Content Standard 1: Number, Number Sense, Computation, and Properties Place Value

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1 Note: Although these are mastery objectives, pacing of content is at the discretion of the teacher. Key: E = Enduring, I = Important, W = Worth being familiar with, S = Assessed at the state and local level, L= Assessed at the local level only Content Standard 1: Number, Number Sense, Computation, and Properties Place Value Identify and use place value positions of whole numbers to 1,000,000. Students will read and write standard numbers up to 1,000,000. Read and write standard and expanded forms through millions place. Fractions A1#2 E/S Ch. 1 pgs. 6-8 Ch. 1: pgs 6-8 Ch. 1: pgs 6-8 Identify, build, write, and compare fractions with like denominators using models, drawings, and numbers. (Fractions are limited to denominators less than or equal to 12) Comparing and Ordering Read, write, compare, and order whole numbers Compare and order numbers to millions (<,>,=) Compare numbers up to 1,000,000. Compare standard numbers using >, <, = to 1,000,000. A2#2 E/S Ch I/S Ch. 2 pgs Ch. 2 pgs Ch. 2 pgs Revised July 2008 Page 1 of 10 Douglas County School District

2 Complete number sentences with appropriate words and symbols (+,, x,, >, <, =). Counting Count by multiples of a given number. Explain relationships between skip counting, repeated addition, and multiples. Facts A1#1 I/L A1#4 Ch. 10 Immediately recall and use A1#4-7 multiplication and corresponding division facts (products to 144). Set fluency goals such as say or write answers per minute. Estimating and Estimation Strategies I/S Ch. 4: pgs Use Mad Minutes & Math Wrap- Ups, etc. for timed tests Arrays and Shares, Packages and Groups Estimate to determine the reasonableness of an answer in mathematical and practical situations. Rounding to the nearest place value given. Round numbers to the highest place value in the number (ie. 3,208 round the nearest thousand) up to hundred thousands. Estimate products using rounding up to 2 digits times 4 digits. A4#3 I/S A4#3 A4#1 A4#1 Ch. 2 pgs Ch 7: pgs Revised July 2008 Page 2 of 10 Douglas County School District

3 Computation Add and subtract multi-digit numbers with and without regrouping A1#6 E/S Mathematical Thinking Ch. 3 : pg , Multiply and divide multi-digits by a one digit whole number with regrouping, including monetary amounts as decimals. Understand dividing large into small groups. -Understand division as repeated subtraction. -Divide number of objects into equal groups (with or without remainders). A1 #4 A1 #5 Money, Miles and Large Numbers Ch. 3 pgs Ch. 6. Ch. 7: pgs Packages and Groups Ch. 4: pgs Ch. 4: pgs (x) Ch. 6: pgs ( ) Ch. 9: pgs Ch. 4: pgs ; pgs ; pgs Solving Problems and Number Theory Ch. 4: pgs Generate and solve addition, subtraction, multiplication, and division problems using whole numbers in practical situations. A1#8 E/S Embedded Content Standard 2: Patterns, Functions, and Algebra Patterns Identify, describe, and represent patterns and relationships in the number system, including A1#1, 4, 9 D1# E/S Ch. 18: pgs Ch 4: pgs Revised July 2008 Page 3 of 10 Douglas County School District

4 arithmetic and geometric sequences. Explain relationships between skip counting, repeated addition, and multiples. Variables and Unknowns Houghton Mifflin: Daily Reviews Model, explain, and solve open E2 #1 number sentences involving addition, subtraction, multiplication, and division Select the solution to an equation from a given set of numbers Number Sentences, Expressions, and Polynomials I/S Ch. 4: pg 93 Complete number sentences with the appropriate words and symbols (+, -, x,, >, <, =) Relations and Functions I/S Linear Equations and Inequalities Algebraic Representations and Applications Content Standard 3: Measurement Comparison, Estimation, and Conversion Estimate temperature in practical situations Estimate and convert units of measure for length, area, and weight with the same measurement system (customary and metric) Customary units for length B1#1 E/S B3#1, Ch. 12: pgs Ch. 12: pgs Ch. 12: pgs Ch. 12: pgs Revised July 2008 Page 4 of 10 Douglas County School District

5 include inch, foot, yard, and mile. Metric units for length include millimeter, centimeter, meter, kilometer. Customary units for weight include ounce, pound, and ton. Metric units for weight include milligram, gram, and kilogram. Precision in Measurements Ch. 13: pgs Ch. 13: pgs Measure length to the nearest ½ in. and ¼ in. B1#1 E/S Ch. 12: pgs Measure length, area, temperature, and weight to the required degree of accuracy in customary and metric systems. Length and weight Ch. 12 Temp. Ch 13 Area Ch. 18 Formulas Define, describe and determine the perimeter of polygons and area of rectangles (including squares). Money B2#1 I/S Ch. 18 Determine totals for monetary amounts in practical situations. Use money notation to add and subtract given monetary amounts F5# E/S Ch. 3: pgs Mathematical Thinking Ratios and Proportions Time Use A.M. and P.M. appropriately in describing time. Use elapsed time in quarter- B1#5 E/S Ch. 13 Revised July 2008 Page 5 of 10 Douglas County School District

6 hour increments, beginning on the quarter-hour, to determine start, end, and elapsed time. Ch. 13 Recognize the number of weeks in a year, days in a year, and days in a month. Content Standard 4: Spatial Relationships, Geometry, and Logic Two Dimensional Shapes Identify, draw, and classify angles, including straight, right, obtuse, and acute D1#1 I/S Congruence, Similarity, and Transformations Identify shapes that are congruent, similar, and/or symmetrical using a variety of methods including transformational motions. D1#1 I/S D3# Coordinate Geometry and Lines of Symmetry Ch. 13 Seeing Solids and Silhouettes, Sunken Ships and Grid Patterns Ch. 16: pgs Identify coordinates for a given point in the first quadrant I/L Sunken Ships and Grid Patterns Locate points of given coordinates on a grid in the first quadrant. Three Dimensional Figures Identify, describe, and classify two and three dimensional figures by relevant properties including the number of vertices, edges, and shapes of faces, using models Two dimensional figures include circle triangle, rectangle, square, rhombus, pentagon, hexagon, octagon, D3#2 E/S Ch. 17: pgs Revised July 2008 Page 6 of 10 Douglas County School District

7 and trapezoid. Three dimensional figures include cube, cone, sphere, rectangular prism, triangular prism, and cylinder. Algebraic Connections Lines, Angles, and their Properties Identify, draw, label, and describe points, line segments, rays, and angles. Triangles D1#1 I/S Ch 16: pgs Constructions Logic Use the connectors and, or, and not to describe the members of a set. Content Standard 5: Data Analysis Data Collection and Organization I/L Ex.: Sort and classify angles using Venn Diagrams Pose questions that can be used to guide the collection of categorical and numerical data. Organize and represent data using a variety of graphical representations including frequency tables and line plots. C5#1 I/S C4#1 Mathematical Thinking, Changes Over Time, The Shape of Data. Ch. 15: pgs Ch. 14: pgs Ch. 14: pgs Ch. 23: pgs Data displays may include Revised July 2008 Page 7 of 10 Douglas County School District

8 tables/charts, bar graphs, frequency tables, number lines, pictographs, or line plots. Central Tendency and Data Distribution Model and compute range Model the measures of central tendency for (average/mean), mode and median Interpretation of Data Interpret data and make predictions using frequency tables and line plots. Permutations and Combinations C3#1 I/L C1#1 C4#1 C4#1 I/S Ch. 14 Ch. 14 Changes Over Time, The Shape of Data Ch. 13 Experimental and Theoretical Probability Conduct simple probability experiments using concrete materials. Represent the results of simple probability experiments as fractions to make predictions about future events. Statistical Inferences C3#1 I/L Ch. 23: pgs Ch. 23: pgs Revised July 2008 Page 8 of 10 Douglas County School District

9 Process Standard: Problem Solving Use resources throughout Houghton Mifflin text and Investigations K-12 Formulate their own problems Find solutions to problems from everyday situations Develop and apply strategies to solve a variety of problems Integrate mathematical reasoning, communication and connections 3-5 Generalize and apply previous experiences and strategies to new problem solving situations Determine an efficient strategy, verify, interpret, and evaluate the results with respect to the original problem Try more than one strategy when the first strategy proves to be unproductive Interpret and solve a variety of mathematical problems by paraphrasing Identify necessary and extraneous information Check the reasonableness of a solution Use technology, including calculators, to develop mathematical concepts Process Standard: Use resources throughout Houghton Mifflin text and Mathematical Communication Investigations K-12 Translate information into mathematical language and symbols Process information mathematically Present results in written, oral, and visual formats Discuss and exchange ideas about mathematics as a part of learning Read a variety of fiction and nonfiction texts to learn about mathematics Use mathematical notation to communicate and explain problems 3-5 Use inquiry techniques to solve mathematical problems Use a variety of methods to represent and communicate mathematical ideas through oral, verbal, and written formats Identify and translate key words and phrases that imply mathematical operations Use everyday language, both orally and in writing, to communicate strategies and solutions to mathematical problems Revised July 2008 Page 9 of 10 Douglas County School District

10 Process Standard: Mathematical Reasoning Use resources throughout Houghton Mifflin text and Investigations K-12 Reinforce and extend their logical reasoning abilities Reflect on, clarify, and justify their thinking Ask questions to extend their thinking Use patterns and relationships to analyze mathematical situations Determine relevant, irrelevant, and /or sufficient information to solve mathematical problems 3-5 Draw logical conclusions about mathematical problems Follow a logical argument and judge its validity Review and refine the assumptions and steps used to derive conclusions in mathematical arguments Justify and explain the solutions to problems using manipulatives and physical models Process Standard: Mathematical Connections Use resources throughout Houghton Mifflin text and Investigations K-12 Link new concepts to prior knowledge Identify relationships between content strands Integrate mathematics with other disciplines Allow the flexibility to approach problems in a variety of ways within and beyond the field of mathematics 3-5 Use mathematical ideas from one area of mathematics to explain an idea from another area of mathematics Use physical models to explain the relationship between concepts and procedures Apply mathematical thinking and modeling to solve problems that arise in other disciplines, such as rhythm in music and motion in science Identify, explain, and use mathematics in everyday life Revised July 2008 Page 10 of 10 Douglas County School District

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