Math In Service Goals Fluency Basic facts Fluency

Math In – Service

Goals ~ • Fluency: Basic facts • Fluency: Procedures and Computation • Improved Vocabulary • Conceptual Understanding • Improved Problem Solving

Required Fluencies When it comes to measuring the full range of standards, usually the first thing that comes to mind are content standards that call for conceptual understanding. However, the standards also address another aspect of mathematical attainment namely; whether students can perform calculations and solve problems quickly and accurately.

Basic Facts and Procedures Resources v. Flash Cards v. Facts Practice v. Computer games v. Acel Math v. Simple Solutions

Assessing Basic Facts q. Pre test/Post tests q. Quizzes q. Exit Tickets

Basic Computation and Procedures v. Simple Solutions v. Accelerated Math v. Interventions and Remediation v. Khan Academy

Vocabulary, Signs and Symbols • Journals • Posters • Word Wall

Linking Concepts and Fluency For grades 1 through 4, basic facts for all four operations are major parts of thematics curriculum. "What is 6 + 7? " Although we eventually want computational fluency by our students, an initial explanation might be : "I know that 6 + 6 = 12; since 7 is 1 more than 6, then 6 + 7 must be 1 more than 12, or 13.

Linking Concepts to Procedures Alexa ate 2/6 of a chocolate cake and Steven ate 6/10 of a strawberry cake. How much was eaten altogether? Student answer: 3/5 + 6/10 = 9/15 This reasoning is common. Why?

Linking Concepts to Procedures The student is probably trying to devise a procedure to add fractions and is making a mistake most likely comes from misapplication of whole-number knowledge to fractions. What might be a good strategy to demonstrate this concept?

Conceptual Understanding and Estimation In grades 5 through 6, operations with decimals are common topics. "What is 6. 345 x 5. 28? " A student has conceptual understanding of the mathematics when he or she can explain that 335. 016 cannot possibly be the correct. Why?

Linking Concepts to Procedure Why the change of mean, mode, median and range to grade 7 and 8? Isn’t this an easy concept?

Linking concept to Procedures? Theo scores 81, 79, 84, 86 and 81 on 5 math tests. He scores a 51 on his next test. Without computing the mean, median, mode or range, tell how his last grade will affect each statistical measure. Do you think the average best represents this set of data? Why or why not?

Linking Concepts to Procedures Easy procedures, but more difficulty concepts.

Conceptual or Procedural?

Focus on Problem Solving Guided Discovery

Problem Solving Mathematical Practice #1 Make sense of problems and persevere in solving them.

Problem Solving True or False: Addition, Subtraction, Multiplication and Division are problem solving strategies?

Steps to Problem Solving • • Find the Question(s): Underline Circle Key words and numbers Choose a strategy(ies) Apply the strategy(ies): Show Work Circle your final answer Check: Does my answer make sense? Did I answer the question?

Problem Solving Strategies v Logic v Guess and Check v Number Sentence ( Equation) v Chart v Draw a Picture or diagram v Make a Model v Work Backwards v Find a Pattern v Combo Meal ~ Use more than one strategy

Select strategies Apply the strategy ? Final Answer in proper form. Does it make sense? Did I answer the question? Underline Key words and circle key numbers Calculations/Notes/

Assessment • • • 20 points for the question 30 points for the strategy 30 points for the application 10 points for work 10 points for the final answer

Assessmsnts Summative assessments vs Formative assessments,

Formative Assessments Formative assessments: collecting information that can use to improve instruction and student learning while it’s happening. q Provides information on what the students understand q Reveal misconceptions q Occurs as part of daily instruction q Guides instruction and planning

Formative Assessments Formative assessments have the goal of providing feed back: Feedback to students to increase understanding and Feedback to teachers to improve planning and instruction

Formative Assesments • There are 30 cubes that make up a train. Each cube is ¾ inches long. How long is the train when all 30 cubes are snapped together? • Provide 2 strategies to solve this problem.

Summative Assessments are used to evaluate student learning, skill acquisition, and academic achievement at the conclusion of a defined instructional period—typically at the end of a chapter, project, unit, course, semester, program, or school year. Generally speaking, summative assessments are defined by three major criteria:

Summative Assessments The tests, assignments, or projects are used to determine whether students have learned what they were expected to learn or to determine whether and to what degree students have learned the material they have been taught.

Summative Assessments Summative assessments are given at the conclusion of a specific instructional period, and therefore they are generally evaluative. They determine progress and achievement,

Summative Assessments Summative assessment results are often recorded as scores or grades that are then factored into a student’s permanent academic record. They end up as letter grades on a report card or test score.

Summative Assessments While summative assessments are typically a major component of the grading process in most districts, schools, and courses, not all assessments considered to be summative are graded. What are some examples? •

Formative vs Summative In other words, formative assessments are often said to be for learning, while summative assessments are of learning

Bloom’s Taxonomy Create Evaluate Apply Understanding Remembering

Summative Assessments • Questioning is a potentially powerful tool that teachers can use to help students better understand academic content and to assess student understanding. • Summative Assessments need to include all levels of questioning.

Types of Questions Matching • Good for: • Remembering, Understanding Application, Analysis, and Evaluation levels • Types: • Question/Right answer • Incomplete statement • Best answer

Types of Questions True/False • Good for: • Remembering and Understanding • Evaluating student understanding of popular misconceptions • Concepts with two logical responses • Advantages: • Can test large amounts of content • Students can answer 3 -4 questions per minute

Types of Questions Completion • Good for: • Remembering and Understanding level • • • Types: Terms with definitions Phrases with other phrases Parts with larger units Problems with solutions

Types of Questions Multiple Choice Good for: • Application, synthesis, analysis, and evaluation levels • • Types: Question/Right answer Incomplete statement Best answer

Types of Questions Short Answer • Good for: • Application, synthesis, analysis, and evaluation levels • • • Advantages: Easy to construct Good for "who, " what, " where, " "when" content Minimizes guessing Encourages more intensive study-student must know the answer vs. recognizing the answer.

Type and Level? In the equation below, what is the value of ? (2 + 4) × 5 = ? + 20 Darline has a special purse that can hold 20 lipsticks. How many purse does Darline need if she has 420 lipsticks? A. 20 B. 22 C. 23 D. 21

Type and Level? • Represent the following situation with an integer. Then put them in order A loss of 12 dollars ______ 5 feet above sea level ______ a debit of 20 dollars ______ A gain of 50 dollars ______

• Add 2/3 and 5/6 _______ Write the answer for number 10 as a mixed number _________ Write the answer for number 10 in lowest terms _________

• What information could you find with the following situation? Noemy bought a box of apples for $4. 20. She now has $2. 35 in her purse. A. Noemy's allowance every month B. How much the apples cost C. How much money Noemy had before buying the apples D. How many apples are there in the box

• You want to share 1000 dollars between you and 5 friends. Can you share the money evenly? What is the maximum amount that can be shared evenly? What is then the leftover as a fraction?