Concept Fifth Grade: Third Nine Weeks *Revised 6/1/15. Time Key Content Key Vocabulary

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1 Algebra: Expressions and Equations Concept Fifth Grade: Third Nine Weeks *Revised 6/1/15 Cumulative Review Time Key Content Key Vocabulary 1 week Review first semester material especially positive rational number applications Readiness Standards 5.4B Represent and solve multi-step problems involving the four operations with whole numbers using equations with a letter standing for the unknown quantity 5.4C Generate a numerical pattern when given a rule in the form y=ax or y=x+a and graph 5.4F Simplify numerical expressions that do not involve exponents, including up to two levels of grouping 5.8C Graph in the first quadrant of the coordinate plane ordered pairs of numbers arising from mathematical and real-world problems, including those generated by number patterns or found in an input-output table Supporting Standards 5.4D Recognize the difference between additive and multiplicative numerical patterns given in a table or graph 5.4E Describe the meaning of parentheses and brackets in a numeric expression 5.8A Describe the key attributes of the coordinate plane, including perpendicular number lines (axes) where the intersection (origin) of the two lines coincides with zero on each number line and the given point (0,0); the x-coordinate, the first number in an ordered pair, indicates the movement parallel to the x-axis starting at the origin; and the y-coordinate, the second number, indicates movement parallel to the y-axis starting at the origin 5.8B Describe the process for graphing ordered pairs of numbers in the first quadrant of the coordinate plane 3 weeks Describe what parentheses and brackets mean in a numeric expression Simplify numerical expressions that do not involve exponents including up to 2 levels of grouping Represent and solve multi-step problems involving all 4 operations with whole numbers using equations containing a variable *Consider using a balance scale to demonstrate that what is on what side of the equation must be the same as what is on the other side of the equation to show equality Describe and graph ordered pairs in the first quadrant of a coordinate graph from a table and in real-world situations Recognize the difference between additive and multiplicative patterns in a table and graph *Note that multiplicative patterns will graph through the origin Vocabulary: Numerical pattern, rule, additive pattern, multiplicative pattern, function table, input/output table, multiple representations, parentheses, brackets, numeric expression, grouping symbols, order of operations, equations, numerical expressions, algebraic expressions, unknown, variable, evaluate, coordinate graph, x-axis, y-axis, origin, x-coordinate, y- coordinate quadrant, coordinate plane, ordered pair, linear graph Book Reference: Topics Suggested Materials: Balance scale (such as ones used in science) Coordinate Grids Graph Paper Topics Generate a number pattern when given a rule in the form y = ax or y = x +a

2 Geometry and Measurement Interactive Notebook: Expressions and Algebra Interactive Notebooks: (left side) Describe the Order of Operations and why it is important to use the order of operations when evaluating an expression. (pg. 503, SE) What do you do if there are parentheses inside of some brackets? Would it change the answer if you ignored the parentheses? Give an example defending your answer. Explain the difference between a numerical expression and an algebraic expression. Give an example of both including using a graph. What are the similarities and differences between expressions and equations? In an ordered pair, what do the two numbers represent and how does that affect the way you would graph it on a coordinate plane? How do you take data from an input-output table and graph it on a coordinate grid? What are the differences between additive and multiplicative patterns in a table? In a graph? How do you determine a rule from a pattern of numbers? What is the difference between y=ax and y= a+x? (right side) Sticky note vocabulary. Generate some words that may stand for the various operations in algebraic expressions such as (+) could be sum or total. The operation goes on the sticky note and the words go underneath it in the notebook. *Be sure to reiterate that some words could have more than one meaning or operation attached to it and so looking at the context of the problem is essential!* Label all parts of a coordinate grid on graph paper or create a foldable Readiness Standards 5.4H Represent and solve problems related to perimeter and/or area and related to volume 5.5A Classify two-dimensional figures in a hierarchy of sets and subsets using graphic organizers based on their attributes and properties Supporting Standards 5.4G (not tested) Use concrete objects and pictorial models to develop the formulas for the volume of a rectangular prism, including the special form for a cube (V=l x w x h, V=s x s x s, and V=B x h) 5.6A Recognize a cube with side length of 1 unit as a unit cube having one cubic unit of volume and the volume of a threedimensional figure as the number of units (n cubic units) needed to fill it with no gaps or overlaps if possible 5.6B Determine the volume of a rectangular prism with whole number side lengths in problems related to the number of layers times the number of unit cubes in the area of the base 5.7 solve problems by calculating conversions within a measurement system, customary, or metric 3 ½ weeks Identify polygons including regular polygons based on attributes Classify 2D figures using a graphic organizer *consider building shapes on a geoboard or with pattern blocks or drawing on graph paper to discriminate *Consider playing Three Facts and a Fib using geometry terms! Use appropriate formulas to estimate and find perimeter and area of polygons *consider building polygons or drawing on graph paper Represent and solve problems relating perimeter, area and /or volume *More key content on next page Vocabulary: Two-dimensional figures: triangles (acute, obtuse, right, equilateral, isosceles, scalene), quadrilaterals (square, rectangle, parallelogram, trapezoid, rhombus), polygons, pentagon, hexagon, octagon, regular polygon, nonpolygons, circles, ovals, attributes, adjacent, opposite, properties, vertex (vertices),side, parallel, perpendicular, perimeter, area, composite shape, square unit, length, width, base,height, volume, cubic units, dimensions, face, formulas, rectangular prism, cube, conversion, Customary System (inch, foot, yard, mile, cup, fluid ounce, pint, quart, gallon, ton, pound, ounce), Metric System (kilometer, meter, centimeter, millimeter, liter, milliliter, milligram, gram, kilogram), capacity, weight, mass

3 Geometry and Measurement continued Recognize a unit cube and how it relates to the volume of a 3D figure *build with unit cubes to discover the formulas! Discover the formulas for volume using concrete objects and pictorial models and use these discoveries to teach (standards 5.4G, 5.6A and 5.6B) Use the appropriate formula to find volume of a rectangular prism and a cube. *Stress the importance of the capital B in the volume formula! Convert within a measurement system (customary and metric) *consider setting up tables to help solve conversions! Show how to read and use the formula chart Book Reference: Topics Suggested Materials: Graph Paper Unit Cubes (centimeter, unifix, connecting) Geoboards Rulers STAAR Formula Charts Capacity Measuring Containers (*use household items!) Metric Measuring Tools (*see science teacher for supplies) Pattern blocks Topics *There is an auto-scored online (optional) Benchmark Test for Topics 9-12 at PearsonTexas.com (pg. 668B, TE)

4 Data, Graphs and Financial Literacy Interactive Notebook: Geometry and Measurement Interactive Notebooks: (left side) Graph a polygon on a coordinate plane taped only at the top to your notebook and label the vertices with letters. Write the ordered pairs of each of the vertices underneath your coordinate grid (as an answer key) Trade with another classmate and solve each other s. Create a Frayer Model of polygons including non-examples. Make sure to include regular polygons (polygons with congruent sides) as part of the Frayer! Analyze the relationships between perimeter, area, and volume. How are they the same? different? Give real-life examples of each. Give two different ways to find the area of a composite shape. Use examples in your description with a visual representation. Create a real-life problem using perimeter, area, or volume. Write your story problem and then show how to solve including using a visual, writing the formula, and solving for the given question. What are the possible steps to take to change from a large customary unit such as a mile into a small customary unit such as an inch? (For instance changing ½ mile into inches) What are the possible steps to change a small metric unit such as millimeters into a large metric unit such as kilometers? Do you have to solve customary and metric conversions the same? Why or why not? (right side) Show how quadrilaterals relate to each other by drawing the Venn Diagram on (pg. 619C, TE or pg. 652, SE) Create a geometry terms flipbook Perimeter, area, and volume foldable Use pictures or images to help students identify with the various measurements. Create a measurement flip book for reference. (Integrate this topic with science!) How to convert measurements Readiness Standards Represent data in categories using frequency tables, bar 5.9C Solve one-and two-step problems using data from a frequency graphs, dot plots, and stem-andleaf plots (including the use of table, dot plot, bar graph, stem-and-leaf plot, or scatterplot decimals and fractions) *consider using the Intervention Activity: Making Dot Plots (pg. 809, TE) Supporting Standards 5.9A Represent categorical data with bar graphs or frequency tables and numerical data, including data sets of measurements in fractions or decimals, with dot plots or stem-and-leaf plots 5.9B Represent discrete paired data on a scatterplot 5.10A define income tax, payroll tax, sales tax, and property tax 5.10B explain the difference between gross income and net income 5.10E describe actions that might be taken to balance a budget when expenses exceed income 5.10F balance a simple budget 2 weeks *consider using the Intervention Activity: Reading Stem and Leaf Plots (pg. 833, TE) *consider using Intervention Activity: Reading Scatterplots (pg. 845, TE) Solve 1 and 2 step problems using data from graphs including: frequency tables, bar graphs, dot plots, stem-and-leaf plots, and scatterplots *More Key Content on next page Vocabulary: Dot plot, data, outlier, frequency table, numerical data, bar graph, scale, interval, categorical data, survey, sample, stem-and-leaf plot, scatterplot, trend, discrete data, income tax, payroll tax, property tax, gross income, net income, budget, expenses, income, balanced budget, simple budget, check, debit, credit, deposit, withdrawal Book Reference: Topics *Suggested Materials on next page

5 Interactive Notebook: Data, Graphs and Financial Literacy Data, Graphs and Financial Literacy continued Represent discrete paired data on a scatterplot Define various taxes (income, payroll, sales, property) *consider using Intervention Activity with all students to aid with how to calculate sales tax (pg. 877A, TE) Explain the difference between gross and net income Describe how to balance a budget so that expenses do not exceed income Balance a simple budget Understand the pros and cons of various methods of payment Suggested Materials: Graph Paper Rulers Restaurant Menus Advertisements Paycheck stubs Bank statements Checkbook or savings account register Topic 16 Topic 15 Explore how to keep financial records Interactive Notebooks: (left side) What does the term frequency table mean? How is this the same or different from a tally chart? In a dot plot, how would you know how many people had been surveyed? How would this change if the key was different? What is the difference between a scale and an interval? On a Stem-and-Leaf Plot, what do the stems represent? the leaves? How would you show a three-digit number such as 100? Explain what a scatterplot is and how a trend line can be used to make predictions. What are the similarities and differences between the 3 types of taxes? Identify the advantages and disadvantages of different methods of payment. What is the difference between gross and net income? (right side) Create a foldable showing the various types of graphs and what each is best used for Create a mini book of financial terms and financial literacy concepts Steps on how to calculate tax Example of a paycheck stub to show gross/net income and other deductions to salary including insurance, social security, etc. Example of a bank register and check with vocabulary and how to fill out

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