unit 5 - Using Models to Add and Subtract Decimals and Fractions
Adding & Subtracting Decimals
STANDARDS
5.NBT.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.
QUESTIONS TO CONSIDERIs my answer reasonable?
What connections can I make between the models we've used, my place value knowledge, and vertically aligning like place values to add and subtract decimals? |
VIDEOS |
Add & Subtract Fractions - unlike denominator
Standards
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1: 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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2: 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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
5.NF.1: 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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
5.NF.2: 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. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.
GUIDING QUESTIONS
- How are fractions related?
- How might addition and subtraction of fractions be used in real life?
VOCABULARYbenchmark fraction: common fractions that are used to compare against; common benchmark fractions include 1/10, 1/4, 1/2, and 3/4.
denominator: the number below the line in a common fraction; a divisor equivalent: equal fraction: a part of a whole mixed number: a number consisting of an integer and a proper fraction numerator: represents the number of equal parts in a fraction unit fraction: a fraction with a numerator 1 |
VIDEOSWCPSS Video Support (from YouTube Channel):
BrainPOP- Fractions Study Jams- Fractions |
UNIT 6 - mULTIPLYING AND DIVIDING WHOLE NUMBERS
Video Resources: Wake County Academics YouTube Channel
Multiplying Decimals Videos
Decimal x Whole with Grids
Decimal x Whole with Grids Video 2
Decimal x Whole Number with Number Lines
Decimal x Whole with Number Lines Video 2
Decimal x Decimal with Area Model
Decimal x Decimal with Base Ten Blocks
Decimal x Decimal with Number Lines
Dividing Decimals Videos
Whole divided by Decimal with Base Ten Blocks
Whole divided by Decimal with Grids
Decimal divided by Whole with Number Lines
Decimal divided by Whole with Base Ten Blocks
Decimal divided by Whole with Grids
Decimal divided by Decimal with Number Lines
Decimals divided by Decimals with Grids
Decimal x Whole with Grids
Decimal x Whole with Grids Video 2
Decimal x Whole Number with Number Lines
Decimal x Whole with Number Lines Video 2
Decimal x Decimal with Area Model
Decimal x Decimal with Base Ten Blocks
Decimal x Decimal with Number Lines
Dividing Decimals Videos
Whole divided by Decimal with Base Ten Blocks
Whole divided by Decimal with Grids
Decimal divided by Whole with Number Lines
Decimal divided by Whole with Base Ten Blocks
Decimal divided by Whole with Grids
Decimal divided by Decimal with Number Lines
Decimals divided by Decimals with Grids
Multiplying Whole Numbers
Unit Overview for Parents - how to support your son or daughter at home: https://drive.google.com/file/d/10jHbd_Ryf2vK2Hvli4xdshu4Hmv7qe5a/view
5.NBT.5 Fluently multiply multi-digit whole numbers with the standard algorithm.
Unit Overview for Parents - how to support your son or daughter at home: https://drive.google.com/file/d/10jHbd_Ryf2vK2Hvli4xdshu4Hmv7qe5a/view
5.NBT.5 Fluently multiply multi-digit whole numbers with the standard algorithm.
Multiplication Strategies
Partial Products
Students apply their understanding of the value of digits in order to find partial products (part of the total product). They then add the partial products together to find the product. While this most closely resembles the standard algorithm, students are considering the value of the digits as they multiply instead of simply following a procedure. |
UNIT 4 - Understanding Place Value in the Context of Metric Measurement
GUIDING QUESTIONS
What patterns exist in our place value system?
What relationships exist between place value and measurement systems?
What patterns exist in our place value system?
What relationships exist between place value and measurement systems?
Decimal Place Value
5.NBT.3 READ, WRITE, AND COMPARE DECIMALS TO THOUSANDTHS.
a. Read and write decimals to thousandths using base-ten
numerals, number names, and expanded form
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.4 Use place value understanding to round decimals to any place.
a. Read and write decimals to thousandths using base-ten
numerals, number names, and expanded form
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.4 Use place value understanding to round decimals to any place.
expanded formA way to write a number that shows the sum of the values of each digit in the number. Students will learn 3 different ways to write a number in expanded form.
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512.58
500 + 10 + 2 + 0.5 + 0.08 or 5(100) + 1(10) + 2(1) + 5(0.1) + 8(0.01) or 5(100) + 1(10) + 2(1) + 5(1/10) + 8(1/100) |
ROUNDING DECIMALS
Students will use visual models (number lines and base-ten grids) to round decimal numbers).
Base-ten GridsStudents use base-ten grids to represent one whole. In the example to the right, each grid is broken in to 100 smaller sections. Each smaller section holds a value of 0.01, or one hundredth. Ten hundredths is equal to 0.1 or one tenth. We can use this knowledge to help round to the nearest tenth.
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