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Draft 3/21/06 Lansing School District Curriculum 7th Grade: The main areas of emphasis for seventh grade are: (6th grade honors curriculum) Communication Discuss, write, or draw to show depth of mathematical ideas and relationships Develop math vocabulary and symbols Reflect on or clarify thinking about mathematical ideas and situations Restate math concepts Explain and justify answers Develop rules and procedures Explain methods of solving a problem Describe what extra information is needed to solve a problem 1 Year long instructional strategies, processes, skill development, or content expectations Reasoning Connections Problem Solving Verify and justify Recognize mathematical connections that Use students prior answers occur in everyday experience knowledge of mathematical content and process Use logical spatial and Recognize relationships using number lines, proportional calendars, graphing, and money reasoning Solve a simpler problem to suggest a solution for a Recognize mathematical relationships that more complex problem Generalize from a set occur between various mathematical topics of observations Identify mathematical concepts that occur in Solve multi-step problems Evaluate accuracy of a other disciplines solution to a problem Recognize the need for math in order to Formulate problems for real world situations pursue various careers Solve a variety of non-routine, real Use mathematics to describe the physical Use manipulative world problems world Draw a figure Make and test Use technology to enhance mathematical conjectures understanding Guess and check Look for a pattern Retell a story problem Explain a problem solution Make a list Simplify Draw a diagram or table Work backwards Data Analysis Collect, organize, interpret and describe data from tables Analyze data Analyze patterns Formulate and solve problems using given data Construct and interpret graphs Create a variety of graphic displays using appropriate scales with given sets of numerical data Draft 3/21/06 Integration Teacher Notes Curriculum What do we want students to learn? Instructional Strategies How will we deliver the curriculum? Resources What materials/resources will we need to ensure mastery. Assessment How will we know if students learn? 1st Quarterly focused instructional strategies, processes, skill development, or content expectations Unit: Math Toolbox 1 for Seventh Seventh Grade Level Content Problem-solving skills Grade (St. Clair County) Expectations Students will use one or more of Use resources to assess, re-teach the following problem solving concepts Pilot Items N.FL.07.07 strategies to demonstrate Create a Human Number Line to Solve problems involving mastery in tested content areas: explore integers MEAP released items operations with integers. Draw a Diagram N.FL.07.09 Make a Model Develop and analyze algorithms Coach Estimate results of Guess and Test for computing with integers and computations with rational Work Backward develop fluency in their use numbers. Find a Pattern (assess student thinking for N.FL.07.08 Make a Table alternative algorithms) Holt Middle School Math Add, subtract, multiply and Solve a Simpler Course 3 Ch divide negative rational Problem Use concrete objects and numbers. Use Logical Reasoning pictures to develop and analyze A.FO.07.12 1.1 – 1.6, 2.1 – 2.5, 3.1 – Use a Venn Diagram algorithms for computing with Add, subtract, and multiply 3.5, 8.1, Lab 8A, 8.5, 8.6 Make an Organized fractions, decimals and integers simple algebraic expressions List of the first degree, e.g., (92x www.nctm.org Explore and discuss the + 8y) – 5x + y, or – 2x (5x – Effective Questioning (see ILLUMINATIONS relationship between fractions, 4), and justify using appendix) Figure This decimals and percents properties of real numbers. www.lessonplanspage.com www.mathgoodies.com www.math.com coolmath4kids.com mathforum.org/dr.math edhelper.com thatquiz.com Classroom observation and discussion Student Reasoning and Justification Student Math Journals (Writing & Reflection) Holt Middle School Math Course 3: Chapter tests End-of-chapter review pages Cumulative assessment 2 Draft 3/21/06 Connected Mathematics Project Units: Check-up Quiz Unit Test Unit Project Give students grades in fraction form for them to compute (ongoing) Peer grading Integration Teacher Notes Curriculum What do we want students to learn? Instructional Strategies How will we deliver the curriculum? Assessment How will we know if students learn? 2nd Quarterly focused instructional strategies, processes, skill development, or content expectations Unit: Explore and discuss different uses of Holt Middle School N.ME.07.01 variables Understand derived quantities such as density, velocity, and Math Course 3 Use symbolic algebra to represent weighted averages situations A.FO.07.13 Ch 3.6, 3.7, 10.1- 10.5 From applied situations, generate Explore and discuss the use of inverse and solve linear equations of the Math Toolbox 1 for Seventh relationships to solve problems form ax + b = c and ax + b = cx + Grade d, and interpret solutions. Explore and discuss alternative ways to A.FO.07.08 www.nctm.org Know that the solution to a linear think about solving problems (undo, cover ILLUMINATIONS equation corresponds to the point at up method, hands on equations) Figure This which its graph crosses the x-axis. (Redefining the zero for the equation Explore and discuss equivalent forms for www.lessonplanspage.com where y = 0). simple algebraic expressions www.mathgoodies.com www.math.com coolmath4kids.com mathforum.org/dr.math Explore and discuss using the inverse 3 Resources What materials/resources will we need to ensure mastery. Students will use one or more of the following problem solving strategies to demonstrate mastery in tested content areas: Draw a Diagram Make a Model Guess and Test Work Backward Find a Pattern Make a Table Solve a Simpler Problem Use Logical Reasoning Use a Venn Diagram Draft 3/21/06 relationship of squaring and finding square roots edhelper.com thatquiz.com Make an Organized List Effective Questioning (see appendix) Classroom observation and discussion Student Reasoning and Justification Student Math Journals (Writing & Reflection) Holt Middle School Math Course 3: Chapter tests End-of-chapter review pages Cumulative assessment Connected Mathematics Project Units: Check-up Quiz Unit Test Unit Project Give students grades in fraction form for them to compute (ongoing) Peer grading 4 Draft 3/21/06 Integration Teacher Notes 5 Curriculum What do we want students to learn? Instructional Strategies How will we deliver the curriculum? Resources Assessment What materials/resources How will we know if will we need to ensure students learn? mastery. 3rd Quarterly focused instructional strategies, processes, skill development, or content expectations Unit: Explore and discuss linear and A.PA.07.11 Holt Middle School Math Course 3 Students will use one or more of the Understand and use basic nonlinear functions following problem solving strategies properties of real numbers: additive and multiplicative Use concrete objects and real-life Ch 5.5, Lab 5A, 11.1 -11.3, Lab 5B to demonstrate mastery in tested content areas: identities, additive and situations to explore and discuss multiplicative inverses, slope concepts Draw a Diagram www.nctm.org commutative, associative, and Make a Model the distributive property of Explore and discuss calculating the Guess and Test slope using rise/run, y=mx + b, (y2 – ILLUMINATIONS multiplication over addition. Work Backward Figure This y1)/(x2 – x1) G.SR.07.01 Find a Pattern Use a ruler and other tools to Make a Table www.lessonplanspage.com Explore relationships between draw squares, rectangles, Solve a Simpler Problem www.mathgoodies.com triangles and parallelograms with symbolic expressions and graphs of Use Logical Reasoning www.math.com lines, paying particular attention to specified dimensions. Use a Venn Diagram coolmath4kids.com the meaning of slope and intercept G.SR.07.02 Make an Organized List mathforum.org/dr.math Use compass and straightedge edhelper.com Explore and discuss multiple ways to perform basic geometric Effective Questioning (see appendix) thatquiz.com of solving equations (inverse constructions: the perpendicular bisector of a segment, an equilateral triangle, and the bisector of an angle; understand informal justifications. A.RP.07.02 Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. A.PA.07.03 Given a directly proportional or linear situation, graph and interpret the slope and intercept(s) in terms of the original situation; evaluate y = kx operations, isolating the variable, undo, cover up method) Explore and discuss variety form of linear equations and their graphs(slope-intercept form, point slope form,) Represent, analyze, and generalize patterns with tables, graphs, words, and symbolic rules (direct variation, line of best fit, functions, inverse variation) Classroom observation and discussion Student Reasoning and Justification Student Math Journals (Writing & Reflection) Holt Middle School Math Course 3: Chapter tests End-of-chapter review pages Cumulative assessment Connected Mathematics Project Units: Draft 3/21/06 for specific x values, given k, e.g., weight vs. volume of water, base cost plus cost per unit. A.PA.07.04 For directly proportional or linear situations, solve applied problems using graphs and equations, e.g., the heights and volume of a container with uniform cross-section, height of water in a tank being filled at a constant rate, degrees Celsius and degrees Fahrenheit, distance and time under constant speed. A.PA.07.09 Recognize inversely proportional relationships in contextual situations; know that quantities are inversely proportional if their product is constant, e.g., the length and width of a rectangle with fixed area and that an inversely proportional relationship is of the form y = k/x where k is some non-zero number. A.RP.07.10 Know that the graph of y = k/x is not a line; know its shape; and know that it crosses neither the x nor the y-axis. A.PA.07.06 Calculate the slope from the graph of a linear function as the ratio of “rise/run” for a pair of points on the graph, and express the answer as a fraction and a decimal; understand that linear functions have slope that is a constant rate of change. A.PA.07.05 Understand and use directly proportional relationships of the 6 Check-up Quiz Unit Test Unit Project Give students grades in fraction form for them to compute (ongoing) Peer grading Draft 3/21/06 form y = mx, and distinguish from linear relationships of the form y = mx + b, b non-zero; understand that in a directly proportional relationship between two quantities one quantity is a constant multiple of the other quantity. A.PA.07.07 Represent linear functions in the form y = x + b, y = mx, and y = mx + b, and graph, interpreting slope and y-intercept. Integration Teacher Notes 7 Resources What materials/resources will we need to ensure mastery. 4th Quarterly focused instructional strategies, processes, skill development, or content expectations Unit: Use concrete objects to explore and Holt Middle School Math Course 3 D.AN.07.03 discuss geometric figures Calculate and interpret relative frequencies and cumulative Ch 3.8, 3.9, Lab 3B, 4.1-4.5, 4.7, Describe, classify, and understand frequencies for given data sets. 5.3, 5.6, 7.1-7.4, 7.6, 7.7, 9.1, 9.2, relationships among types of twoD.AN.07.04 9.4, 9.7, 11.7 and three-dimensional objects Find and interpret the median, quartiles, and inter-quartile range The Math Form-Ask Dr. Math Use coordinate geometry to of a given set of data. Archives: Triangle Congruence. represent and examine the properties D.RE.07.01 http://mathforum.org/library/drmath/ of geometric shapes Represent and interpret data sets/select/dm_tri_congruence.html using circle graphs, stem and Describe sizes, positions, and leaf plots, histograms, and boxwww.nctm.org orientations of shapes under and-whisker plots and select ILLUMINATIONS transformations such as scaling appropriate representation to Figure This address specific questions. Explore and discuss solving D.AN.07.02 Create and interpret scatter plots problems involving scale factors, www.lessonplanspage.com and use an estimated line of best using ratio and proportion www.mathgoodies.com fit to answer questions about the www.math.com Curriculum What do we want students to learn? Instructional Strategies How will we deliver the curriculum? Assessment How will we know if students learn? Students will use one or more of the following problem solving strategies to demonstrate mastery in tested content areas: Draw a Diagram Make a Model Guess and Test Work Backward Find a Pattern Make a Table Solve a Simpler Problem Use Logical Reasoning Use a Venn Diagram Make an Organized List Effective Questioning (see appendix) Draft 3/21/06 data. G.TR.07.03 Understand that in similar polygons, corresponding angles are congruent and the ratios of corresponding sides are equal; understand the concepts of similar figures and scale factor. G.TR.07.05 Show that two triangles are similar using the criteria: corresponding angles are congruent (AAA similarity); the ratios of two pairs of corresponding sides are equal and the included angles are congruent (SAS similarity); ratios of all pairs of corresponding sides are equal (SSS similarity); use these criteria to solve problems and to justify arguments. G.TR.07.04 Solve problems about similar figures and scale drawings. G.TR.07.06 Understand and use the fact that when two triangles are similar with scale factor of r, their areas are related by a factor of r2. N.MR.07.04 Convert ratio quantities between different systems of units such as feet per second to miles per hour. N.FL.07.03 Calculate rates of change including speed. N.FL.07.02 Solve problems involving derived quantities. N.FL.07.05 Solve simple proportion problems using such methods as unit rate, scaling, finding equivalent 8 Use concrete data and real-life situations to design studies, collect data, display data and interpret data Model discuss organizing data, measures of central tendency, and variability Explore and discuss the correspondence between data sets and their graphical representations Explore and discuss using the inverse relationship of squaring and finding square roots coolmath4kids.com mathforum.org/dr.math edhelper.com thatquiz.com Classroom observation and discussion Student Reasoning and Justification Student Math Journals (Writing & Reflection) Holt Middle School Math Course 3: Chapter tests End-of-chapter review pages Cumulative assessment Connected Mathematics Project Units: Check-up Quiz Unit Test Unit Project Give students grades in fraction form for them to compute (ongoing) Peer grading Draft 3/21/06 fractions, and solving the proportion equation a/b = c/d; know how to see patterns about proportional situations in tables. A.PA.07.01 Recognize when information given in a table, graph, or formula suggests a proportional or linear relationship. N.MR.07.06 Understand the concept of square root and cube root, and estimate using calculators 9