This microcredential represents a teacher’s ability to understand and respond to progressions related to addition and subtraction with rational numbers, including conceptualizations, properties, strategies, and representations, by planning and implementing instruction based on the Standards for Mathematical Practice and Effective Mathematics Teaching Practices. It includes selecting, using, and adapting mathematics curricula and teaching materials, including the integration of mathematical tools and technology, as well as using and analyzing formative and summative assessments to determine where students are in learning addition and subtraction with rational numbers. This is the fifth of seven microcredentials in the Elementary Mathematics Endorsement: Rational Numbers and Proportional Reasoning. These microcredentials can be earned in any order.
To earn this microcredential you will need to collect and submit three sets of evidence demonstrating your effective and consistent use of appropriate instructional strategies for teaching addition and subtraction with rational numbers. You will also complete a short written or video reflective analysis.
Students benefit from opportunities to work with addition or subtraction of rational numbers in real world context. As they work through different representations of addition and subtraction of rational numbers, students determine when procedural thinking is appropriate and how numerical representations and procedures have meaning rather than simply being a disassociated set of steps to follow.
Addition and subtraction with rational numbers includes the following:
A rational number is any number that can be expressed as a fraction or ratio of two integers. For example, 3/4, 8.75, 2, and -6 are all considered rational numbers. Note that integers, or "whole numbers", are rational numbers. This is because they can be expressed as fractions.
Mrs. Spencer is ready for her students to start to think about adding and subtracting rational numbers. She presents them with a problem to find a solution to. After a party, Bob had 2/8 of a pan of brownies left over in one pan and ¼ of a pan of brownies left over in a pan. He put the brownies together in one pan. How much of a pan of brownies were left over from his party? Students recognized from the context of the story that the two fractional amounts of brownies needed to be combined. Many saw this action as addition. Students tried many different ways to combine the brownies, but the one thing that continued to elude them is how they could “name” the total amount of brownies in the pan. Finally, one student noticed that she could cut the larger piece in half (¼ = 2/8) and then all of the pieces would be the same size. Mrs. Spencer was pleased and plans to pursue the idea of making same sized pieces over the next few days.
Submit TWO of the evidence options to demonstrate your effective and consistent preparation and planning for instruction on addition and subtraction of rational numbers.
Design a unit that could be used in 5th or 6th grade to help students deeply understand the concepts of fraction addition and subtraction. This unit plan should include:
In a separate section of the unit plan, cite the sources you used to develop your explanations. See the Resources section below for examples of sources to cite.
Submit an 8-10 minute video demonstrating your understanding of addition and subtraction of fractions in either 4th or 5th grade across all three domains of understanding (conceptual, representational, procedural). The video should include the following pieces:
Submit an 8-10 minute video demonstrating your understanding of addition and subtraction of decimals in either 5th or 6th grade across all three domains of understanding (conceptual, representational, procedural). The video should include the following pieces:
Submit ONE of the evidence options to demonstrate your effective and consistent implementation of appropriate pedagogical practices for instruction on addition and subtraction with rational numbers.
Submit a lesson plan that demonstrates how you have helped students become proficient in addition and subtraction of fractions or addition and subtraction of decimals. The lesson plan should clearly illustrate how the instruction effectively helps students progress from conceptual understanding towards procedural fluency. The lesson plan should include the following:
In a separate section of the lesson plan, include citations for research supporting your instructional approach. (See the resources section for examples to cite.)
Teach a lesson focused on some aspect of fraction or decimal addition and/or subtraction. Using student work as a formative tool, find a misconception that needs to be addressed. In your submission:
Criterion 1: Evidence demonstrates an understanding of a clear learning trajectory that helps students move from conceptual understanding to procedural fluency.
Criterion 2: Evidence demonstrates the candidate's understanding of fraction and decimal concepts.
Criterion 3: Evidence demonstrates the understanding of and use of effective teaching practices designed to help students understand fraction and decimal concepts.
What effect does a deficit in addition and subtraction of rational numbers have on students’ math success in future grade levels? Include at least one example standard and how that standard is affected by concepts.
Reflect on the changes you will make in your practice based on your engagement with this microcredential.
Criterion 1: The reflection indicates that the educator understands concepts founded in addition and subtraction of rational numbers.
Criterion 2: The reflection indicates that the educator understands the impact/importance that adding and subtracting rational numbers has on future success in mathematics.
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