 Number and Operations in Base Ten Understand the place value system. 5.NBT.5: 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. Exponents and powers of 10 Multiply by powers of ten Divide by powers of ten Multiply and divide by powers of ten 5.NBT.5: 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. Exponents and powers of 10 Multiply by powers of ten Divide by powers of ten Multiply and divide by powers of ten 5.NBT.6: Read, write, and compare decimals to thousandths. 5.NBT.6: Read, write, and compare decimals to thousandths. 5.NBT.6.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Base-ten numerals Number names Expanded form 5.NBT.6.a: Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). Base-ten numerals Number names Expanded form 5.NBT.6.b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. 5.NBT.6.b: Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. Perform operations with multi-digit whole numbers and with decimals to hundredths. 5.NBT.8: Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply by 2-digit numbers Multiply by 3-digit numbers Multiply three or more numbers 5.NBT.8: Fluently multiply multi-digit whole numbers using the standard algorithm. Multiply by 2-digit numbers Multiply by 3-digit numbers Multiply three or more numbers 5.NBT.9: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 2-digit and 3-digit dividends 4-digit dividends Strategies 5.NBT.9: Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. 2-digit and 3-digit dividends 4-digit dividends Strategies 5.NBT.10: 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. Add and subtract Multiply decimals and whole numbers Multiply two decimals Divide 32. Mixed operations 5.NBT.10: 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. Add and subtract Multiply decimals and whole numbers Multiply two decimals Divide 32. Mixed operations
 Number and Operations-Fractions Use equivalent fractions as a strategy to add and subtract fractions. 5.NF.11: 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 fractions Subtract fractions Add and subtract mixed numbers 5.NF.11: 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 fractions Subtract fractions Add and subtract mixed numbers 5.NF.12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Like denominators Unlike denominators 5.NF.12: Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. Like denominators Unlike denominators Apply and extend previous understandings of multiplication and division to multiply and divide fractions. 5.NF.14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.14: Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. 5.NF.14.a: 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. Multiply fractions by whole numbers Multiply two fractions Multiply mixed numbers 5.NF.14.a: 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. Multiply fractions by whole numbers Multiply two fractions Multiply mixed numbers 5.NF.14.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. Multiply fractions with models Area and perimeter 5.NF.14.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. Multiply fractions with models Area and perimeter 5.NF.17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 5.NF.17: Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. 5.NF.17.a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 5.NF.17.a: Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. 5.NF.17.b: Interpret division of a whole number by a unit fraction, and compute such quotients. 5.NF.17.b: Interpret division of a whole number by a unit fraction, and compute such quotients. 5.NF.17.c: Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. 5.NF.17.c: Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem.
 Measurement and Data Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition. 5.MD.22: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.22: Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 5.MD.22.a: 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, e.g., to represent the associative property of multiplication. 5.MD.22.a: 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, e.g., to represent the associative property of multiplication. 5.MD.22.b: 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. 5.MD.22.b: 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. 5.MD.22.c: 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. 5.MD.22.c: 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.
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