Integers Unit
Big Ideas,
Learning Goals, & Related Skills
Big Ideas:
GLCEs:
Assessment Plan Analysis
Differentiating Instruction
Extra Materials/Tasks
Big Ideas:
- Students will develop a meaning for integers by understanding real world examples of positive and negative numbers, such as temperature
- Students will be able to compare integer quantities by using positive and negative numbers in computations.
GLCEs:
- N.FL.06.09 Add and multiply integers between -10 and 10; subtract and divide integers using the related facts. Use the number line and chip models for addition and subtraction.
- N.MR.06.08 Understand integer subtraction as the inverse of integer addition. Understand integer division as the inverse of integer multiplication.
- N.ME.06.17 Locate negative rational numbers (including integers) on the number line; know that numbers and their negatives add to 0, and are on opposite sides and at equal distance from 0 on a number line.
- N.ME.06.20 Know that the absolute value of a number is the value of the number ignoring the sign; or is the distance of the number from 0.
- N.ME.06.05 Order rational numbers and place them on the number line.
- A.FO.06.11 Relate simple linear equations with integer coefficients, e.g., 3x = 8 or x + 5 = 10, to particular contexts and solve.
- SWBAT compare and order integers and determine absolute value
- SWBAT use integer chips to model integer addition, subtraction, multiplication and division
- SWBAT add, subtract, multiply and divide integers
- SWBAT solve one step equations with integers
Assessment Plan Analysis
- The pre-assessment tested student’s knowledge of number lines, adding, subtracting and multiplying integers, using integers in equations and ordering integers from least to greatest. Although it did not test any high order math skills or use of integer chips, this is okay because students have yet to learn about chips or about integer concepts enough to complete these tasks successfully.
- The formative assessments are given after each section is taught to assess whether students understood the lesson for that day. The textbook, Holt Mathematics, is designed around Michigan’s GLCES making it easy for teachers to teach the necessary concepts to students. The formative assessments that go along with each section allow me, as the teacher, to know whether or not students are meeting a GLCE and whether or not it requires more attention.
- For formative assessments, I will also be using integer chips that are recommended in the lab section of the textbook. We will practice using this model throughout the unit so students have a tangible reinforcement of the concept of integers.
- Formative assessments will also appear as short quizzes. The problems from these quizzes will be taken directly from homework. Students won’t be tricked or see something they haven’t seen before. I will give one after learning about adding and subtracting integers, another after multiplying and dividing integers and then another with equations with integers. Each quiz will have some information from the previous quiz; i.e. the multiplying and dividing quiz will have a few adding and subtracting problems as well.
- The summative assessment will be a test that looks at each objective taught. I will be using the Ready To Go On format, but adding an integer model question and a real world (problem solving) question to gauge whether or not students can apply these concepts to more complex ideas. These questions will be directly tied to the GLCEs and objectives.
- In order to be successful in these assessments, students will have to be successful when learning the concepts in each section. The textbook comes with PowerPoints that guide instruction and give students the students opportunities for practice. This practice is then extended to the worksheets. We will also be solving more complicated questions together (as whole group instruction) and manipulating integer chips to represent positive and negative numbers. All of these activities combined will prepare students for success when it comes time for the summative assessment at the end of the unit.
- I expect students to struggle the most with subtracting integers and solving equations using integers. These concepts can be tricky to students first experiencing them and may require more in-depth teaching. Using integers chips and real world examples will be helpful for students and will not only be fun but somewhat easy too. I also think adding and multiplying/dividing won’t be too difficult for students. It may take a little practice at first, but I anticipate overall success in these areas.
- My formative assessments are easy to grade and not long in volume. I believe they will give me access to student’s ability in a wide variety of problems and will allow me to make decisions about whether or not students need more time on a specific concept. This could be as specific as subtracting integers. If students really struggle in this area, we can spend extra time practicing with chips or using in depth discourse.
- Students are required to do a certain amount of reading when it comes to problem solving assessments. The problems sometimes require translating math problems from words to numbers. I have already created an aid at each table that lists different words that mean each operation. If a student is consistently successful when completing numbers-only problems but makes careless mistakes when solving word problems, it may be the reading that is the issue. I could offer these students a different formative assessment (we have many different levels) that will tell me more about their abilities. I could also form higher order problems with very little words and see how the student does on these problems. From there I can assess if it is a reading issue or a conceptual knowledge issue.
- The learning styles emphasized by these assessments include auditory, kinesthetic, visual and logical learning styles. We’ll talk about math concepts, manipulate objects to reinforce these concepts, look at diagrams and compute problems about integers. I could also have students work in groups for the interpersonal learners. I am not sure if there is a musical way to represent integers, but this would be another learning style I could attend to with the right resources.
Differentiating Instruction
- I know that my ASD students are visual learners. These students learn and see in pictures. Using aids like number lines and chips will help these learners see the concepts around integers in a way that will support their learning. I will also need to remember to keep my words to a minimum since this can be confusing for them. Giving concise, explicit directions is the best way for me to maximize their success.
- I am also aware that I have many Title 1 students in my classroom. These students are not reading and comprehending at grade level. This may mean that long word problems are setting them up for failure. By giving them word problems that aren’t lengthy or tricky, I can still access their conceptual learning without demanding too much of their comprehension skills.
- I can think of a few students who struggle mathematically. Sometimes, these students will need more help when completing formative assessments. They will require me to be available to answer their questions and check their progress to make sure they’re on the right track. Some students still struggle with adding while others are not at a level developmentally that abstract thinking comes easy. Creating activities in class to show concepts in tangible ways will help these students if they are struggling to understand.
- If students are more successful than I originally suspected, I may have more time to test their high-order thinking with open-ended word problems and discourse. Through this model, struggling math students will also be given more insight on the ways to think about these problems and how good math learners combine knowledge of different math concepts to reach an answer.
Extra Materials/Tasks
- Bring a thermometer, talk about sea-level, digging a hole with a ladder, underground parking, etc are some ideas to build an activity with shifts one way, and back again. Play banker with monopoly money and introduce the concept of owing
- http://www.youtube.com/watch?v=kOLfvdEv0yM
- http://www.youtube.com/watch?v=6EWq9EZmIKg&feature=related