The School District of Palm Beach County Fifth Grade Mathematics Scope rd Trimester

Transcription

1 Unit & Go Math! & lessons from each Measurement and Data MA.5.G.5.3 MD.1.1 Convert like measurement units within a given measurement system. Convert among different-sized standard measurement units within a given measurement system, and use these conversions in solving multi-step, real world problems. Benchmarks Next Generation Standards Solve problems requiring attention to approximation, selection of appropriate measuring tools, and precision of measurements. Units of Measure February 13 - February 28 compare, contrast, and convert customary units of length and weight. compare, contrast, and convert customary units of capacity. convert measurement units to solve multistep problems. compare, contrast, and convert metric units. solve problems about customary and metric conversion using the strategy make a table. convert units of time to solve elapsed time problems. estimate customary and metric measurements using benchmarks. determine precise measures and when an estimate or a more precise measure is more appropriate. 10.1/ / Precision capacity, cup, fluid ounce, gallon, pint, quart, foot, inch, length, mile, yard, ounce, pound, ton, weight, gram, kilogram, mass, milligram, kilometer, liter, milliliter, centimeter, decimeter, dekameter, kilometer, meter, millimeter, elapsed time, customary, metric

2 Unit & Go Math! & lessons from each Measurement and Data Geometry MA.5.G.3.1 Geometric measurement: understand concepts of volume. MD.3.3 Classify two-dimensional figures into categories base on their properties. G.2.4 G.2.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. Classify two-dimensional figures in a hierarchy based on properties. Benchmarks Next Generation Standards Analyze and compare the properties of two-dimensional figures and three-dimensional solids (polyhedra), including the number of edges, faces, vertices, and types of faces 2- and 3- Dimensional Figures March 3 - March 12 identify and classify polygons. classify and compare triangles and quadrilaterals using their properties. identify, describe, and classify three-dimensional figures. identify the faces, edges, and vertices of threedimensional solid figures. build and identify models of prisms and pyramids. draw and identify different views of three-dimensional solid figures. 11.1/ / base, congruent, decagonal prism, edge, face, hexagonal prism, lateral face, net, octagonal prism, pentagonal pyramid, polyhedron, prism, pyramid, vertex, heptagon, nonagon, polygon, regular polygon, parallel, perpendicular, paralleogram, quadrilateral, rectangle, rhombus, trapezoid, equilateral, isosceles, scalene, acute, obtuse, & right triangle

3 Unit & Go Math! & lessons from each Measurement and Data Geometric measurement: understand concepts of volume. MD.3.3 MD.3. MD.3. MD.3.5c MD.3.5b MD.3.5a MD.3.3b MD.3.3a 4 5 Recognize volume as an attribute of solid figures and understand concepts of volume measurement. A cube with side length 1 unit, called a unit cube, is said to have one cubic unit of volume, and can be used to measure volume. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft., and improvised units. Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. Find the volume of a right rectangular prism with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes. Apply the formulas V = l w h and V = b h for rectangular prisms to find volumes of right rectangular prisms with whole number edge lengths in the context of solving real world and mathematical problems. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems. Volume and Area March 13 - April 21 understand unit cubes and how they can be used to build a solid figure. count unit cubes that fill a solid figure to find volume. estimate the volume of a rectangular prism. find the volume of rectangular prisms. use a formula to find the volume of a rectangular prism. use the strategy make a table to compare volumes. find the volume of combined rectangular prisms. derive and apply the formula for the area of a parallelogram from the area of a rectangle. derive and apply the formula for the area of a triangle from the area of a rectangle and a parallelogram. derive and apply the formula for the area of a trapezoid from the area of a parallelogram. find and describe the surface area of rectangular prisms. determine the surface area of rectangular prisms / / cubic unit, unit cube, volume, area, base, diagonal, formula, height, layer, rectangular prism, surface area, width Benchmarks Next Generation Standards MA.5.G.3.2 Describe, define, and determine surface area and volume of prisms by using appropriate units and selecting strategies and tools. MA.5.G.5.4 Derive and apply formulas for areas of parallelograms, triangles, and trapezoids from the area of a rectangle. FCAT Testing Window - April 22 to May 7

4 Unit & Go Math! & lessons from each Number and Operations in Base Ten NBT.1.2 Understand the place value system. Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Applying Multiplication and Division of Decimals May 8 - May 14 multiply a decimal and a whole number using drawings and place value. place the decimal point in decimal multiplication. model division by decimals. place the decimal point in decimal division. solve multistep decimal problems using the strategy work backward / with / No new words. Build on prior knowledge.

5 Unit & Go Math! Number and Operations- Fractions NF.2.7a NF.2.7 NF.2.6 NF.2.5b NF.2.5a NF.2.5 NF.2.4b NF.2.4a NF.2.4 NF.2.3 Apply and extend previous understandings of multiplication and division to fractions. Interpret a fraction as division of the numerator by the denominator (a/b = a b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. Interpret the product (a/b) q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a q b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas. Interpret multiplication as scaling (resizing), by: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number; explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n a)/(n b) to the effect of multiplying a/b by 1. Solve real world problems involving multiplication of fractions and mixed numbers. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 1 Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. Multiplication and Division of Fractions May 15 - May 29 model the product of a fraction and a whole number. multiply fractions and whole numbers. multiply fractions using models. relate the size of the product compared to the size of one factor when multiplying fractions. use a model to multiply two mixed numbers and find the area of a rectangle. relate the size of the product to the factors when multiplying fractions greater than one. solve problems using the strategy guess, check, and revise. interpret a fraction as division and solve whole-number division problems that result in a fraction or mixed number. divide a whole number by a fraction and divide a fraction by a whole number. represent division by drawing diagrams and writing story problems and equations. & lessons from each row should be combined.* 7.1/ / / / / No new words. Build on prior knowledge. NF.2.7b NF.2.7c Interpret division of a whole number by a unit fraction, and compute such quotients. Solve real world problems involving division of unit fractions by nonzero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. The end of year assessment may be given at the teacher's discretion.

6 Unit & Go Math! & lessons from each Operations and Algebraic Thinking OA.2.3 Analyze patterns and relationships. Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. identify, describe, and create numeric patterns with decimals and fractions. make and use line plots with fractions to solve problems. use two rules to generate a numerical pattern and identify the relationship between the corresponding terms in the patterns. graph the relationship between two numerical patterns on a coordinate grid. 3.10/ / number pair, pattern, rule, sequence, term Number and Operations- Fractions Number and Operations in Base Ten Use equivalent fractions as a strategy to add and subtract fractions. NF.1.1 Perform operations with multi-digit whole numbers and with decimals to hundredths. NBT.2.7 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Rules and Relationships May 30 - June 4 Measurement and Data MD.2.2 Represent and interpret data. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally. The end of year assessment may be given at the teacher's discretion. June 5 - End of Third Trimester