GradeDomain KCounting & Cardinality K-5Operations & Algebraic Thinking Number & Operations in Base Ten Measurement & Data Geometry 3-5Number & Operations – Fractions 6-8Ratios & Proportional Relationships The Number System Expressions & Equations Geometry Statistics & Probability 8Functions Domains of the Common Core State Standards (CCSS) for Mathematics
The CCSS Requires Three Shifts in Mathematics 1.Focus: Emphasize key areas of instruction, focus on standards. 2. Coherence: Think across grades, and link to major topics. 3. Rigor: In major topics, pursue conceptual understanding, procedural skills and fluency, and application.
Standards for Mathematical Practice Habits of Mind of a Productive Mathematical Thinker MP. 1 Make sense of problems and persevere in solving them. MP. 6 Attend to Precision Reasoning and Explaining MP. 2 Reason abstractly and quantitatively. MP. 3 Construct viable arguments and critique the reasoning of others. Modeling Using Tools MP. 4 Model with mathematics. MP. 5 Use appropriate tools strategically Seeing Structure and Generalizing MP. 7 Look for and make sense of structure. MP. 8 Look for and express regularity in repeated reasoning.
What can I expect to see… in the classroom Teaching to mastery Concrete-pictorial-abstract model Differentiation Intentional progression of skills
ETSD Focus for Math Continued transition to Math in Focus Increased emphasis on problem solving Continued focus on number and operation (elem.-base ten, algebraic thinking & fractions; middle – number system, expressions & equations) Increased emphasis on geometry & data Integration of Math Practice Standards (reason abstractly, demo. perseverance)
Grade: Sixth Grade 5 Material Mastered Multiplication & division of whole numbers, fractions, decimals Solve one step equations using inverse operation Bar Model Technique Topics Emphasized Number system includes positive & negative numbers Dividing by fractions Ratio, Rates, Percents Expressions & inequalities Manipulatives Concrete materials and visuals should still be incorporated Utilize Virtual Manipulatives Algebra tiles, unit cubes, and counters Bar Models Bar Modeling technique should be emphasized Use previous grade materials for support as needed (e.g. Reteach, Extra Practice), as well as Transition Guide 6
Skill Trace: Multiplication Grade 1 - Adding the Same Number Big Idea: Multiplying is the same as adding equal groups. 2 + 2 + 2 means 3 twos or 3 groups of 2.
Skill Trace: Multiplication Grade 2 - How to Multiply Big Idea: Multiplication and division use equal groups. 5 + 5 + 5 = 3 x 5
Skill Trace: Multiplication Grade 3 - Multiplication Big Ideas: Many models can be used to multiply, including mental math. Numbers up to 3 digits can be multiplied with or without regrouping. 5 x 6 = ? 5 rows of 6 = 30
Real World Multiplication Problems Grade 3, Unit 9 Two-step Problems Using Bar Modeling Multiplication in Action
Anchor Task: One bag of peanuts costs $5. Alicia wants to buy 8 bags but she only has $33. How much more money does she need? Part 1: What else do we need to know? ? $5
One bag of peanuts costs $5. Alicia wants to buy 8 bags but she has only $33. How much more money does she need? Part 2: Now we can solve.. If 8 bags will cost $40 and she only has $33. How much more money does she need? 40 -33 $7 $40 $33 ?
Let ’ s Practice Pat is 12 years old. James is 3 times as old as Pat. Raymond is 9 years younger than James. How old is Raymond? Pat James Raymond
Solution Pat is 12 years old. James is 3 times as old as Pat. Raymond is 9 years younger than James. How old is Raymond? 12 36 9 ? ? = 27 Pat James Raymond
Skill Trace: Multiplication Grade 4 - Whole Number Multiplication Big Ideas: Place value is used to multiply and divide multi-digit numbers. Estimation can be used to check the reasonableness of an answer.
Skill Trace: Multiplication Grade 5 - Multiplying Fractions, Mixed Numbers & Decimals Big Ideas: Patterns can be used to help multiply and divide numbers. Multiplication can be used to solve real-world problems. Whole numbers, fractions, and mixed numbers can be multiplied or divided in any combination. Decimals can be multiplied in the same way as whole numbers.
What can I expect to see… at home Same math, different focus -Focus on understanding, as opposed to memorization -More rigorous tasks Math talk -More focused vocabulary -Explanation of answers Independent practice of concepts -Homework -Games Online resources (Think Central) -Student textbook -Background videos/podcasts -Virtual manipulatives
Technology Resources Think Central (Grades K-5) https://www-k6.thinkcentral.com Houghton Mifflin Harcourt: Singapore Math http://www.hmhco.com/shop/education- curriculum/math/math-in-focus-singapore-math
Recommended Websites/Apps Arcademic Skill Builders ( http://www.arcademics.com/) http://www.arcademics.com/ Calculation Nation ( http://calculationnation.nctm.org ) http://calculationnation.nctm.org Cool Math ( http://www.coolmath4kids.com) http://www.coolmath4kids.com Fun 4 the Brain ( http://www.fun4thebrain.com/) http://www.fun4thebrain.com/ IXL (http://www.ixl.com/Math)http://www.ixl.com/Math Math Bingo ( http://www.abcya.com/math_bingo.htm) http://www.abcya.com/math_bingo.htm Math Playground ( http://www.mathplayground.com/) http://www.mathplayground.com/ National Council for Teachers of Mathematics ( http://www.nctm.org/mobileapps/) http://www.nctm.org/mobileapps/ Splash Math ( https://www.splashmath.com/) https://www.splashmath.com/ Thinking Blocks ( http://www.thinkingblocks.com ) http://www.thinkingblocks.com
The Butterfly What can we learn from the development of a butterfly? First there is the egg which hatches into a caterpillar. The caterpillar eats and grows. At the right time, it makes a chrysalis out of its own body. While in the chrysalis, the caterpillar changes into a butterfly. When the butterfly is ready, it starts to break through the chrysalis. First, a small hole appears. The butterfly is then forced to struggle to come through the hole. This can take some time. If you try to “help” the butterfly by cutting the chrysalis, the butterfly will come out easily but it will never fly. Your “help” has destroyed the butterfly. The butterfly can fly because it has to struggle to come out. The pushing forces lots of enzymes from the body to the wing tips. This strengthens the muscles, and reduces the body weight. In this way, the butterfly will be able to fly the moment it comes out of the chrysalis. Otherwise it will simply fall to the ground and soon die. If the butterfly is not left to struggle to come out of the chrysalis, it will never fly. We can learn an important lesson from the butterfly.
Reflection Use the exit slip, to reflect back on tonight’s presentation and leave it by the door on your way out. Thank you for attending this evening!