Fifth Grade Guide to Plan for Success 2017-2018 Contents Contents................................................................................................................ 1 Monthly and Daily Overview of Fifth Grade............................................................................... 2 Operations with Whole Numbers........................................................................................... 3 Know, Understand, Do (Aug. – Oct.).....................................................................................5 August - October.......................................................................................................7 Decimals............................................................................................................... 10 Know, Understand, Do (Nov. – Dec.)....................................................................................11 November - December...................................................................................................13 Add, Subtract and Multiply Fractions................................................................................... 15 Know, Understand, Do (Jan.)...........................................................................................17 January...............................................................................................................18 Dividing Fractions and Volume.......................................................................................... 20 Know, Understand, Do (Feb. – March)...................................................................................22 February and March....................................................................................................23 Geometry Day:.......................................................................................................... 25 Quadrilaterals and Coordinate Planes (One Day a Week throughout the Year).............................................25 Know, Understand, Do..................................................................................................27 1 Updated 11/6/17
Monthly and Daily Overview of Fifth Grade.......................................................................................................................................................................................................................2
Operations with Whole Numbers.........................................................................................................................................................................................................................................3
Know, Understand, Do (Aug. – Oct.)...............................................................................................................................................................................................................................5
August - October................................................................................................................................................................................................................................................................7
Know, Understand, Do (Nov. – Dec.)..............................................................................................................................................................................................................................11
November - December.....................................................................................................................................................................................................................................................13
Add, Subtract and Multiply Fractions...............................................................................................................................................................................................................................15
Know, Understand, Do (Jan.)..........................................................................................................................................................................................................................................17
Dividing Fractions and Volume..........................................................................................................................................................................................................................................20
Know, Understand, Do (Feb. – March)..........................................................................................................................................................................................................................22
February and March........................................................................................................................................................................................................................................................23
Quadrilaterals and Coordinate Planes (One Day a Week throughout the Year)......................................................................................................................................................25
Reference Sheet given for the FSA-on the last page of the hyperlinked document
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Operations with Whole Numbers Aug-Oct
DecimalsNov.-Dec.
Add/Sub and Multiply FractionsJan.
Divide Fractions and Volume
Feb.-March
Review April-May
One Day a Week: Geometry Day
First half of the year:QuadrilateralsReview attributes of the shapes and apply to the hierarchy.Put them in a Venn diagramExplore!Math talk and reasoning is essential throughout
Standards (not listed in order) Test SpecificationsMAFS.5.OA.1.1: DOK 1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
MAFS.5.OA.1.2: DOK 2Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.
MAFS.5.NBT.2.5: DOK 1Fluency Standard should be practiced all year longFLUENTLY multiply multi-digit whole numbers using the standard algorithm. (4th grade 2 X 2 and 4 X 1) In fourth grade, students developed understanding of multiplication through using various strategies. While the standard algorithm is mentioned, alternative strategies are also appropriate to help students develop conceptual understanding. The size of the numbers should NOT exceed a five-digit factor by a two-digit factor unless students are using previous learned strategies such as properties of operations
MAFS.5.NBT.1.1: DOK 1Recognize that in a multi-digit number, a digit in one place represents10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
MAFS.5.NBT.1.2: DOK 2Explain 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.
MAFS.5.NBT.2.6: DOK 2 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. Division problems can include remainders.
MAFS.5.MD.1.1: DOK 2Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Know, Understand, Do (Aug. – Oct.) Recognize and explain the pattern in the number of zeros.
o Refrain from saying, “add a zero”. Instead refer to the decimalo Practice where the decimal point is in any number (ex. Where is the decimal point in this number:
5? What about 50? Is that larger or smaller?)o Relate to the powers of ten. Video
Use a calculator. Have students do 10 x 10, then 10 x 10 x 10, and continue doing that pattern, asking the students what they notice.
Students write the power of ten and other ways of writing the number. Interpret numerical expressions without evaluating them (ex. Two times the difference of eight and one= 2 x (8-1) or fifteen minus the sum of six and seven = 15 – (6 + 7))—Not enough of this in Go-Math, Use Ready Teacher ToolboxWrite simple expressionsUse parenthesis, brackets, or braces in numerical expressions with whole numbers, fractions, and decimals.Evaluate expressions
Fluently multiply up to five digits by two digits with standard algorithmReview what fourth grade taught: partial products and area model to connect to the standard algorithm and reasonableness Estimate first-what is reasonable? Students compute the first factor times the ones place and the first factor times the tens place (relates to powers of ten) example: 6,892 x 42 = 7,000 x 2 = 14,000 and 7,000 x 40 = 280,000, so answer should be around 14,000 + 280,000 = 294,000Order to teach: 4 digit x 1 digit; 5 digit x 1 digit; 2 digit x 2 digit; 3 digit x 2 digit; 4 digit x 2 digit; 5 digit x 2 digit
Conceptual Understanding: Find quotients of up to four-digit dividends and two-digit divisors with and without remainderso Context needed!o Divisor is number of groups or the size of groupso Use equations, rectangular arrays, area model, partial quotients (expectation)o Fourth grade used strategies to divide one-digit divisorso Check your answer with the inverse operation (adding the remainder)
Use MD.1.1 to practice your multiplication and division standards (example: I have 45 gallons, how many cups? 288 inches is how many feet?)
Sequence of Skills: August - October
Skill Notes Problem of the Day Examples ResourcesPlace Value Find the decimal in the number (even when it is a whole Explain how you can use place value Ideas from:
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Fifth Grade Guide to Plan for Success 2017-2018
Understanding with reference to the decimal
Goal: Noticing the pattern of the decimal moving-making the number bigger or smaller
number) Refer to fourth grade’s skill of ten times a number New-the digit to the right is 1/10 the digit to the left.
Example: Start with the number 5 Where is the decimal? Mark it. Make 50. Where is the decimal? What happened? Make 500. Where is the decimal? What happened?
Repeat with going the other way and starting with a larger number. (decimals aren’t the focus here)
If understanding is there combine this with powers of ten
patterns to describe how 50 and 5,000 compare.
Go Math Page 7, number 17
GM- 1.1, 1.2, 1,5TT- Unit 1, Lesson 1-2
Quadrilateral Flipchart Aug-Dec
Expressions, Multiplication and Division Flipchart
Powers of Ten
Not a requirement to do negative powers of ten
Use problems with large numbers. Underline one of the digits. When showing the value of the digit, record it in multiple
ways:o Powers of ten o Expanded formo If I didn’t have ______, how could I make it with
tens?, hundreds?, thousands? Etc.
569,24360,000, 6 ten thousands, 6 x 10^4, 60 thousands, 600 hundreds, 6,000 tens
The U.S. Census Bureau has a population clock on the internet. On a recent day, the U.S. population was listed as 310,763,136.
Justin said that multiplying 8.0 by 10^6 would increase the value of the 8 because there would be 6 more zeros to the right of the decimal point. Is this true?
**Questions to elicit thinking in Ready Teacher Toolbox-Unit 1, Lesson 1-2
Powers of ten VideoIdeas from:GM- 1.1, 1.2, 1,5TT- Unit 1, Lesson 1-2
Engage NY Divide by 10
August-October Cont’d
Skill Notes Problem of the Day Examples ResourcesExpressions Practice interpreting and writing simple expressions
By starting with this problem of the day, it opens the discussion of why parenthesis are needed.
Evaluate expressions with parenthesis, braces, and
Six times the sum of three plus four Ideas from:GM-1.3, 1.10, 1.11, 1.12TT- Unit 3, Lesson 19
(needs to be revisited after teaching decimals and fractions are taught)
brackets
Multiplication
Fluency Standard-standard algorithm a requirement
Use with a context
Infuse MD.1.1 conversions
Review what fourth grade taught: partial products and area model to connect to the standard algorithm and reasonableness
Estimate first-what is reasonable? Students compute the first factor times the ones place and the first factor times the tens place (relates to powers of ten) example: 6,892 x 42 = 7,000 x 2 = 14,000 and 7,000 x 40 = 280,000, so answer should be around 14,000 + 280,000 = 294,000
Order to teach: 4 digit x 1 digit; 5 digit x 1 digit; 2 digit x 2 digit; 3 digit x 2 digit; 4 digit x 2 digit; 5 digit x 2 digit
Lesson from Engage NY
Ideas from:GM- 1.6 (starting at 4 digit x 1 digit); 1.7 (not 4 digit x 3 digit); 1.8 (to get ready for division strategies)TT:
August-October Cont’d
Skill Notes Problem of the Day Examples ResourcesDivision Find quotients of up to four-digit dividends and
two-digit divisors with and without remaindersZenin’s baby sister weighed 132 ounces at birth. How much did his
Divide 2-to-4 Digit by 1-Digit NumberLesson using area models as a strategy
Context needed!Divisor is number of groups or the size of groupsUse equations, rectangular arrays, area model, partial quotients (expectation)Fourth grade used strategies to divide one-digit divisorsCheck your answer with the inverse operation (and addition for the remainder)
sister weigh in pounds and ounces?
A water cooler holds 1,284 ounces of water. How many more 6 ounce than 12 ounce glasses can be filled from a full cooler?
A baker was going to arrange 432 desserts into rows of 28. The baker divides 432 by 28 and gets a quotient of 15 with remainder 12. Is he right? Explain what the quotient and remainder represent.
for multi-digit division: LearnZillion, Use an Area Model of 4-digit dividends by 2 digit divisorsEngage NY Estimating with 2-Digit DivisorsEngage NY ALL of module 2, Topic F
Decimals November – December
Standards Test SpecificationsMAFS.5.NBT.1.1: DOK 1
Recognize that in a multi-digit number, a digit in one place represents10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.
MAFS.5.NBT.1.2: DOK 2Explain 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.
MAFS.5.NBT.1.3: DOK 2Read, write, and compare decimals to thousandths.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).b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.
MAFS.5.NBT.1.4: DOK 1Use place value understanding to round decimals to any place.
MAFS.5.NBT.2.7: DOK 2Add, 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.
MAFS.5.MD.1.1: DOK 2Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.
Know, Understand, Do (Nov. – Dec.)
Recognize and explain the pattern in the number of zeros. o Refrain from saying, “add a zero”. Instead refer to the decimal
o Practice where the decimal point is in any number Relate to the pattern of place value (ten x a number and 1/10 of a number) with a decimal moving to the left and the right (bigger and smaller) (ex. Where is the decimal point in this number: 5? What about 50? Is that larger or smaller?)
o Relate to the powers of ten. Video Use a calculator. Have students do 10 x 10, then 10 x 10 x 10, and continue doing that
pattern, asking the students what they notice. Students write the power of ten and other ways of writing the number.
o Pose problems relating to conversions of measuremento Expand on answers by having the students convert metric units from the answers. Use MD.1.1 to continue practicing your multiplication and division standards (example: I have 45 gallons, how many cups? 288 inches is how many feet?)Read, write and compare decimals to the thousandths (progression from fourth grade decimals to the hundredths)o Review tenths and hundredths o Before using whole numbers with your decimals, make sure they understand the decimal o Use expanded form, base-ten numerals, and number nameso Relate to the pattern of place value (ten x a number and 1/10 of a number) with a decimal moving to the left and
the right (bigger and smaller)o Relate to zero, half, and whole o Use a meter stick with thousandths-meter is 1, decimeter is a tenth, centimeter is a hundredth, a millimeter is a
thousandtho Use base ten model –tenths=ten rods, hundredths=ones, thousandths=a one cut into to ten
o Estimate first o Line up place values (be sure to give examples and non-examples) o Real-world examples (context)
Multiply and divide decimals to the hundredthso Estimate first o Be sure that each time you do the problems, you are questioning for reasoning, “How do you know the decimal is
in the right place?”o Students use concrete models and pictorial representationso Strategies based on place value, and properties of operations
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Fifth Grade Guide to Plan for Success 2017-2018
November - DecemberSkill Notes Problem of the
Day ExamplesResources
Decimal DevelopmentGoal: Introduction to thousandths and relationship of decimals on the meter stick
How big/small are decimals?
How can you write the number?
*Use only decimals-no whole numbers Put .53 on the board
What does that mean?Where is it on the meter stick? (middle because it is half)What if I added a digit 4 to the right?Is the number bigger or smaller? How do you know?
What would happen if I move the decimal to the right? To the left?How can I write/show this number (expanded form and others)?o 5/10 + 3/100 + 4/1,000 o 534/1000 o 53/100 + 4/1000 o (5 x .1) + ( 3 x .01) + (4 x .001)o .5 + .03 + .004
Quadrilateral Flipchart Aug-Dec
Decimal Flipchart
Use a meter stick meter is 1, decimeter is a tenth, centimeter is a hundredth, a millimeter is a thousandthZoomable number line
Lesson about naming decimals in expanded, unit and word form: EngageNY, Module 1, Lesson 5
GM: 3.1, 3.2TT:Unit 1, Lesson 3
Compare Decimals Teach for place value understanding to recognize patterns
Show it on the meter stickUse benchmarks – 0, .5, 1 to help with the visual understanding of the size of the decimals
Zoomable number line
GM: 3.3TT: Unit 1, Lesson 4
Round Decimals Teach for place value understanding to recognize patterns before going to “easy to remember song”
When rounding to the nearest tenth, create a number line from one tenth to another. Ask them to label the intervals.Plot is on the meter stickWhat two tenths is it in-between?What is in the middle?What happens to the number when I round it to the nearest tenth? Nearest hundredth?
Zoomable number line
Lesson about using number lines and place value to round a given decimal number.EngageNY Module 1, Lesson 7TT: Unit 1, Lesson 4
Metric Conversions Goal:Students are able to reason if the answer would be larger or smaller when converting from one unit to another.
Have students estimate amounts and practice measuring things around the classroom with a meter stick. If items were measured in cm, ask them to tell you how many millimeters, etc.
Relate to the powers of ten Converting between metric units: kilometer (km), meter (m), centimeter (cm), kilogram (kg), gram (g), milligram (mg), liter (L), milliliter (mL)
Find problems with mass, capacity, and linear measurement in metric units
One kilogram is equivalent to 1,000 grams. How many kilograms are equivalent to 450 grams?
Will the number be greater or less than 450? How do you know?
To help picture: The centimeter cube, if it were hollow, holds a milliliter of water and a thousand cube holds a liter.
You can model it with a T-Chart
Ideas from: GM-10.5, 10.6TT-Unit 4, Lesson 21
Add and Subtract Decimals to HUNDREDTHSUse real-world problems
Estimate first Line up place values (be sure to give examples and non-examples)
Use real-world problems (can use MD.1.1 conversions)Three boxes of cereal have masses of 379.4 grams, 424.25 grams, and 379.37 grams. What’s the difference between the box with the greatest mass and the box of cereal with the least mass?
Ideas from:GM-3.5, 3.6TT- Unit 1, Lesson 7
Multiplying and Dividing Decimals to HUNDREDTHSUse real-world problems to make sense. After you teach the concept of how to solve it, mix up problems for students to determine which operation they do and why.
Estimate first Be sure that each time you do the problems, you are questioning for reasoning, “How do you know the decimal is in the right place?”When multiplying decimals x decimals, students should reason whether the product will be greater or less than the number being multiplied (why?) Students use concrete models and pictorial representationsStrategies based on place value, and properties of operations
Use real-world problems(can use MD.1.1 conversions)Hayden made a sign that is 1.4. Meters long and 1.2 meters wide to post on the wall of his store. How many square meters of wall will the sign cover?
Multiply and Divide Decimal Flipchart
Centimeter grid paper
Ideas from:GM-Chapter 4 & 5 (minus 5.8)TT: Unit 1, Lesson 8, Lesson 9Math In Action
Standards FSA Test SpecsMAFS.5.NF.1.1: DOK 2Add 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.) It is not necessary to find a least common denominator to calculate sums of fractions, and in fact the effort of finding a least common denominator is a distraction from understanding adding fractions.
MAFS.5.NF.1.2: DOK 2Solve 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.
MAFS.5.MD.2.2: DOK 2Make 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.
MAFS.5.NF.2.3 DOK 2Interpret 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, e.g. by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?
MAFS.5.NF.2.4: DOK 2Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.
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. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)
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.
MAFS.5.NF.2.6: DOK 2Solve real world problems involving multiplication of fractions and mixed numbers, e.g. by using visual fraction models or equations to represent the problem. This standard could include fraction by a fraction, fraction by a mixed number or mixed number by a mixed number.
MAFS.5.NF.2.5: DOK 3Interpret multiplication as scaling (resizing), by:
a. 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.
b. 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×a) / (n×b) to the effect of multiplying a/b by 1.
This standard should not be taught in isolation, but explored and discussed when students are working with NF.2.4
Know, Understand, Do (Jan.)Add and subtract fractions
o Review understanding of fractions greater than one and mixed numbers and their relationship.
o Check for understanding of finding a common denominator (learned in fourth grade) Fourth grade introduced equivalent fractions are fractions x 1 (the identity property). If you give a fraction, they should be able to give you an equivalent fraction and explain why.
o Estimate by thinking of benchmarks of zero, half, and one to think of the reasonableness of the answero Use real-life word problems o Mix addition and subtraction o
Represent and interpret data of measurement of fractions ½, ¼, and 1/8 in a line plot o Solve problems involving information presented in the line plot
Use in a real-world Context:Interpret a fraction as division of the numerator by the denominator
Solve word problems involving division of whole numbers leading into a fractionUse visual fraction models.
Fraction times a whole number (extension of fourth grade) o Relate to repeated addition o Interpret if the product will be greater or less than the given number. How do you know?o Students create a story context for an equation o Use visual fraction models
Fraction times a fraction o Use visual fraction models o Find the area of a rectangle with fractional side lengthso Interpret if the product will be greater or less than the given number. How do you
know?o ½ x 1/3 means ½ of a 1/3 piece
January Skill Notes Problem of the Day
ExamplesResources
Review of Fractions from 4th Grade
Fourth grade introduced equivalent fractions are fractions x 1 (the identity property). If you give a
Introduction to addition and subtraction of fractions
Use real-world problems
fraction, they should be able to give you an equivalent fraction and explain why.
Relate place value understanding of whole numbers and decimals to why fractions need to have common denominators. (tenths added to tenths)
Before they add, they need to estimate compared to benchmarks of 0, ½, and 1 (to think of reasonableness)
students to add or subtract like denominators.
Add, subtract, and multiply fractions flipchart
Engage NY Module 4 Flipchart- Multiplying and Dividing Fractions
Dividing Fractions Flipchart
Adding and subtracting with unlike denominators
Use real-world problemsMix addition and subtraction
Check for understanding of finding a common denominator (learned in fourth grade)Estimate by thinking of benchmarks of zero, half, and one to think of the reasonableness of the answerUse real-life world problems Mix addition and subtraction problems
GM: Chapter 6 ( mix lessons of adding and subtracting so they are not isolated)TT: Unit 2, lesson 10, 11
Adding and Subtracting with fractions greater than one and mixed numbers
Check for understanding of mixed numbers and fractions greater than one with visual models (example: 2 ¾ = 1 7/4 = 11/4)
January Cont’d
Skill Notes Problem of the Day Examples
Resources
Represent and Interpret Data
Fractions ½, ¼, and 1/8 in a line plot Solve problems involving information presented in the line plot
Line Plot Game from Illustrative Math TaskGM-9.1 Not enough exposure in Go Math TT: Unit 4, Lesson 23
Practice with creating line plots and analyzing data that requires fraction operations: EngageNY, Module 4, Lesson 1
Represent Fractions as Division
Real-World Problems
Solve word problems involving division of whole numbers leading into a fractionUse visual fraction models.
Multiplication of a Whole Number by a Fraction
Real-World Problems
Multiplication is repeated addition Reason about the size of the product and explain
Multiplication of a Fraction by a Fraction
Real-World Problems
Reason about the size of the product and explain Show by area of a rectangle (dimensions are fractional parts)-shows the size of the product being smaller
Dividing Fractions and VolumeFebruary - March
Standards Test Specifications MAFS.5.NF.2.7: DOK 2Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.1
a.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) × 4 = 1/3.
4 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 × (1/5) = 4.
b. 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 many1/3-cup servings are in 2 cups of raisins?
MAFS.5.MD.3.3: DOK 1Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
a. 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.
b. 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.
MAFS.5.MD.3.4: DOK 1Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft. and improvised units.MAFS.5.MD.3.5: DOK 2Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
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.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.
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.
Know, Understand, Do (Feb. – March)
Use in a real-world Contexts:Division of a whole number by a unit fraction and Division of a unit fraction by a whole number
Use real world context to make meaning of the dividend and divisor.Show using visual models Relate division of fractions to division of whole numbers (example: 4 divided by 1/3 means how many 1/3 are in 4)
Volume:Concept development for all prisms learned in middle school. It is important not to go straight to the standard algorithm!
Students should experience filling rectangular prisms without gaps or overlaps to determine cubic units3D means cubic unitsRepeated addition with the area of the base Volume = area of the base x heightConnect two rectangular prisms to find the volume
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Fifth Grade Guide to Plan for Success 2017-2018
February and March Skill Notes Problem of the Day Examples Resources
Divide a whole number by a unit fraction
Real-World Problems*Conceptual Understanding
Use real world context to make meaning of the dividend and divisor.Show using visual models Relate division of fractions to division of whole numbers (example: 4 divided by 1/3 means how many 1/3 are in 4 and opposite 1/3 divided by 4 means I am taking a 1/3 section and dividing it into four pieces.)Check it with the inverse
Charlotte has 6 apples that she wants to share. If she cuts them in ½, how many friends can she share with?
Mia walks a 2 mile fitness trail. She stops to exercise every 1/5 mile. How many times does Mia stops to exercise?
Coordinate Plane Flipchart
Engage NY Module 4 Flipchart-Multiplying and Dividing Fractions
Dividing Fractions Flipchart
Use problems found in GM, but expect them to show you visually and with a written context why the answer is reasonable.
With 6 cubes build a rectangle and relate it to a one story building.If we wanted to make it two stories, how many cubes would we need?How does the volume change each time we add a new floor?Now what are the dimensions of our rectangular prisms?Relate to length x width x height, repeated addition of the base, or base x heightCould we build a building with the same number of cubic units with different dimensions?
Fill centimeter cube boxes with centimeter cubes
Minecraft volume lesson
Three Act Tasks:Penny CubePop TopGot CubesPacking SugarOverflowAmerican Flagthe Fish TankPopcorn, Anyone LessonGM: Chapter 11TT: Unit 4 Lesson 24-27
Connect Two Rectangular Prisms
Use in context:Real-World Examples:Wedding cakes, stairs, towers, robots, pools, skyscrapers
Geometry Day: Quadrilaterals and Coordinate Planes (One Day a Week throughout the Year)
Standards FSA Test SpecsMAFS.5.G.1.1: DOK 1Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
MAFS.5.G.1.2: DOK 2Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
MAFS.5.OA.2.3: DOK 2Generate 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. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences,
and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.Classify two-dimensional figures into categories based on their properties.
MAFS.5.G.2.3: DOK 2Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category.For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles.
MAFS.5.G.2.4: DOK 2Classify two-dimensional figures in a hierarchy based on properties
o Create Venn diagramso Describe attributes o Depending on the program used, trapezoids have two definitions iReady has the inclusive definition of trapezoids—at least one set of a parallel linesGo-Math has the exclusive definition of trapezoids-only one set of parallel lines
Classification FlipchartPolygon Capture RulesPolygon Capture Game CardsPolygon Capture Cards
Students plot points on the coordinate grid based on a set of ordered pairs recognizing the first number is the x-axis (origin across) and the second number is the y-axis (origin vertically)
o Plot points based on a real-world problemo Name the coordinate from a plotted point o Follow directions to create a path from one point and determine another o Show a relationship between two patterns.
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