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Welcome! O Thank you for coming! O Please sign in. Past and Present… O In the past, Math instruction focused on computation. O Now, Math instruction focuses on APPLICATION through the use of critical thinking skills, higher order thinking and depth of knowledge in order to solve/analyze multi-step problems. Fluency By Grade level Grade Standard Required Fluency K K.OA.5 Add/subtract within 5 1 1.OA.6 Add/subtract within 10 2 2.OA.2 2.NBT.5 Add/subtract within 20 Add/subtract within 100 3 3.OA.7 3.NBT.2 Multiply/divide within 100 Add/subtract within 1000 4 4.NBT.4 Add/subtract within 1,000,000 5 5.NBT.5 Multi-digit multiplication 6 6.NS.2,3 Multi-digit division Multi-digit decimal operations At school… Mathematics Teaching Practices: 1 – Establish Mathematics Goals to Focus on Learning. 2 – Implement Tasks that promote reasoning and problem solving. 3 – Use and connect mathematical representations. 4 – Facilitate meaningful mathematical discourse. 5 – Pose purposeful questions. 6 – Build procedural fluency from conceptual understanding. 7 – Support productive struggle in learning mathematics. 8 – Elicit and use evidence of student thinking. Math series Student textbook & practice book Math Chapters- Topic Breakdown Chap. Topic Chap. Topic 1 Number Concepts 7 Time & Money 2 Numbers to 1,000 8 Length in Customary Units 3 Basic Facts & Relationships 9 Length in Metric Units 4 2-Digit Addition 10 Data 5 2-Digit Subtraction 11 Geometry & Fractions Concepts 6 3-Digit Addition & Subtraction During instruction students … O Use the textbook O Use manipulatives and math tools O Use their Math Journals to explore/write about: O O O O O “Essential Question, Problem of the Day, justify their work/answers Use task cards, anchor sheets Participate in “Math Talks” and cooperative learning groups Math drills Computer programs for enrichment/remediation Whole Group/Small group/Independent instruction Three types of Mathematical understanding- CPR O Conceptual -- What do students need to know? O Procedural -- What do students need to do? O Representational -- What do students need to show? How can we get our students to UNDERSTAND math? O Students can understand Math by: building FLUENCY and using STRATEGIES. 3 Elements of Fluency O Accuracy (Correctness) O Efficiency (Quick retrieval of facts both written and oral.) O Flexibility (Use of strategies to help with recall.) O Reading/Writing capability also play a major role. Prerequisites O Before children can conceptually understand addition and subtraction facts they must first have one-toone correspondence, conservation of numbers, and they must know the counting sequence. Counting Sequence O Knowing the counting sequence is as simple as knowing what number comes next. Just because a child knows the counting sequence does not mean that they understand numbers, but it is an important step in the development of numbers. One-to-one Correspondence O Understanding that one item is represented by a unique count. Conservation of Number O The final item counted tells the number in the group. Seven items are counted so there are seven items in the group. Why learn strategies? O Students can develop fluency with their addition and subtraction facts if they memorize strategies such as: the Doubles facts & the Tens facts. The rest of the facts can be derived using strategies. O Efficient use of strategies leads to a better understanding of numbers, and the properties of addition. O Better conceptual understanding promotes long lasting procedural understanding and ultimately results in quick retrieval of all facts. That is the goal. Quick retrieval of all facts. Strategies that promote understanding… “Teachable” moments for parents: Using a hundreds chart to practice counting patterns. Addition Charts Adding Zeros: Identity property of Addition Count on strategy: +/- 1 and 2 Adding Doubles Doubles +/- 1 How does it work? O 6 + 6 = 12 so, O 6 + 7 = 13 because O 6 + 6 + 1 = 12 + 1 = 13 Or O 7 + 7 = 14 so, O 6 + 7 = 13 because O (7 - 1) + 7 = 14 – 1 = 13 Make a ten Add tens and ones Adding tens and ones places an emphasis on place value and expanded form. How does it work? 8 + 6 = 14 Use a visual model to promote “Cardinality”. Cardinality is recognizing a number by the configuration – no counting needed. 8 + (2 + 4) = 14 Decompose 6 into 2 and 4 (8 + 2) + 4 = 14 Use the Associative Property to make a ten with 8 and 2 10 + 4 = 14 Now the number is in expanded form and place value makes it easy to add. Subtraction O Think addition when solving subtraction problems. Fact families and related math facts. O 9 – 5 = 4 because O5 + 4 = 9 Equal Groups O Sarah has three pages of stickers. There are four stickers on each page. How many stickers are there? Array Model O Max made three rows of tiles. He put four tiles in each row. How many tiles are there? What to Do When Teaching Basic Facts O Develop conceptual understanding using O O O O O O O O strategies Ask students to self-monitor Focus on self-improvement Drill in short time segments Work on facts over time Involve families Make practice/drill enjoyable Use technology Emphasize the importance of quick recall of facts More “to Do-s”… O Practice makes BETTER! O Use manipulatives, anchor sheets, & task cards. O SHOW YOUR WORK! O Explain your answer. Know the “WHY” Attack Word Problems with CUBES… C U B E S Circle the numbers Underline important words/math vocabulary Box the question Evaluate the information Solve the problem Build Math Vocabulary Addition Words Subtraction Words Add Plus All together Total Combine Gets More join Sum Difference Minus Subtract Less How many more? How much more? How many were left? What Not to Do When Teaching Basic Facts O Don’t use lengthy drilling O Don’t proceed through the facts in order from 0 to 9 O Don’t move to memorization too soon O Don’t use facts as a barrier to good mathematics Remediation O Focus on reasoning strategies O Recognize that more drill will not work O Provide hope O Inventory the known and unknown facts O Diagnose strengths and weaknesses O Build in success O Provide engaging activities TESTING O Second Grade- SAT O Third Grade-FSA SAT- The Math portion of the SAT is auditory. Questions are read aloud to students. FSA- Third Grade Sample Page Looking ahead to Third Grade… O Upon entering third grade, your child should have 1. 2. 3. 4. 5. show mastered: Adding/subtracting with regrouping Telling time Counting money Estimating 10-100 Math operations Start practicing multiplication BEFORE the third grade school year; during the summer. Promote good study habits. Third Grade FOCUS Here are some strategies that will help your child get ready for third grade. Multiplying Zeros Multiply by 1: Multiplicative Identity Multiply by 2: Doubling 2 x 8 = 8 + 8 = 16 Multiply by 10 Multiply by 5 Division O Think multiplication when solving division problems. O 24 ÷ 6 = O 6 x __ = 24 Resource Websites O www.flstandards.org O www.dadeschools.net O www.iReady.com O www.ixl.com O www.thinkcentral.com O www.brainpopjr.com Contact me with questions Email: [email protected]