mind. Students can complete all or only certain problems as verbally directed by you, the teacher. Refer to the “Uses” section of this job aid for more details. 

Q: What is the purpose of the “I'm Finished” button? 

A: The “I'm Finished” button is a way for the student to let you know that they are done working on the problem and are ready for you to review their work. This allows the student to move on to another problem and gives you time to conference and provide feedback prior to the student prior to turning it in for grading. Students can return to the problem to make necessary edits as long as they have not clicked the “Turn In” button on the Introduction screen. 

Q: What is the purpose of the “Turn In” button? 

A: The “Turn In” button should only be clicked when the student is finished with all of the required problems s/he was supposed to complete. Any problems marked “I'm Finished”, indicated with a checkered flag, will be auto-scored (if applicable) when the student clicks “Turn In”. If a problem has not been marked as finished, Classworks will not score it when it is turned in. 

Q: How do I know which differentiated problem my students should complete? 

A: The differentiated problems all address the same grade level standard but allow for different entry points to support all learners. You know your students best and their level of understanding will vary for each concept. Here is a general guideline: Progressing: For students that are still working towards mastery of the concept. Meeting: For students who have a foundational understanding of the concept but are still developing the conceptual understanding. Expanding: Students who are ready for a more in-depth exploration of the standard, are able to make connections and apply the skills necessary to communicate and provide reasoning for the conclusions made. 

Q: How is the investigative problem unique? 

A: The complexity of the investigative question is similar to a meeting problem; however, it requires higher order thinking in the way students must critique, reason, and communicate their understanding.


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