Recognize angles as geometric shapes that are formed wherever two rays share a common endpoint, and understand concepts of angle measurement.
This concept will be utilized and reminded throughout the unit. It is specifically addressed during the first two lessons when the concept of what an angle is, is being introduced.
Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
These concepts will be utilized and the vocabulary will be encouraged to be used during discussions and explanations throughout the entire unit. The vocabulary will be specifically taught during the first two lessons.
An angle is measured with reference to a circle with its center at the common endpoint of the rays, by considering the fraction of the circular arc between the points where the two rays intersect the circle. An angle that turns through 1/360 of a circle is called a “one-degree angle,” and can be used to measure angles.
Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.
The ability to add and subtract ( and multiply or divide) angle measures will be introduced and used past lesson five. The students will learn to draw the angle/diagram to then take the information then know to fill in the equation.
Measure angles in whole-number degrees using a protractor. Sketch angles of specified measure.
The students will be using a hands on protractor during the fourth lesson in this unit. From lesson four on the students will occasionally practice with a hands on protractor, but will complete the majority of their practice with various types of digital protractors.
Through a game students will practice drawing a specified angle measure, they will also be asked to complete this during class discussion and partner questions.
CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Towards the end of this unit students are consistently reading information given in a problem, interpreting what the information is telling them and then sorting the information into an equation to eventually solve. For many students these types of problems will require a great deal of perseverance.
CCSS.MATH.PRACTICE.MP2 Reason abstractly and quantitatively.
The last few lessons in this unit will give students information about specific angles, some will have a diagram some will not. The student will be required to reason abstractly, meaning in a way which is not right in front of them and is a different way of thinking. The students will need to think quantitatively because in order to check their work or use reason they must understand the quantity of certain angles and use that knowledge to reason if they are at least in the ballpark.
CCSS.MATH.PRACTICE.MP4 Model with mathematics.
This unit requires students to use multiple types of manipulative and draw diagrams to help them solve. In order to be successful in a deep understanding of these concepts most students will need the use of this model.
CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
This unit design will include group and partner discussions of most of the problems. After providing an answer I will ask the rest of the group if they agree or disagree. If the students disagree they will be asked to re-explain or expand.
CCSS.MATH.PRACTICE.MP6 Attend to precision.
For of this unit students will be asked to estimate many angle measures, however while using a protractor the students will be asked to be precise in their found measurements. In addition to this students will need to be specific about the reasoning they use when adding and subtracting angles. During these types of questions students will need to have the exact answer because if they do not, this means that they are making a miscalculation or are misunderstanding the question.
SS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
During this unit students will use pattern blocks, protractors, graph paper, diagrams, and rulers throughout the unit. The students will be taught how to use how to use each tool, and then these tools will be available to the students at all times after being taught how to use them. When presenting a problem the students will be asked how they would like to go about solving such a problem.
CCSS.MATH.PRACTICE.MP7 Look for and make use of structure.
This unit will contain the geometric vocabulary the students will be introduced to this in a structured way and the vocabulary will be utilized in a constructive format. This vocabulary and geometric language (angle HAF) will help the students understand what the symbols mean in order to then understand the whole problem.
CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
During these students will need to memorize how much a right and straight angle is worth, from there students will have to realize that this will always be true. When introduced to a problem they will need to look for reasoning based on these pieces of knowledge because in many geometry situations the reasoning will be based on these facts.