What is Applied Mathematics?

Applied Mathematics problem-solving activities are intellectual challenges that enhance mathematical development.

• Kindergarten: 27 Activities
• Grades 1-8: 43 Activities per grade
• Up to 4 problems per activity (3 differentiated, 1 investigative)

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

Two Types of Problems

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

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: Used 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 to their level of competency, while still addressing the same on-grade level standard.

OR

• Use the meeting problem to help teach a concept to the 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 who 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.

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.

See Applied Mathematics: Accessing Resources, Reviewing, and Grading for more information

Grading assesses students' 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