Products and Quotients with Decimals Unit
The Products and Quotients with Decimals Unit involves using patterns and place value to develop strategies to multiply and divide decimals. Questions to answer may include:
Grade 5
Operations with Whole Numbers Unit
The Operations with Whole Numbers Unit involves using patterns and place value to apply strategies to perform all four operations with whole numbers. Questions to answer may include:
- How are the properties of place value (additive, multiplicative, base-ten & positional) useful in applying efficient procedures for adding, subtracting, multiplying and dividing whole numbers?
- How can mental math, rounding, and/or the use of compatible numbers help to determine whether a solution is reasonable?
- How does an expression differ from an equation?
Grade 5 - Operations with Whole Numbers Unit
Decimal Place Value Unit
The Decimal Place Value Unit involves understanding and representing the relative position, magnitude and relationships within the numeration system in order to answer questions such as:
- How can you use the additive property of place value to decompose this decimal number?
- How can you use the multiplicative property of place value to describe the meaning of each digit in the number 0.123?
- How can you use the base ten property of place value to explain the relationship between each of the digits in the number 5.555?
Grade 5 - Decimal Place Value Unit
5.NF.B.7c
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. For example, how much chocolate will each person get if 3 people share `1/2` lb of chocolate equally? How many `1/3`-cup servings are in 2 cups of raisins?
5.NF.B.7b
Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (`1/5`), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (`1/5`) = 20 because 20 x (`1/5`) = 4.
5.NF.B.5b
Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); 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 x a))/((n x b))` to the effect of multiplying `a/b` by 1.
5.NF.B.7a
Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (`1/3`) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (`1/3`) ÷ 4 = `1/12` because (`1/12`) x 4 = `1/3`.
5.NF.B.4a
Interpret the product (`a/b`) x q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (`2/3`) x 4 = `8/3`, and create a story context for this equation. Do the same with (`2/3`) x (`4/5`) = `8/15`. (In general, (`a/b`) x (`c/d`) = `sf text(ac)/(sf text(bd)`.)
5.NBT.A.3a
Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x `(1/10)` + 9 x `(1/100)` + 2 x `(1/1000)`.
5.MD.C.5b
Apply the formulas V = l x w x h and V = b x 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.