MATHEMATICS GRADE 1 UNIT 1 BUILDING CULTURE AND ESTABLISHING STRUCTURE: A WEEK OF INSPIRATIONAL MATH “This week is about inspiring students through open, beautiful and creative math. We have chosen the different tasks so that students see math as a broad, interesting and visual subject that involves deep thinking. Students will learn important growth mindset messages that will help them feel confident, try harder all year, persist with open and difficult problems and embrace mistakes and challenge. All tasks are low floor and high ceiling – they are accessible to all students and they extend to high levels.” (Jo Boaler, youcubed.org) K­2nd 3rd­5th 6th­8th Week of Inspirational Math for Primary Grades: https://drive.google.com/open?id=19BpgpJnxTnmiBtvbJ_weVPKUHJvf
HAuPbMmSJD9I7lA youcubed.org (must register for lesson access: use Grades 3­4 lesson plan & media) youcubed.org (must register for lesson access: use Grades 5­9+ lesson plan & media) PLANNING FOR MATHEMATICAL EQUITY & ACCESS POINTS Backwards Mapping ●
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Identify the Learning for the UNIT of instruction Determine Success Criteria How will we ensure a balance of conceptual, procedural, and application of mathematics learning? How will I connect the math learning using progressions so there is a better understanding? Anticipate student learning, multiple representations, misconceptions/errors How will we ensure the mathematical practices are evident in the learning? Build on what they already know Environmental ●
How will we ensure students are engaged in a 21st Century Learning Environment to include collaboration, creativity, critical thinking, communication. . . Establish and practice structures As a team, what structures will be in place to ensure our students are provided a positive math culture, environment, and experience around mathematics. How do we ensure a positive math culture where students can feel comfortable and have a growth mindset ●
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Language ● What language will students utilize to support content and language demands? ● Plan for academic conversations ● What vocabulary, sentence structures and language functions will students need to master? ​
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FUNCTION PLANNING FOR MATHEMATICAL EQUITY & ACCESS POINTS (continued) Instructional ●
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Set Purpose, Goals, Expectations, Objectives. How will students be engaged in behaviors that promote the mathematical practices? Prepare for think alouds and modeling that will be most effective. What questions, prompts, and cues will we use? What resources will I utilize? (framework, tasks, videos, thinking maps, text, ...) Promote perseverance Use the Gradual Release of Responsibility (GRR) and give students opportunity to enter at different points Make connections between different representations Allow all students the opportunity to enter the learning with a “hook”, a real life situation, an open­ended question, 3­ACT math task, etc. Formative Assessment ●
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How will we check for understanding? How will we provide feedback? Monitor student learning and look for misconceptions/errors. Assess students in critical thinking­MP­provide tools that are necessary, they make connections, they conceptualize the math, they discover and explore, they struggle productively, engage in discourse. ​
ADDRESSING THE LANGUAGE GAP VOCABULARY What words will students need to learn and apply? (Tier 2 or 3 Words) STRUCTURE How will students use those words in sentences? (Simple, Compound, Complex) PLC PLANNING What do I want my students to know and be able to do? How will we know if they have learned it? How will we respond when learning has not occurred? How will we respond when learning has already occurred? FUNCTION How will students use those sentences to DESCRIBE, RETELL, JUSTIFY, EXPLAIN Etc… (Language demands from the standards) What do I want my students to know and be able to do? UNIT OVERVIEW A critical area of instruction for students in grade one is to develop an understanding of and strategies for addition and subtraction within 20. First­grade students also become fluent with these operations within 10. ESSENTIAL QUESTIONS ➢ What strategies can I use to solve addition and subtraction problems? ➢ How do I know which operation (+,­) to use? ➢ How do I know where to begin? What do I do when I get stuck? ➢ How will I know the result is reasonable? ➢ How does addition and subtraction relate to each other? ➢ What does the equal sign mean? ➢ How do I know when an equation is equal? MATHEMATICAL PRACTICES 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 UNIT 1 LEARNING SBAC Targets STANDARDS FRAMEWORK NOTES TARGET A: Major​
Represent and solve problems involving Addition and Subtraction. 1.OA.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, ​
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equations with a symbol for the unknown number to represent the problem. Solve problems with unknowns in all positions (see p. 92 of FW). Develop use of Level 2 “count on” method (see p. 91 of FW). TARGET B: Major​
Understand and apply properties of operations and the relationship between addition and subtraction. 1.OA.3​
Apply properties of operations as strategies to add and subtract. Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.) Apply properties of operation, but not necessary to name them. Related facts help develop an understanding of the relationship between addition and subtraction. TARGET C: Major Add and subtract within 20. 1.OA.6​
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 – 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13) Various strategies: adding with a ten frame, making tens, counting on, making 10 and decomposing a number, creating an easier problem with known sums, decomposing the number you subtract, the relationship between addition and subtraction, comparison bars, math drawings, number bonds, hundreds charts, number lines, and base ten models. TARGET D: Major Work with addition and subtraction equations. 1.OA.7​
Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 – 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. See page 101 in Framework. 1.OA.8​
Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = □ – 3, 6 + 6 = □. See page 101 in Framework Major (Priority) ­​
Areas of intensive focus where students need fluent understanding and application of the core concepts. These clusters require greater emphasis than the others based on the depth of the ideas, the time that they take to master, and/or their importance to future mathematics or the demands of college and career readiness Supporting​
­ Rethinking and linking; areas where some material is being covered, but in a way that applies core understanding; designed to support and strengthen Additiona​
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Expose students to other subjects; may not connect tightly or explicitly to the major work of the grade COMMON MISCONCEPTIONS: Operations and Algebraic Thinking ●
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Some students misunderstand the meaning of the equal sign. The equal sign means is the same as, but many primary students think the equal sign means the answer is coming up to the right of the equal sign. When students are introduced only to examples of number sentences with the operation to the left of the equal sign and the answer to the right, they overgeneralize the meaning of the equal sign, which creates this misconception. First­graders should see equations written in multiple ways—for example, 5 + 7 = 12 and 12 = 5 + 7. The put together/take apart (with both addends unknown) problems are particularly helpful for eliciting equations such as 12 = 5 + 7 (with the sum to the left of the equal sign). Consider this problem: “Robbie puts 12 balls in a basket. Some of the balls are orange and the rest are black. How many are orange and how many are black?” These equations can be introduced in kindergarten with small numbers (e.g., 5 = 4 + 1), and they should be used throughout grade one. Many students assume key words or phrases in a problem suggest the same operation every time. For example, students might assume the word left always means they need to subtract to find a solution. To help students avoid this misconception, include problems in which key words represent different operations. For example, “Joe took 8 stickers he no longer wanted and gave them to Anna. Now Joe has 11 stickers left. How many stickers did Joe have to begin with?” Facilitate students’ understanding of scenarios represented in word problems. Students should analyze word problems (MP.1, MP.2 ) and not rely on key words. Adapted from KATM 2012, 1st Grade Flipbook. Students may assume that the commutative property applies to subtraction. After students have discovered and applied the commutative property of addition, ask them to investigate whether this property works for subtraction. Have students share and discuss their reasoning with each other; guide them to conclude that the commutative property does not apply to subtraction (adapted from KATM 2012, 1st Grade Flipbook). This may be challenging. Students might think they can switch the addends in subtraction equations because of their work with related­fact equations using the commutative property for addition. Although 10 – 2 = 8 and 10 – 8 = 2 are related equations, they do not constitute an example of the commutative property because the differences are not the same. Students also need to understand that they cannot switch the total and an addend (for example: 10 – 2 and 2 – 10) and get the same difference How will we know if they have learned it? SUCCESS CRITERIA: WHAT DOES LEARNING LOOK LIKE ●
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The student models and solves addition and subtraction word problems using objects, drawings, and equations with unknown numbers in different positions (e.g., 6+__=8, __+2=8, 6+2=__). The student uses a symbol for an unknown number in an addition or subtraction problem (within 20) The student shows that the sum of any number and 0 does not change that number. The student shows that changing the order of the addends (numbers) does not change the sum. The student adds and subtracts within 10 easily. The student adds and subtracts by counting or counting back (e.g., 1+5=6, 7­5=2). The student adds and subtracts by making 10. (e.g., 7+3=10, 10­6=4). The student adds and subtracts by using doubles (or halves). (e.g., 4+4=8, 6­3=3). ●
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The student adds and subtracts by adding 10. (e.g., 5+10=15, 17­10=7). The student finds the unknown value in an addition or subtraction equation when two out of three numbers in the equation are given​
. The student explains that the equal sign means “same as.” The student compares the value of both sides of an equation and determine whether the equation is true or false. ❖ Formative assessment methods to consider: immediate feedback, questioning, overheard discourse, goal­setting and attainment, multiple representations, rubric, error analysis, CFA development, self­assessment How will we respond when learning has not occurred? Professional Learning Communities will develop and implement Response to Intervention. (see progressions) How will we respond when learning has already occurred? Professional Learning Communities will develop and implement Enrichment. PROGRESSIONS Mathematics standards are not isolated concepts.​
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COHERENCE MAP­ACHIEVE THE CORE Standards relate to one another, both within and across grades. The Coherence Map illustrates the coherent structure of the Common Core State Standards for Mathematics. ●
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Build student understanding by linking together concepts within and across grades. Identify gaps in a student's knowledge by tracing a standard back through its logical prerequisites. Visualize and understand how supporting standards relate to the major work of the grade. Previous Grades First Second In kindergarten, students added and subtracted small numbers and developed fluency with these operations with whole numbers within 5. In kindergarten, students worked with the following types of addition and subtraction situations: add to (with result unknown); take from (with result unknown); and put together/take apart A critical area of instruction for students in grade one is to develop an understanding of and strategies for addition and subtraction within 20. First­grade students also become fluent with these operations within 10. Students understand subtraction as an unknown­addend. They connect ​
counting on​
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counting back​
to addition and subtraction. Students are introduced to a new type of addition and subtraction problem­ “compare” problems. This includes solving one step word problems, finding the unknowns in all positions, applying properties of operations In grade two, is building fluency with addition and subtraction. Second­grade students fluently add and subtract within 20 and solve addition and subtraction word problems involving unknown quantities in all positions within 100. Grade­two students also work with equal groups of objects to gain the foundations for multiplication.Grade­two students extend their work with addition and subtraction word problems to solve with 100 and to represent and solve two­step (with total unknown and both addends unknown). as strategies to add and subtract, using various strategies to add word problems of all types. Grade two students use a and subtract within 20, expressing the meaning of an equal sign. range of methods, often mastering more complex strategies and begin to apply their understanding of place value. RESOURCES Mathematics Framework NUMBER TALKS 3­ACT Math Tasks KHAN ACADEMY McGRAW TEXT ● Chapter 1 ● Chapter 2 Ready Common Core iReady VOCABULARY add, part, whole, addition number sentence, equal (=), plus (+), sum, horizontal, vertical, in all, same, false, true, part, whole, missing, number, sum, add, addition number sentence, subtract, difference, minus (­), subtraction number sentence, compare, how many, model, compare, difference, minus, difference, related facts, model Additional Sources: Howard County Public School System, Tucson Unified School District