• Units should be based on the content standards only – not resources or favorite activities. Even “Common Core” resources should be examined very closely!
• All eight of the Standards for Mathematical Practice should be in every unit, although all eight will not necessarily be in every lesson within the unit.
• Hard to shift from what we’ve always done, or what might be assessed during the transition years.
• Get to know the critical areas for each grade level or conceptual area in High School.
• This is the “text” developed in the standards prior to the Overview.
• Make a workable list of non-negotiables.
Mathematics | Grade 4 In Grade 4, instructional time should focus on three critical areas: (1) developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry.
• What will students come to Understand, Know and Be Able To Do as a result of the learning in this unit?
• What do you think? What is the difference between understanding, knowing and being able to do in math? What are the connections?
Planning a Focused Curriculum
Facts (Columbus came to the “New World”)
Vocabulary (voyage, scurvy)
Concepts (exploration, change)
Principles/Generalizations/Big Ideas (Change can be both positive and negative. Exploration results in change. People’s perspectives affect how they respond to change).
Skills
Basic (literacy, numeracy)
Thinking (analysis, evidence of reasoning,
questioning)
Of the Discipline (graphing/math/social
studies)
Planning (goal setting; use of time)
Social
KNOW
UNDERSTAND
BE ABLE TO DO
In general, these are held steady as a core for nearly all learners
in a differentiated classroom.*
*Exception--linear skills and information that can be assessed for mastery in the sequence (e.g. spelling) Source: Tomlinson, C. A. (1999). The differentiated classroom:
Responding to the needs of all learners. Alexandria, VA: ASCD. Used with permission.
The “DO” portion encourages the students to “think” like the professionals who use the knowledge and skill daily as a matter of how they do business. It answers the question, if students have truly come to Know and Understand, what should they now be able to do?
This is what it means to “be like” a mathematician, an analyst, or an economist.
8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
• 2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: – 100 can be thought of as a bundle of ten tens — called a “hundred.”
– The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).
• 2.NBT.5 Add and subtract within 20 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction
• 2.NBT.8 Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
• 2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, ..., and represent whole-number sums and differences within 100 on a number line diagram. (Use as a strategy for addition)
• U1: The value of a digit will change based on its placement in a number.
• U2: A number can be represented in different ways based on its placement. (The 1 in the number 216 could be expressed as 10 or one group of ten ones.)
• U3: combining groups of 10s can make the next place value level (ten ones equals one ten, ten tens equals one hundred, etc)
• U4: Only things that are alike (place value) can be added together.
Unpacking UnitsThemes in K-12 Content Standards - U
1. Properties of operations: their role in arithmetic and algebra
2. Mental math and [algebra vs. algorithms]3. Units and unitizing4. Operations and the problems they solve5. Quantities-variables-functions-modeling6. Number-Operations-Expressions-Equation7. Modeling8. Practices
• After the units have been determined and unpacked, align the resource.
• Common core has the shift of “Focused” and “Coherent.” You can not be focused if you teach every page of a resource. Pick and choose, and even go out of sequence!
• Align your resource to the units. Do not write your units from the resource!
• (D1, D3, Practice 1and 3) Mary says that a 2 is a 2, no matter where it is in a number. It is always worth the same.– How would you answer Mary?– Expand 23 and 52. Explain to Mary what the 2 is
worth in each number.
• (D2, D4, Practice 2 and 3) Explain why groups of 10 are important to place value. Give an example.
