Unit Planning for 5th Grade Mathematics
Content Area / Mathematics / Grade Level / 5thGrade Mrs. McQuittyCourse Name/Course Code
Standard / Grade Level Expectations (GLE) / GLE Code
- Number Sense, Properties, and Operations
- The decimal number system describes place value patterns and relationships that are repeated in large and small numbers and forms the foundation for efficient algorithms
- Formulate, represent, and use algorithms with multi-digit whole numbers and decimals with flexibility, accuracy, and efficiency
- Formulate, represent, and use algorithms to add and subtract fractions with flexibility, accuracy, and efficiency
- The concepts of multiplication and division can be applied to multiply and divide fractions
- Patterns, Functions, and Algebraic Structures
- Number patterns are based on operations and relationships
- Data Analysis, Statistics, and Probability
- Visual displays are used to interpret data
- Shape, Dimension, and Geometric Relationships
- Properties of multiplication and addition provide the foundation for volume an attribute of solids
- Geometric figures can be described by their attributes and specific locations in the plane
Colorado 21st Century Skills
Critical Thinking and Reasoning: Thinking Deeply, Thinking Differently
Information Literacy: Untangling the Web
Collaboration: Working Together, Learning Together
Self-Direction: Own Your Learning
Invention: Creating Solutions / Mathematical Practices:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make use of structure.
- Look for and express regularity in repeated reasoning.
Unit Titles / Length of Unit/Contact Hours / Unit Number/Sequence
Doctor We Still Need to Operate. . . / 12 weeks / 1
Fraction Reaction / 10 weeks / 2
“X” Marks the Spot / 5-6 weeks / 3
Pump Up the Volume / 4 weeks / 4
Unit Title / Doctor We Still Need to Operate . . . / Length of Unit / 12 weeks
Focusing Lens / Structure
Systems / Standards and Grade Level Expectations Addressed in this Unit / MA10-GR.5-S.1-GLE.1, MA10-GR.5-S.1-GLE.2
Dividend / divisor = quotient
Inquiry Questions (Engaging- Debatable): /
- How are mathematical operations related? (MA10-GR.5-S.1-GLE.2-IQ.1)
- Why is zero important in our place value system? (MA10-GR.5-S.1-GLE.1-IQ.4)
Unit Strands / Number and Operations in Base Ten, Operations and Algebraic Thinking, Measurement and Data
Concepts / Measurements, equivalence, ratio, conversion, unit, measurement systems, multiplication, division, constant rate (factor), place value, decimal system, decimals, powers of ten, digits, magnitude, standard algorithm, partial products, properties of operations, distributive property, relationship, rounding, addition, subtraction, denominator, numerator, product, dividend, divisor, quotient, fractions, order of operations, solutions, compare
Generalizations
My students will Understand that… / Guiding Questions
FactualConceptual
A constant application of multiplication by 10 to obtain the next higher unit, or division by 10 to obtain the next lower unit, demonstrates 10 as the constant rate/factor of composing and decomposing place value units in our decimal system (MA10-GR.5-S.1-GLE.1-EO.a.i, a.ii, b.i, b.ii) / What is the relationship between 654 and 65.4?
10 times greater or less
What would it mean if we did not have a place value system?
Numbers would have no value; History of Zero and Place Value
What is the purpose of the decimal point? To separate the whole numbers from the parts of a whole. / Why is dividing by 10 the equivalent to multiplication by 1/10?
1/10=.1 one tenth. Dividing by 10 you are dividing by tenths
How does understanding our place value system help to read, write and compare decimals? It gives order and value to our number system.
Multiplication or division by a power of 10 increases or decreases their place value to a magnitude equivalent to the power of 10 (MA10-GR.5-S.1-GLE.1-EO.a.i, a.ii)
So, each time we need to show a bigger number we just add one columnto the leftand we know it is always10 times biggerthan the column on its right. / What is the purpose of our place value system? (MA10-GR.5-S.1-GLE.1-IQ.3) To give numbers value and a specific place in our system. Think about $. Would you rather have $32 or $324? How do you know one is worth more than the other? / Why is a place value system beneficial? (MA10-GR.5-S.1-GLE.1-IQ.1) It gives our numbers an order and value and worth. Otherwise our numbers would have no meaning.
Why do you move the decimal point two places to the right when multiply 100 and two places to the left when dividing by 100? 2 zeros in 100= 2 places holders= move 2 places.
Multiplying makes numbers larger and dividing makes them smaller.
In the standard algorithm for multiplication of whole numbers, the power of 10 represented by the place value of the digit multiplier determines the corresponding amount to shift the partial products to the left (MA10-GR.5-S.1-GLE.2-EO.a) / What makes one strategy or algorithm better than another? (MA10-GR.5-S.1-GLE.2-IQ.2) Speed and accuracy
How many place values does the partial product shift when multiplying by the digit in the hundreds place? 2 / Why do you shift partial products over one place value when multiplying by the digit in the tens place? You are moving from the ones to the tens place. You are enlarging the number 10 times greater therefore you need a place holder.
Place value, properties of operations and the relationship between multiplication and division support the division of multi-digit numbers. (MA10-GR.5-S.1-GLE.2-EO.b) / How is multiplication used when dividing multi-digit numbers? To determine how many times the divisor goes into the dividend.
What is the role of place value in the division algorithm? / How does the relationship between multiplication and division support division when using the standard algorithm? (MA10-GR.5-S.1-GLE.2-IQ.1) Since they are inverse operations, you can use them to solve for the other and check answers.
As with the rounding of whole numbers, the accurate rounding of decimals depends upon place value concepts and an attention to context (MA10-GR.5-S.1-GLE.1-EO.c) / How do you round a decimal number to the nearest hundredth? Look at the thousandths, 1 place to the right, and follow the same rounding rules. 5+ round up, 4- stays the same. / How is rounding of decimal numbers similar and different from rounding whole numbers? Use same methods, but sometimes the decimal rounds up to a whole number and a whole number never rounds down to a decimal.
The algorithm for the addition and subtraction of decimals, a simple extension of the algorithm for whole numbers, requires precise attention to place value such that digits with corresponding place values are aligned prior to joining or separating (MA10-GR.5-S.1-GLE.2-EO.c) / How many tenths make one whole? 10
How many hundredths make a whole? 100
How many thousandths make a whole? 1,000 / Why is it important that digits with the same place value are aligned when adding or subtracting using the standard algorithm? To keep the math problem in the same value. You would not want the values to get mixed up.
The algorithm for multiplication of decimals relies on the equivalence of a decimal to a corresponding fraction with a denominator that is a power of ten (MA10-GR.5-S.1-GLE.2-EO.c) / How do you determine the location of the decimal point in the product of two decimal numbers? Count how many place values are behind each decimal to move the decimal over that many place values. / How does multiplication of fractions justify the standard algorithm for multiplication of decimals? Fractions and decimals are parts of a whole so they are equivalent, just in different forms.
The algorithm for the division of decimals dictates that the decimal point in the dividend correspond to the location of the decimal point in the quotient and when a decimal appears in the divisor both divisor and dividend both must be multiplied by the same power of ten to eliminate it (MA10-GR.5-S.1-GLE.2-EO.c) / When using the standard algorithm for division, what strategy provides a method for handling division of decimals? The strategy the student is most comfortable with. / Why does the multiplication of the divisor and dividend by the same power of ten create an equivalent division problem? (hint: a/b is the same as a divided by b) Multiplication is the inverse operation of division.
Universal order of operation ensures uniformity and accuracy of solutions. (MA10-GR.5-S.1-GLE.2-EO.d) / What is the order of operations? P E M D A S
Please Excuse My Dear Aunt Sally
Parentheses, Exponents, Multiplication, Division, Addition, Subtraction / Why does order of operations matter? The system ensures the correct answer every time.
Key Knowledge and Skills:
My students will… / What students will know and be able to do are so closely linked in the concept-based discipline of mathematics. Therefore, in the mathematics samples what students should know and do are combined.
- Recognize that in a multi-digit number, a digit in one place represents 10 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 (MA10-GR.5-S.1-GLE.1-EO.a)Place Value Power point.ppt Meaning of Whole Numbers Place value problem of the day; place value wkst place value crossword place value homework money-digits
- Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10 (MA10-GR.5-S.1-GLE.1-EO.a.i, a.ii) power of 10 video explaination Multiply And Divide Decimals By Powers Of 10
- Use whole number exponents to denote power of 10 (MA10-GR.5-S.1-GLE.1-EO.a.iii) Mult by 10 Math\Number Sense\Powers of 10\div by 10.pdf; Math\Number Sense\Powers of 10\Multiply And Divide Decimals By Powers Of 10.doc; Math\Number Sense\Powers of 10\patterns power of 10 div.pdf; Math\Number Sense\Powers of 10\power of 10.doc; Math\Number Sense\Powers of 10\powers of 10 crit think.pdf; Math\Number Sense\Powers of 10\mult by 10.pdf
- Read and write decimals to thousandths using base-ten numerals, number names, and expanded form (MA10-GR.5-S.1-GLE.1-EO.b.i) Expanded Form with Whole Numbers and Decimals read write dec read write numbers read write numbers (2 numbers spelled out WholeNumbersIntegers1place value review place value
- Compare two decimal s to thousandths based on meanings of the digits in each place, using >, =, < symbols to record the comparisons (MA10-GR.5-S.1-GLE.1-EO.b.ii) Compare-decimals compare-decimals2 comparing order dec ordering-cards-set-h_TZQQZ ordering-cards-set-i_TWFDD ordering-cards-set-l comparing decimals; number_lines_decimals number_lines_decimals 2 number_lines_decimals 3 decimals_ordering_hundredthsdecimals_ordering_thousandthsdecimals_ordering_hundredths_002decimals_ordering_thousandths_002.comparing_decimals_thousandths_001
- Use place value understanding to round decimals to any place (MA10-GR.5-S.1-GLE.1-EO.c)matching-placevalue matching-placevalue-decimals decimal-hundredths-tenths; six-digit-place-value-match
- Fluently multiply multi-digit whole numbers using the standard algorithm (MA10-GR.5-S.1-GLE.2-EO.a)multiplication guide lesson book WholeNumbersIntegers3 fact family triangles; mult 2x2 Mult 1 Mult 3x2; Lattice_Multiplication_1 multiplication-bingo-coloring Multply Whole Numbers 3-3 pg. 15 multiplciation2-mixed multiplication-crossword fruitstand-multiplication-harder word problem; mult crit think mult word problems puzzle-math-pirate-3x2_crit think
- 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 the relationship between multiplication and division; illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. (MA10-GR.5-S.1-GLE.2-EO.b.i, b.ii)MultiplicationDivisionFactTriangles Div by 1 long-division-multiplication-word-problems diggie-multiply-2digx2dig Div by 2 Div 1x4 Div 2 digits Div 2x4; division-2-3-digitdividends-2; division-crossword long-division-2digit-divisors-remainders long-division-money long-division-multiplication-word-problems; long-division-wordproblems
- Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used (MA10-GR.5-S.1-GLE.1-EO.c.i, c.ii)Addition and Subtraction of Decimals; Decimal Intro Decimal place value through millionths Multiplication and Division of Decimals; Add dec add dec 2 sub dec sub dec 2 mult decmult dec 2 mult dec 3 div dec div dec 2 div dec by 2 digits; add-sub-mult-div dec book
- Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols (MA10-GR.5-S.1-GLE.1-EO.d.i)Exponents 1A Exponents 1B order of operations 1 Order of Operations Orders of Operation\order of opp 1 order of opp order of opps 4 steps order of opp crit think order of opp critcal thinking
- Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them (MA10-GR.5-S.1-GLE.1-EO.d.iiexpressions Numerical Expressions basic-algebra2 basic-algebra1 basic-algebra4 basic-algebra10 scales-addition-equations balancing-basic-equations-xvalue-add-subtract
- Convert among different-sized standard measurement units within a given measurement system and use these conversions in solving multi-step, real world problems (MA10-GR.5-S.1-GLE.1-EO.d.i, d.ii)5MD1-metriclength1 5MD1-metriclength2 5MD1-metriclength3 5MD1-metricmass1 5MD1-metricmasscapacity1 5MD1-metricmasscapacity3 5MD1-metricmass1 5MD1-metricmasscapacity4 5MD1-metricvolume1 5MD1-TLM4 5MD1-uscapacity1 5MD1-uslength1.pdf; 5MD1-uslength2 5MD1-uslength3 5MD1-usweightcapacity1 5MD1-usweightcapacity2 5MD1-usweightcapacity3
Critical Language: includes the Academic and Technical vocabulary, semantics, and discourse which are particular to and necessary for accessing a given discipline.
EXAMPLE: A student in Language Arts can demonstrate the ability to apply and comprehend critical language through the following statement: “Mark Twain exposes the hypocrisy of slavery through the use of satire.”
A student in ______can demonstrate the ability to apply and comprehend critical language through the following statement(s): / When converting a 42 centimeters to meters, I first need to remember there are 100 centimeters in 1 meter. This means I will need to divide 42 centimeters by 100 to find out the equivalent number of meters, because I am dividing by a power of ten the digits will remain the same in my answer I simply move the decimal point two places to the left because 100 is 102, thus the answer is 0.42 meters.
Academic Vocabulary: / Measurements, centimeter, meters, inches, feet, convert, conversions, parenthesis, measurement systems, multiplication, division, relationship, rounding, addition, subtraction, fractions, explain, compare, fluently
Technical Vocabulary: / Dividend, divisor, quotient, tenths, hundredths, thousandths, metric, order of operations, exponents, equivalence, units, place value, decimals, powers of ten, digits, standard algorithm, denominator, numerator, product, quotient, divisor, factor, quotient, partial products
Additional lessons covered on state test
●Squares, primes, composites, factors, multiples- Compare products to factors Products, Multiples, Factors factor-tree-1 factor-tree-2 factor-tree-3 factor-tree-4_Finding factors gcf gcf-2 least-common-multiple least-common-multiple2 least-common-multiple3 least-common-multiples6 Practice 9-2 Primes and Composites prime-composite prime-composite2 prime-composite3 prime-composite-crit think prime-composite-table squares_all _Factoring_numbers hard
●Even and odd- even-odd activity 1 Even and odd products Even and Odd activity even-baseball even-odd-match_SORTT even-odd-sums even-odd-wordproblems Even__Odd_Number_Maze Even__Odd_Number_Maze_2 even-odd-crit think cootie-catcher-odds-evens
●Properties of addition- Properties.ppt property_definition properties lesson bkaddition-properties-basic addition-properties-firstbasic addition-properties-intermediate; addition-properties-variables-basic Multiplication Associative H-2 addition-properties-crit think; Properties crit thinkProperties of math worksheet property_identitying property_working PropertyCards.doc
Unit Title / Fraction ReactionLyrics - Fractions and Decimals Fractions and Decimals / Length of Unit / 10 weeksFocusing Lens / Interpretation
Relationships / Standards and Grade Level Expectations Addressed in this Unit / MA10-GR.5-S.1-GLE.3, MA10-GR.5-S.1-GLE.4
Inquiry Questions (Engaging- Debatable): /
- How do operations with fractions compare to operations with whole numbers? (MA10-GR.5-S.1-GLE.3-IQ.1)
- Why are there more fractions than whole numbers? (MA10-GR.5-S.1-GLE.3-IQ.2)
Unit Strands / Number and Operations – Fractions
Concepts / Denominator, numerator, fraction, addition, subtraction, common denominators, multiplication, division, whole number, unit fraction, expressions, area model, 1X1 unit square, partitioning, representation, rectangular regions, product, quotient, scaling (resizing), comparison, factor, estimation, real world problems, contexts, equal groups, fair sharing, rates, measurement, arrays, area,
Generalizations
My students will Understandthat… / Guiding Questions
FactualConceptual
The addition and subtraction of fractions necessitates common denominators in order to join or separate same size parts in the numerators of the fractions (MA10-GR.5-S.1-GLE.3-EO.a.i, a.ii) / What does the denominator of a fraction describe?The total quantity of the objects.
How do you add or subtract fractions with different denominators? Find a common denominator 1st using LCM.
How can visual models be used represent and solve addition and subtraction of fraction problems involving unlike denominators?Using graph paper, draw shapes
How can equations be used represent and solve addition and subtraction of fraction problems involving unlike denominators?Paper and pencil method. / Why does 2/3 + 3/4 not equal 3/6?Because 2/3 & ¾ are both more than a ½ which is = 3/6.
When adding fractions with a common denominator why does the denominator stay the same? You are not changing the total quantity amount.
Why do you need equivalent fractions when adding or subtracting? Otherwise you change the quantity and total.
Why is it important to use benchmark fractions and number sense to estimate mentally the sums and differences of fractions?To check your answers quickly.
The rewriting of an equation that multiplies a fraction by a whole number as a combination of whole number multiplication and division creates an equivalent equation (MA10-GR.5-S.1-GLE.4-EO.c) / How can you rewrite (3/4) x 5 as an expression involving multiplication and division of whole numbers?
¾ x 5/1 or ¾ / 1/5 / Why is helpful to interpret multiplication of fractions by whole numbers as multiplication and division of whole numbers?
They are inverse operations. Understand that they work together because they are opposite.