One Day a Week: - Sarasota County Schools



TOC \o "1-3" \h \z \u Monthly and Daily Overview FSA Reporting Categories PAGEREF _Toc513191063 \h 2Operations with Whole Numbers (August – October) PAGEREF _Toc513191064 \h 3August - October Test Specifications PAGEREF _Toc513191065 \h 5Know, Understand, Do (Aug. – Oct.) PAGEREF _Toc513191066 \h 6Sequence of Skills: August - October PAGEREF _Toc513191067 \h 7Decimals (November – December) PAGEREF _Toc513191068 \h 11November – December Test Specifications PAGEREF _Toc513191069 \h 14Know, Understand, Do (Nov. – Dec.) PAGEREF _Toc513191070 \h 15Sequence of Skills: November - December PAGEREF _Toc513191071 \h 17January: Add, Subtract and Multiply Fractions PAGEREF _Toc513191072 \h 19January Test Specifications PAGEREF _Toc513191073 \h 22Know, Understand, Do (Jan.) PAGEREF _Toc513191074 \h 23Sequence of Skills: January PAGEREF _Toc513191075 \h 24February – May: Dividing Fractions and Volume PAGEREF _Toc513191076 \h 27February – May Test Specifications PAGEREF _Toc513191077 \h 29Know, Understand, Do (Feb. – March) PAGEREF _Toc513191078 \h 30Sequence of Skills: February and March PAGEREF _Toc513191079 \h 31Geometry Day: PAGEREF _Toc513191080 \h 33August – December: Quadrilaterals PAGEREF _Toc513191081 \h 33January - May: Coordinate Grids PAGEREF _Toc513191082 \h 34Geometry All Year Test Specifications PAGEREF _Toc513191083 \h 35Know, Understand, Do (Geometry All Year) PAGEREF _Toc513191084 \h 363641725489585One Day a Week: Geometry DayFirst 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 throughoutSecond half of the year:Coordinate Planes00One Day a Week: Geometry DayFirst 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 throughoutSecond half of the year:Coordinate Planes175260100901500556514099631500Monthly and Daily Overview FSA Reporting Categories Monthly Assessments are located on BlackboardReference Sheet given for the FSA-on the last page of the hyperlinked document.Operations with Whole Numbers (August – October)Standards and DOKSuccess Criteria Teacher NotesAugustMAFS.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.I can draw and model to explain how a digit’s position affects its value.I can explain what’s happening to the value of a digit as it is placed in different places in the numeral.I can model and explain how a digit in one place represents ten times what it represents in the place to its right.I can model and explain how a digit in one place represents 110 what it represents in the place to its left.I can write a number that is a tenth of a number or ten times a number.Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10.Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10.I can explain what happens to a number when the decimal is moved right or left. I can write numbers in expanded form, standard form, and with powers of 10 written as 10 raised to a whole number exponent.When given a number, I can write it in expanded form using powers of ten with a whole number exponent to represent each digit. Have students locate where the decimals are/would be in the whole numbers. In August through October, decimals are not the focus. SeptemberMAFS.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.I can explain how to use the order of operations to evaluate numeric expressions. I can evaluate a numerical expression with brackets, parentheses, or braces.When evaluating a numeric expression, I can explain each step in the process. When given a numerical expression in words, I can write a numeric expression. When given a numeric expression, I can write an expression in words.I can explain why my numerical expression makes sense based on the words used in a mathematical expression.When given an evaluated expression, I can identify what step is incorrect and correct it. In fifth grade, students work with exponents only dealing with powers of ten (5.NBT.2). Students are expected toevaluate an expression that has a power of ten in it.Standards and DOKSuccess Criteria Teacher NotesSeptember and OctoberMAFS.5.NBT.2.5: DOK 1FLUENTLY multiply multi-digit whole numbers using the standard algorithm. I can write a reasonable estimate for a multi-digit multiplication equation and explain whether my estimate is high or low. I can solve a multi-digit multiplication equation using partial products or area models. I can solve a multi-digit multiplication equation using the standard algorithm. I can explain why a zero is put in the second row when solving. I can find the missing digit(s) in the factor(s) when given a solved equation. I can solve for a missing digit in the product. I can check the reasonableness of my answer based on my estimate. Fluency Standard should be practiced all year long (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 This standard refers to fluency which means accuracy (correct answer), efficiency (a reasonable amount of steps), and flexibility (using strategies such as the distributive property or breaking numbers apart also using strategies according to the numbers in the problem.)Use real-world measurement problems that involve multiplication. OctoberMAFS.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. I can determine a reasonable estimate for a multi-digit division problem. I can find the most reasonable partial quotient using my understanding of powers of ten. I can draw and solve the division problem by using partial quotients. I can draw and solve the division problem by using a rectangular array.I can draw and solve the division problem by using an area model.I can explain how to divide by thinking what times the divisor gets me close to the dividend. I can explain what a remainder means.I can show my division answer is correct by multiplying the quotient by the divisor to get the dividend. Long Division is not a requirement!!!!!!!This is for conceptual understanding, meaning the students need to understand what they are doing throughout, not just following steps or procedures. Use real-world measurement problems that involve division. All YearMAFS.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.I can determine if the converted amount will be more or less units than the original unit, and explain my reasoning. I can make a multiplication or division equation to convert units within a measurement system. I can make an equation to solve multi-step, real world problems that involve converting units.*I can explain how my understanding of place value and decimals help me convert among the metric system. Have the students use reference sheet in class and on the tests all year!!!! This standard is throughout the year. Use real-world measurement problems that involve multiplication and division. *Decimals & metric system are not addressed at this point in the year. August - October Test Specifications Know, Understand, Do (Aug. – Oct.) Recognize and explain the pattern in the number of zeros.Refrain from saying, “add a zero”. Instead refer to the decimalPractice 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?)Relate to the powers of ten. Video1034034014617700092218159654100Use 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. 6776545175879700Interpret 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 expressions692787210096500Use parenthesis, brackets, or braces in numerical expressions with whole numbers, fractions, and decimals.Evaluate expressions 9255688326623600Fluently 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 digitConceptual Understanding: Find quotients of up to four-digit dividends and two-digit divisors with and without remaindersContext 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 (adding the remainder)490961734169000Use 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 - OctoberSkillNotesProblem of the Day ExamplesResourcesPlace Value Understanding with reference to the decimalGoal: Noticing the pattern of the decimal moving-making the number bigger or smaller Find the decimal in the number (even when it is a whole number)Refer to fourth grade’s skill of ten times a numberNew-the digit to the right is 1/10 the digit to the left.Example: Start with the number 5Where 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 tenExplain how you can use place value patterns to describe how 50 and 5,000 compare. Go Math Page 7, number 17Ideas from: GM- 1.1, 1.2, 1,5TT- Unit 1, Lesson 1-2 HYPERLINK "" Quadrilateral Flipchart Aug-DecExpressions, Multiplication and Division FlipchartPowers of Ten Not a requirement to do negative powers of tenUse problems with large numbers. Underline one of the digits. When showing the value of the digit, record it in multiple ways:Powers of ten Expanded formIf 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 tensThe 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 1-2Powers of ten VideoIdeas from:GM- 1.1, 1.2, 1,5TT- Unit 1, Lesson 1-2Engage NY Divide by 10August-October Cont’dSkillNotesProblem of the Day ExamplesResourcesExpressions (needs to be revisited after teaching decimals and fractions are taught)Practice interpreting and writing simple expressionsBy starting with this problem of the day, it opens the discussion of why parenthesis are needed.Evaluate expressions with parenthesis, braces, and brackets Six times the sum of three plus four Ideas from:GM-1.3, 1.10, 1.11, 1.12TT- Unit 3, Lesson 19Multiplication Fluency Standard-standard algorithm a requirementUse with a contextInfuse MD.1.1 conversionsReview what fourth grade taught: partial products and area model to connect to the standard algorithm and reasonableness 1590675144235400Estimate 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 digit195262535814000Lesson from Engage NYIdeas 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:0159766000034226500 August-October Cont’dSkillNotesProblem of the Day ExamplesResourcesDivision Conceptual Understanding!!!!Use with a contextCan infuse MD.1.1 conversionsFind quotients of up to four-digit dividends and two-digit divisors with and without remaindersContext needed!Divisor is number of groups or the size of groupsUse equations, rectangular arrays, area model, partial quotients (expectation)177122188463700Fourth grade used strategies to divide one-digit divisorsCheck your answer with the inverse operation (and addition for the remainder)Zenin’s baby sister weighed 132 ounces at birth. How much did his 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.Divide 2-to-4 Digit by 1-Digit NumberLesson using area models as a strategy 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 F278970131699000Decimals (November – December)Standards and DOKSuccess Criteria Teacher NotesMAFS.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.I can draw and model to explain how a digit’s position affects its value.I can explain what’s happening to the value of a digit as it is placed in different places in the numeral.I can model and explain how a digit in one place represents ten times what it represents in the place to its right.I can model and explain how a digit in one place represents 110 what it represents in the place to its left.I can write a number that is a tenth of a number or ten times a number.Explain the patterns in the number of zeros of the product when multiplying a number by powers of 10.Explain the relationship of the placement of the decimal point when a decimal is multiplied or divided by a power of 10.I can explain what happens to a number when the decimal is moved right or left. I can write numbers with powers of 10 written as 10 raised to a whole number exponent, the expanded form, and standard notation. When given a number, I can write it in expanded form using powers of ten with a whole number exponent to represent each digit. Focus is with decimals and a small whole number.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.I can use place value charts to show decimals to the thousandths. I can use grids to show decimals to the thousandths. I can use pictures to show decimals to the thousandths. I can model a decimal to the thousandths value using a meter stick.I can create a number line, plot my decimal, then justify its location.I can write a decimal in fraction form.I can write a fraction in decimal form.I can explain how decimals and fractions relate. I can read and write decimals to thousandths using number names, word form, and expanded form.I can write a decimal in expanded form with decimals or fractions.I can write the value of each digit to help me compare decimal numbers (up to the thousandths).I can use a visual model to show and justify how two decimal numbers compare.I can write >, <, or = to show a comparison of two decimal numbers that came from the same whole.I can explain how a number in fraction form and a number in decimal form are different ways to represent the same amount.I can use the fraction form of a number to explain whether two decimals are greater than, less than, or equal.I can show how a given decimal can be written as tenths, hundredths, or thousandths. I can use base 10 models and grids to explain why a certain number of tenths would be the same as a certain number of hundredths and a certain number of thousandths. I can use a meter stick model to explain why a certain number of tenths would be the same as a certain number of hundredths and certain number of thousandths. I can round a decimal to any place value and justify my reasoning with a meter stick or number line. Great connections for capacity:A thousand cube = a liter of waterA centimeter cube = a milliliter Students should go beyond simply applying an algorithm or procedure for rounding. The expectation is that students have a deep understanding of place value and number sense and can explain and reason about the answers they get when they round. Students should have numerous experiences using a number line and meter stick to support their work with rounding.Make connections to MD.1.1MAFS.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.Addition and SubtractionI can write a reasonable estimate for an addition or subtraction equation involving decimals.I can check the reasonableness of my answer based on my estimate.I can use models (grids/manipulatives) and drawings based on place value to add or subtract decimals and justify my answer. I can write an equation to solve an addition and subtraction problem involving decimals. I can show my addition or subtraction answer is correct by using the inverse operation to check my answer. Multiplication and DivisionI can write a reasonable estimate for a multiplication or division equation involving decimals. I can check the reasonableness of my answer based on my estimate.I can explain why the product gets smaller when I multiply a decimal by a decimal. I can explain why the value of the digits is important to understand when multiplying and dividing decimals. When given a multiplication equation with decimals, I can determine where to put a decimal in the product based on place value understanding and explain my reasoning. I can use the area model to solve a multiplication equation involving decimals. I can use partial product model to solve a multiplication equation involving decimals. I can use a model (number line, base ten, etc.) to show how to solve a division problem involving decimals. I can explain why decimals are moved and lined up in a division problem. * I can explain what the dividend and divisor mean. November- adding and subtracting December – multiplying and dividingOnly to the hundredths! *Ex. 7 .2, how many .2 are in 7?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.I can determine if the converted amount will be more or less units than the original unit, and explain my reasoning. I can make a multiplication or division equation to convert units within a measurement system. I can make an equation to solve multi-step, real world problems that involve converting units.I can make an equation to solve multi-step, real world problems that involve converting metric units.I can explain how my understanding of place value and decimals help me convert among the metric system. I can use base ten blocks to show the relationship between milliliters and liters. Have the students use reference sheet in class and on the assessments all year!!!! (even if they may not need it)A hollow centimeter cube holds a milliliter water. A hollow decimeter cube (thousand cube) holds a liter of water.This standard is throughout the year.November -January: Using with Decimals-MetricNovember – December Test Specifications Know, Understand, Do (Nov. – Dec.) 9561830190500Recognize and explain the pattern in the number of zeros. 676719514224000Refrain from saying, “add a zero”. Instead refer to the decimalPractice 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?)Relate to the powers of ten. VideoUse 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. Pose problems relating to conversions of measurementExpand 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?)9638665236537500Read, write and compare decimals to the thousandths (progression from fourth grade decimals to the hundredths)Review tenths and hundredths Before using whole numbers with your decimals, make sure they understand the decimal Use expanded form, base-ten numerals, and number namesRelate 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)Relate to zero, half, and whole Use a meter stick with thousandths-meter is 1, decimeter is a tenth, centimeter is a hundredth, a millimeter is a thousandthUse base ten model –tenths=ten rods, hundredths=ones, thousandths=a one cut into to ten 5175392622792ThousandthsHundredthsTenths00ThousandthsHundredthsTenthsAdd and subtract decimals to hundredths 987171025209500Estimate first Line up place values (be sure to give examples and non-examples) Real-world examples (context)8630920182181500Multiply and divide decimals to the hundredthsEstimate 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?”85928203228340Students use concrete models and pictorial representations203009528416255137150285178500Strategies based on place value, and properties of operationsSequence of Skills: November - DecemberSkillNotesProblem of the Day ExamplesResourcesDecimal DevelopmentGoal: Introduction to thousandths and relationship of decimals on the meter stickHow big/small are decimals?How can you write the number?*Use only decimals-no whole numbers Put .53 on the boardWhat 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)?5/10 + 3/100 + 4/1,000 534/1000 53/100 + 4/1000 (5 x .1) + ( 3 x .01) + (4 x .001).5 + .03 + .004Quadrilateral Flipchart Aug-DecDecimal Flipchart21590607695ThousandthsHundredthsTenths00ThousandthsHundredthsTenthsUse 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 5GM: 3.1, 3.2TT:Unit 1, Lesson 3Compare Decimals Teach for place value understanding to recognize patternsShow it on the meter stickUse benchmarks – 0, .5, 1 to help with the visual understanding of the size of the decimalsZoomable number line GM: 3.3TT: Unit 1, Lesson 4Round 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 lineLesson about using number lines and place value to round a given decimal number.EngageNY Module 1, Lesson 7TT: Unit 1, Lesson 4November-December Cont’dSkillNotesProblem of the Day ExamplesResourcesMetric 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 unitsOne 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-ChartIdeas from: GM-10.5, 10.6TT-Unit 4, Lesson 21Add and Subtract Decimals to HUNDREDTHSUse real-world problemsEstimate 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 7Fill Two Game (if you sign up or in, you can download the cards)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. 297823558800Estimate 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?”3251200100266500When 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 operationsUse 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 Flipchart1610360702310-63500196850022435221937300Centimeter grid paperIdeas from:1535802157506300GM-Chapter 4 & 5 (minus 5.8)TT: Unit 1, Lesson 8, Lesson 9Math In Action January: Add, Subtract and Multiply FractionsStandards and DOKSuccess Criteria Teacher NotesMAFS.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.) 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.I can write a reasonable estimate before I add and subtract fractions the benchmarks 0, ?, and 1.I can use visual models, including area models, fraction strips, and number lines, to solve addition and subtraction problems with fractions and mixed numbers. I can explain my solution using models, pictures, words, and numbers. I can explain my answer using models and the benchmarks 0, ? and 1 to determine reasonableness. I can explain why common denominators are needed when adding and subtracting fractions. *I can explain how to use the formula for adding fractions, and explain why it works. (ad + bc) /bd I can use my understanding of multiples to find a common denominator.I can create fractions with like denominators to add and subtract. **I can rewrite a mixed number in multiple ways to subtract fractions. I can write a fraction greater than one in multiple ways. I can create a scenario to represent an addition or subtraction fraction equation. I can solve word problems involving addition and subtraction of fractions with unlike denominators referring to the same whole by creating fractions with common denominators.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.* ab + cd =(ad+bc)bd**Students do not always need to rewrite mixed numbers as fractions greater than one to subtract. Ex. 4 - 213 can be rewritten as 333 - 213MAFS.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.I can explain how a line plot is used to display measurement data.I can determine an appropriate scale needed to create a line plot to organize data. I can create a line plot by drawing a line, then create line segments to partition my line into fractional parts.I can read and interpret the results of measurement data that is plotted on a line plot.I can explain what the data I plotted on my line plot represents. I can generate questions that ask about the data represented on a line plot.When given a problem that relates to the data on a line plot, I can solve it and justify my thinking using a model, picture, or equations.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?I can write a fraction as a division expression. I can write a division expression as a fraction. I can explain how the numerator and denominator relate to a division expression. I can use a multiplication equation to explain what a fraction means. When given a word problem, I can write a division equation and a fraction to show the dividend and divisor. When given a division problem, I can interpret the words to identify what is being shared and represent that as a fraction.I can explain how the numerator and denominator relate to the numbers in the word problem. When given a division word problem, I can draw a model, create a fraction, and explain my answer. I can model problems where the divisor is greater than the dividend and share my thinking about the quotient being a fraction. I can create a division word problem to represent a fraction or a fraction greater than one.Word problems, visuals, fractions, and division equations need to be represented in all lessons!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. 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.2.4I can model a fraction times a whole number using number lines, area models, set models, and bar models. I can write an addition sentence to explain a fraction times a whole number. When given a fraction times a whole number equation, I can create a word problem to represent it. I can explain the meaning of the two factors in a fraction equation. I can model a fraction times a fraction using number lines, area models, and bar models. I can represent a fraction equation by creating a rectangular array and labeling the parts that make up the whole. I can represent a fraction equation by creating a story problem. I can determine what operations are needed to solve a real-world problem involving fractions and represent it with pictures, numbers, or words. I can explain what happens when a fraction is multiplied by another fraction When given an expression involving fractions, whole numbers, or mixed numbers, I can explain whether my product will be greater than, less than, or equal to the size of the factors. NF.2.6 could include fraction by a fraction, fraction by a mixed number or mixed number by a mixed number.23 x 45MAFS.5.OA.1.1: DOK 1Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.I can explain how to use the order of operations to evaluate numeric expressions. I can evaluate a numerical expression with brackets, parentheses, or braces.When evaluating a numeric expression, I can explain each step in the process. Use fractionsPer Test Specifications:Expressions may contain whole numbers and up to one fraction with a denominator of 10 or less.Items may not require division with fractions.January Test Specifications Know, Understand, Do (Jan.)Add and subtract fractionsReview understanding of fractions greater than one and mixed numbers and their relationship.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.Estimate by thinking of benchmarks of zero, half, and one to think of the reasonableness of the answerUse real-life word problems Mix addition and subtraction Represent and interpret data of measurement of fractions ?, ?, and 1/8 in a line plot 87814152195830Solve problems involving information presented in the line plot 7648575239268000Use in a real-world Context:Interpret a fraction as division of the numerator by the denominatorSolve word problems involving division of whole numbers leading into a fractionUse visual fraction models. Practice representing the division equation different ways. (7 ÷ 4, 74, etc.)73881673920515Fraction times a whole number (extension of fourth grade) Relate to repeated addition Interpret if the product will be greater or less than the given number. How do you know?5927090158115Students create a story context for an equation Use visual fraction modelsFraction multiplication represented in an area, set, and length modelFraction times a fraction Use visual fraction models Find the area of a rectangle with fractional side lengthsInterpret if the product will be greater or less than the given number. How do you know?? x 1/3 means ? of a 1/3 piece 89960450588010025019000734822024574500Fraction times a mixed number and vice versa Mixed Number times a mixed numberPartial products and area modelConverting to a fraction greater than one (with understanding, not just a short cut)Sequence of Skills: January SkillNotesProblem of the Day ExamplesResourcesReview of Fractions from 4th Grade Introduction to addition and subtraction of fractionsUse real-world problems 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.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, ?, and 1 (to think of reasonableness)Find a line plot that would require the students to add or subtract like denominators. Coordinate Plane Flipchart Add, subtract, and multiply fractions flipchartEngage NY Module 4 Flipchart-Multiplying and Dividing FractionsDividing Fractions FlipchartSkillNotesProblem of the Day ExamplesResourcesAdding and subtracting with unlike denominatorsUse real-world problemsMix addition and subtractionCheck for understanding of finding a common denominator (learned in fourth grade)Interpret expressions with fractionsEstimate 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, 11Adding and Subtracting with fractions greater than one and mixed numbersCheck for understanding of mixed numbers and fractions greater than one with visual models (example: 2 ? = 1 7/4 = 11/4)Interpret expressions with fractions12050491905641190Represent and Interpret Data Fractions ?, ?, and 1/8 in a line plot Solve problems involving information presented in the line plotLine Plot Game from Illustrative Math TaskGM-9.1 Not enough exposure in Go Math TT: Unit 4, Lesson 23Practice with creating line plots and analyzing data that requires fraction operations: EngageNY, Module 4, Lesson 1Represent Fractions as Division Real-World ProblemsSolve word problems involving division of whole numbers leading into a fractionUse visual fraction models. Practice representing the division equation different ways. (7 ÷ 4, 74, etc.)-59377684500GM- 8.3TT: Unit 2, Lesson 12Sorting Fractions (Mix-N-Match)SkillNotesProblem of the Day ExamplesResourcesMultiplication of a Whole Number by a Fraction and vice versaReal-World ProblemsMultiplication is repeated addition Reason about the size of the product and explain Interpret expressions with fractionsFraction multiplication represented in an area, set, and length model179640613170000-590550Multiplication 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 smaller977900381000-5937643700Multiply mixed numbers by Mixed Numbers and by FractionsReal-World ProblemsPartial products and area modelConverting to a fraction greater than one (with understanding, not just a short cut)Reason about the size of the product and explainA recipe calls for 1 cup of flour but Mel is only making of the recipe. How much flour does Mel need?Candy comes in 3 pound bags. At a party, the class ate 2 bags of candy. How many pounds of candy did they eat?203517590170006540524765000Go Math Lesson 7.8 1270230505February – May: Dividing Fractions and VolumeStandards and DOKSuccess Criteria Teacher NotesMAFS.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.1Interpret 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.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.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?I can model dividing a unit fraction by a whole number and explain my thinking. I can create a story context for a unit fraction divided by a whole number and draw a visual to represent itI can model dividing a whole number by a unit fraction and explain my thinking. I can create a story context for a whole number divided by a unit fraction and draw a visual to represent it.When given a fraction division expression, I can explain whether my quotient will be greater than, less than, or equal to the dividend. I can show the relationship between multiplication and division to explain my answer. *I can explain what the dividend and divisor mean in a fraction expression.I can determine what operations are needed to solve a real-world problem involving fractions and represent it with pictures, numbers, or words. *Ex. 7 14, how many 14 are in 7?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.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.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.I can build a rectangular prism with unit cubes with given dimensions, and write different equations to represent the volume.I can explain how to find volume. I can explain the relationship between height and the number of layers needed to fill a rectangular prism and write it as an equation. Given a picture of a rectangular prism in cubic units, I can label each dimension and find the volume. I can use words such as length, width, height, depth, area of the base, and cubic units to discuss the volume of a rectangular prism. I can explain and model what each part of the volume formulas represents.Given the dimensions of a rectangular prism, I can use the volume formula to find the volume. Given the volume, I can create rectangular prisms and label their dimensions. Given the volume and two dimensions of a rectangular prism, I can find the missing dimension. When given a real world-volume problem, I can solve it and justify my answer. When given a picture of two non-overlapping rectangular prisms, I can find the volume and explain my reasoning. L x W x HV = B x H(area of base x height)February – May Test Specifications 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 numberUse real world context to make meaning of the dividend and divisor.Create a story problem for a given division equation (unit fraction divided by a whole number and whole number divided by a unit fraction)Show using visual models and write equations to matchRelate division of fractions to division of whole numbers (example: 4 divided by 1/3 means how many 1/3 are in 4) 3973195163068000Volume:Concept development for all prisms learned in middle school. It is important not to go straight to the standard algorithm!90091833049314Students 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 volumeSequence of Skills: February and March SkillNotesProblem of the Day ExamplesResourcesDivide a whole number by a unit fractionReal-World Problems*Conceptual UnderstandingUse real world context to make meaning of the dividend and divisor.Show using visual models and write equations to matchCreate a story problem for a given division equation (unit fraction divided by a whole number and whole number divided by a unit fraction)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 inverseCharlotte has 6 apples that she wants to share. If she cuts them in ?, 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 FlipchartEngage NY Module 4 Flipchart-Multiplying and Dividing FractionsDividing Fractions Flipchart09941221772681747890190031646982Use problems found in GM, but expect them to show you visually and with a written context why the answer is reasonable. 3175200653400Divide a unit fraction by a whole numberReal-World Problems*Conceptual UnderstandingFebruary-March Cont’dExperiences with Volume:Area of the BaseWith 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-1139273685Minecraft volume lesson182689599060Three Act Tasks:Penny CubePop TopGot CubesPacking SugarOverflowAmerican Flagthe Fish TankPopcorn, Anyone LessonGM: Chapter 11TT: Unit 4 Lesson 24-27Connect Two Rectangular Prisms Use in context:Real-World Examples:Wedding cakes, stairs, towers, robots, pools, skyscrapersGM: Chapter 11TT: Unit 4 Lesson 24-27Learnzillion lessonGeometry Day: August – December: QuadrilateralsStandards and DOKSuccess Criteria Teacher NotesMAFS.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.I can describe attributes of a shape using words such as regular polygon, irregular polygon, parallel lines, perpendicular lines, obtuse angles, acute angles, right angles, congruent, sides, adjacent sides, opposite sides, and symmetry.I can identify regular and irregular polygons. I can draw or create a shape based on properties given. I can sort and classify two-dimensional figures based on their properties.I can identify and define a parallelogram, rectangle, trapezoid, square, kite, and rhombus.I can classify a quadrilateral in a hierarchy based on the shape’s properties. I can identify how shapes are sorted in a Venn Diagram. I can compare and contrast shapes based on their attributes using a Venn Diagram. When given a shape, I can list all of the categories the shape belongs, and explain why. In the U.S., the term “trapezoid” may have two different meanings. Research identifies these as inclusive and exclusive definitions. The inclusive definition states: A trapezoid is a quadrilateral with at least one pair of parallel sides. The exclusive definition states: A trapezoid is a quadrilateral with exactly one pair of parallel sides. With this definition, a parallelogram is not a trapezoid.January - May: Coordinate GridsStandards and DOKSuccess Criteria Teacher NotesMAFS.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. I can plot a point on a coordinate grid.When given a point on a coordinate grid, I can give the coordinates.I can use the words origin, x-axis, y-axis, left, right, up, down, horizontal, and vertical to describe a point’s position on a coordinate grid. When given a point on a coordinate grid, I can use directions to plot another point. I can locate coordinates on a coordinate grid by using an ordered pair of numbers. I can find the missing coordinate needed on the coordinate grid to create a polygon.I can recognize and describe the connection between the ordered pair and the x- and y-axes from the origin.When given labeled coordinates on a grid, I can explain directions of how to get from one point to another. I can represent real world and mathematical problems by graphing points in the first quadrant.When given two number sequences, I can describe patterns in the terms.I can generate two numerical patterns using two given rules. I can identify and explain relationships between two numerical patterns’ terms. When given a set of mathematical rules, I can make a table, generate a sequence of numbers, create a set of ordered pairs, and then plot them on the coordinate grid. Ex: Using the coordinate grid, which ordered pair represents the location of the School? Explain a possible path from the school to the library. Geometry All Year Test Specifications Know, Understand, Do (Geometry All Year)80181450005814695000Quadrilaterals:Create Venn diagramsDescribe attributes 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 linesClassification Flipchart HYPERLINK "" Polygon Capture Activity9103995190500Students 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)Plot points based on a real-world problemName the coordinate from a plotted point Follow directions to create a path from one point and determine another 36861961403985Show a relationship between two patterns. ................
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