Understanding the Transition to the Updated MA Math

Understanding the Transition to the Updated MA Math Standards in K-5

Key Shifts Frameworks have two components: mathematical content and mathematical practices Content: increased focus on critical areas Practice: K-12 Standards of Mathematical Practice

Supporting Changes in Practice The new standards support improved curriculum and instruction due to increased: FOCUS, via critical areas at each grade level which narrow and deepen the scope of the work COHERENCE, through carefully developed connections within and across grades CLARITY, with precisely worded standards that describe the desired understandings RIGOR, including a focus on application of math skills in context and Standards for Mathematical Practice throughout Pre-K-12

K-8 Content Shifts K-2: focus on place value, systems of tens, and addition and subtraction. 3 -5: focus on multiplication and division (with place value emphasis) and fractions. 6 -8: larger focus on probability, statistics, and geometry, in addition to pre-algebra/algebra concepts.

Organized by Domains Rather than Strands Pre-K-8 Domains Progression Domains PK K 1 2 3 4 5 6 7 8 Counting and Cardinality MA Operations and Algebraic Thinking MA Number and Operations in Base Ten Number and Operations - Fractions Ratios and Proportional Relationships The Number System MA Expressions and Equations Functions Geometry MA Measurement and Data MA Statistics and Probability

A Small Example of Coherence Through the Grades Operations and Algebraic Thinking Pre K Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (using concrete objects with numbers up to 5) K Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from. (using objects, drawings and words with numbers up to 10) 1 Represent and solve problems involving addition and subtraction. (using objects, drawings and equations with an unknown number with numbers up to 20) 2 Represent and solve problems involving addition and subtraction. (one and two step problems with numbers up to 100) 3 Represent and solve problems involving multiplication and division. (using drawings and equations to solve problems within 100) 4 Use the four operations with whole numbers to solve problems (solve multi-step problems with 4 operations including remainders) 5 Write and interpret numerical expressions (use parentheses and operations to write expressions and evaluate them)

An Example of Increased Focus and Clarity Grade 1/2 Span (MA 2000) Massachusetts Grade 2 (January 2011) Comment 2. OA. 4 Use addition to find the total number of 2. G. 7 Relate geometric objects arranged in MA 2011 includes ideas to numbers, e. g. , rectangular arrays with up expressing repeated seeing rows in an array as to 5 rows and up to 5 addition as an equation a model of repeated columns; write an equation and limits size of arrays to addition. to express the total as a 5 x 5 sum of equal addends.

Standards of Mathematical Practice 1. Make sense of problems and persevere in solving them 2. Reason abstractly and quantitatively 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics 5. Use appropriate tools strategically 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Let’s Practice This year I am 4 times the age of my son. My husband, who is a year older than me, is 3 times the age of our older daughter. My younger daughter’s age is the average of the other two children and her age is a whole prime number. What are the ages of my family members this year?

Practice Standards Compared with Habits of Mind Standard of Mathematical Practice Student Friendly Language Make sense of problems and • persevere in solving them • • Construct viable arguments • and critique the reasoning of others • Associated Habits of Mind Understand what is being asked Find ways to model the situation Identify strategies for solving Check if the answer makes sense Find a different strategy when needed • • Persisting Managing impulsivity Thinking Flexibly Applying past knowledge to new situations Communicate mathematical reasoning and ideas using words, numbers, and/or pictures. Understand give feedback on other students’ ideas • Listening with understanding and empathy Thinking flexibly Metacognition Questioning and problem posing Thinking and communicating with clarity and precision • •

New Conference Reports Grade 2 Mathematics ELE DRAFT Mathematical Practices Makes sense of problems and perseveres in solving them. Communicates mathematical reasoning and ideas using words, numbers, and/or pictures. Operations and Algebraic Thinking Represent and solve problems involving addition and subtraction. Add and subtract within 20. Work with equal groups of objects to gain foundations for multiplication. Number and Operations in Base Ten Understand place value. Uses place value understanding and properties of operations to add and subtract. Measurement and Data Measure and estimate length in standard units; Relate addition and subtraction to length. Work with time and money. Represent and interpret data. Geometry Reason with shapes and their attributes.

What can a parent do to help? Ask good questions! Help students communicate mathematically. Encourage perseverance and problem solving. Make connections between math and real life situations. Use estimation and mental math. Play games and solve puzzles.

Help your child communicate his/her mathematical reasoning and ideas Move beyond questions that elicit simple yes/no or one word answers. Ask probing questions that promote problemsolving, reasoning, making connections, and reflection. Encourage your child to explain his/her thinking and problem solving.

Help your child make sense of problems and persevere in solving them Avoid solving the problem for your child. Help your child to plan and reflect: What is the problem asking? What do I know? How does this help me make a plan? Use this information to make a plan and stick with it. Evaluate the plan – Do I need to try something else? Is there a more effective or efficient way to get to the answer? Is my answer reasonable? Do I need a new plan?

Make connections between math and real life situations Model your own math thinking and problem solving. Notice out loud when math is used: measuring for recipes, sewing, and woodworking estimating amounts of paint or wallpaper or to hang pictures using the clock to be on time or plan ahead reading schedules for television, bus or movie times shopping

Use estimation and mental math Most ‘real life’ problem solving is done without pencil and paper. Estimation builds number sense and an understanding of landmark numbers. It also promotes flexible thinking and problem solving, and helps students evaluate the reasonableness and accuracy of their answers.

Play games and solve puzzles Have fun with math! Build strategy and problem solving abilities. Develop and reinforce fundamental math skills in fun and engaging ways. Use questioning to promote deeper thinking. Materials can be very simple (cards and dice. ) Check out games from the Math Resource Center.