Mathematics What’s different with the EIC? EIC aligned to Common Core State Standards Mathematical Practices Formative assessments organized by categories Fewer standards and categories to reflect the K-5 emphasis on number sense Standard algorithms for addition and subtraction in Grade 4
Understanding – Comprehending mathematical concepts, operations, and relations – knowing what mathematical symbols, diagrams, and procedures means. Computing – Carrying out mathematical procedures, such as adding, subtracting, multiplying, and dividing numbers flexibility, accurately, efficiently, and appropriately. Applying – Being able to formulate problems mathematically and to devise strategies for solving them using concepts and procedures appropriately Reasoning – Using logic to explain and justify a solution to a problem or to extend from something known to something not yet known. Engaging – Seeing mathematics as sensible, useful, and doable – if you work at it – and being willing to do the work.
Contents understandings build upon each other. “Conceptual understanding is not an option, it’s an expectation.” – Skip Fennell
Result UnknownChange UnknownStart Unknown Add To 6 children are on the bus. 8 more children get on the bus. How many children are on the bus now? 6 + 8 = ___ From: Grade 1, MP3 FormativesMP3 Formatives Morgan packed 5 toys in the morning. She packed some more toys in the afternoon. Now she has 13 toys packed for her trip. How many toys did Morgan pack in the afternoon? 5 + ___ = 13 13 – 5 = ___ From: Grade 1, MP2 W3 SLTMP2 W3 Lorie saw some birds in her yard yesterday. Today she saw 12 birds. She saw a total of 20 birds on both days. How many birds did Lorie see yesterday? ___ + 12 = 20 20 – 12 = ___ From: Grade 1, MP2 FormativesMP2 Formatives Take From Mia had 13 pencils. She gave 4 pencils to her friend. How many pencils does she have now? 13 – 4 = ___ 4 + ___ = 13 From: Grade 1, MP2 FormativesMP2 Formatives Verna has 10 stickers. She gave some to Tony. Now she has 4 stickers left. How many stickers did she give to Tony? 10 – ___ = 4 From: Grade 1, MP2 W5 SLTMP2 W5 Some dogs were playing in the park. 11 dogs left. Then there were 7 dogs. How many dogs were in the park before? ___ – 11 = 7 7 + 11 = ___ From: Grade 1, MP2 W7 SLTMP2 W7 Total UnknownBoth Addends UnknownAddend Unknown Put Together/ Take Apart Adam has 5 baseballs and 3 soccer balls. How many balls does he have altogether? 5 + 3 = ___ 3 + 5 = ___ From: Grade 1, MP2 FormativesMP2 Formatives Omar has 14 pencils. How many can he keep at home and how many can he take to school? 14 = ___ + ___ From: Grade 1, MP2 W4 SLTMP2 W4 Morgan picked 15 apples. Nine of the apples were red. The rest of the apples were green. How many apples were green? 9 + ___ = 15 15 – 9 = ___ From: Grade 1, MP2 W4 SLTMP2 W4 These are the four most difficult subtypes that should be introduced in Grade 1, but which students may not master until Grade 2.
Difference UnknownBigger UnknownSmaller Unknown Compare “How many more?” Version The baker makes 7 tarts and 4 sticky buns. How many more tarts does the baker make? 7 – 4 = ___ 7 = 4 + ___ From: Grade 1, MP2 W7 SLTMP2 W7 More Version Eli has 13 dominoes. Kim has 6 more dominoes than Eli. How many dominoes does Kim have? 13 + 6 = ___ From: Grade 1, MP2 W6 SLTMP2 W6 Fewer Version Eli has 13 dominoes. Kim has 6 fewer dominoes than Eli. How many dominoes does Kim have? 13 – 6 = ___ ___ + 6 = 13 From: Grade 1, MP2 W6 SLTMP2 W6 “How many fewer?” Version 4 children are climbing. 9 children are playing basketball. How many fewer children are climbing than playing basketball? 9 = 4 + ___ 9 – 4 = ___ From: Grade 1, MP3 W7 SLTMP3 W7 Fewer Version* Eli has 6 fewer dominoes than Kim. Eli has 13 dominoes. How many dominoes does Kim have? 13 + 6 = ___ More Version* Eli has 6 more dominoes than Kim. Eli has 13 dominoes. How many dominoes does Kim have? 13 – 6 = ___ ___ + 6 = 13 Examples of word problems involving 3 addends: Kacie, Pedro, and Luan have 15 pets all together. Kacie has 6 pets and Pedro has 5 pets. How many pets does Luan have? 15 = 6 + 5 + ___ G1 MP2W8 SLTMP2W8 Chris has 3 comic books. Tony gives him 5 comic books. How many more comic books does Chris need to have 11 comic books altogether? 3 + 5 + ___ = 11 G1 MP2W9 SLTMP2W9 These are the four most difficult subtypes that should be introduced in Grade 1, but which students may not master until Grade 2.
Kindergarten1 st Grade2 nd Grade 1.K.B.2 Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem 1.1.B.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.1.B.2 Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. 1.2.B.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.
3 rd Grade4th Grade5 th Grade 1.3.B.6 Understand division as an unknown-factor problem. For example, divide 32 ÷ 8 by finding the number that makes 32 when multiplied by 8. 1.3.B.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. 1.3.B.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 1.4.B.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 x 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of multiplicative comparisons as multiplication equations. 1.4.B.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison. 1.4.B.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. 1.5.B.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. 1.5.B.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product. 1.5.B.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
The Common Core State Standards were only written for mathematics, reading, and writing. The science and social studies curricula were written using the Maryland State Curriculum (that used to be the Voluntary State Curriculum). Students in Grade 5 will continue to take Science MSA in the spring. Science and Social Studies were taught in isolation and now they are integrated into reading and writing. Science now includes an engineering component emphasizing STEM activities.
Reading What’s different with the EIC? Complexity: The standards require regular practice with complex text and its academic language Evidence: The standards emphasize reading and writing grounded in evidence from text, both literary and informational Knowledge: The standards require building knowledge through content rich literature Whole group lessons connected with content
What’s different in writing? Writing in response to content stimuli Writing in response to content stimuli Topic choice for writing often suggested Topic choice for writing often suggested Up to three writing purposes in every marking period…opinion, narrative, informational/ explanatory Up to three writing purposes in every marking period…opinion, narrative, informational/ explanatory Writing in response to literature, integration with information literacy…research Writing in response to literature, integration with information literacy…research Use of new technology Use of new technology
Collaboration – Working effectively and respectfully to reach a group goal. Effort/Motivation/Persistence – Working diligently and applying effective strategies to achieve a goal or solve a problem; continuing in the fact of obstacles and competing pressures. Intellectual Risk Taking – Accepting uncertainty or challenging the norm to reach a goal. Metacognition – Knowing and being aware of one’s own thinking and having the ability to monitor and evaluate one’s own thinking.
Elaboration – Adding details that expand, enrich, or embellish. Flexibility – Being open and responsive to new and diverse ideas and strategies and moving freely among them. Fluency – Generating multiple responses to a problem or idea. Originality – Creating ideas and solutions that are novel or unique to the individual, group, or situation.
Analysis – Breaking down a whole into parts that may not be immediately obvious and examining the parts so that the structure of the whole is understood. Evaluation – Weighing evidence, examining claims, and questioning facts to make judgments based upon criteria. Synthesis – Putting parts together to build understanding of a whole concept or to form a new or unique whole.