STANDARDS FOR MATHEMATICAL CONTENT
MGSE5.NF.1 Add and subtract fractions and mixed numbers with unlike denominators by
finding a common denominator and equivalent fractions to produce like denominators.
MGSE5.NF.2 Solve word problems involving addition and subtraction of fractions, 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 + ½ = 3/7,
by observing that 3/7 < ½.
MGSE5.NF.3 Interpret 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. Example: 3
5
can be interpreted as “3 divided by 5 and as 3 shared by 5”.
MGSE5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction
or whole number by a fraction.
a.Apply and use understanding of multiplication to multiply a fraction or whole number by a
fraction.
Examples: 𝑎
𝑏
×𝑞 as
𝑎
𝑏
×
𝑞
1
and 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.
MGSE5.NF.5 Interpret 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. Example 4 x 10 is twice as large as 2
x 10.
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.
MGSE5.NF.6 Solve real world problems involving multiplication of fractions and mixed
numbers, e.g., by using visual fraction models or equations to represent the problem.
MGSE5.NF.7 Apply 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.
b. 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.
c. 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 ½ lb of chocolate equally? How many 1/3-cup servings are 2 cups of raisins
1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by
reasoning about the relationship between multiplication and division. But division of a fraction by a
fraction is not a requirement at this grade.
MGSE5.MD.2 Make 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
COMMON MISCONCEPTIONS
MGSE5.NF.1, MGSE5.NF.2 – Students often mix up models when adding, subtracting or
comparing fractions. Students will use a circle for thirds and a rectangle for fourths when comparing fractions with thirds and fourths. Remind students that the representations need to be
from the same whole models with the same shape and size.
BIG IDEAS
• A fraction is another representation for division.
• Fractions are relations – the size or amount of the whole matters.
• Fractions may represent division with a quotient less than one.
• Equivalent fractions represent the same value.
• With unit fractions, the greater the denominator, the smaller the equal share.
• Shares don’t have to be congruent to be equivalent.
• Fractions and decimals are different representations for the same amounts and can be
used interchangeably.
ESSENTIAL QUESTIONS
• How are equivalent fractions helpful when solving problems?
• How can a fraction be greater than 1?
• How can a fraction model help us make sense of a problem?
• How can comparing factor size to 1 help us predict what will happen to the product?
• How can decomposing fractions or mixed numbers help us model fraction multiplication?
• How can decomposing fractions or mixed numbers help us multiply fractions?
• How can fractions be used to describe fair shares?
• How can fractions with different denominators be added together?
• How can looking at patterns help us find equivalent fractions?
• How can making equivalent fractions and using models help us solve problems?
• How can modeling an area help us with multiplying fractions?
• How can we describe how much someone gets in a fair-share situation if the fair share is
less than 1?
• How can we describe how much someone gets in a fair-share situation if the fair share is
between two whole numbers?
• How can we model an area with fractional pieces?
• How can we model dividing a unit fraction by a whole number with manipulatives and
diagrams?
• How can we tell if a fraction is greater than, less than, or equal to one whole?
• How does the size of the whole determine the size of the fraction?
• What connections can we make between the models and equations with fractions?
• What do equivalent fractions have to do with adding and subtracting fractions?
• What does dividing a unit fraction by a whole number look like?
• What does dividing a whole number by a unit fraction look like?
• What does it mean to decompose fractions or mixed numbers?
• What models can we use to help us add and subtract fractions with different
denominators?
• What strategies can we use for adding and subtracting fractions with different
denominators?
• When should we use models to solve problems with fractions?
• How can I use a number line to compare relative sizes of fractions?
• How can I use a line plot to compare fractions?
Wednesday, December 20, 2017
6.1 math vocabulary for Unit 4
• Addition Property of Equality: Adding the same number to each side of an equation
produces an equivalent expression.
• Constant of proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the constant of proportionality. In a proportional relationship, y = kx, k is the constant of proportionality, which is the value of the ratio between y and x.
• Dependent variable- A variable that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.
• Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: A=kB, where k is the constant of proportionality.
• Division Property of Equality: States that when both sides of an equation are divided by the same number, the remaining expressions are still equal
• Equation: A mathematical sentence that contains an equal sign
• Independent variable: A variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.
• Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤.
• Inverse Operation: A mathematical process that combines two or more numbers such that its product or sum equals the identity.
• Multiplication Property of Equality: States that when both sides of an equation are multiplied by the same number, the remaining expressions are still equal.
• Proportion: An equation which states that two ratios are equal.
• Solution: the set of all values which, when substituted for unknowns, make an equation true.
• Substitution: the process of replacing a variable in an expression with its actual value.
• Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.
• Term: A number, a variable, or a product of numbers and variables.
• Variable: A letter or symbol used to represent a number or quantities that vary.
• Constant of proportionality: The constant value of the ratio of two proportional quantities x and y; usually written y = kx, where k is the constant of proportionality. In a proportional relationship, y = kx, k is the constant of proportionality, which is the value of the ratio between y and x.
• Dependent variable- A variable that depends on other factors. For example, a test score could be a dependent variable because it could change depending on several factors such as how much you studied, how much sleep you got the night before you took the test, or even how hungry you were when you took it.
• Direct Proportion (Direct Variation): The relation between two quantities whose ratio remains constant. When one variable increases the other increases proportionally: When one variable doubles the other doubles, when one variable triples the other triples, and so on. When A changes by some factor, then B changes by the same factor: A=kB, where k is the constant of proportionality.
• Division Property of Equality: States that when both sides of an equation are divided by the same number, the remaining expressions are still equal
• Equation: A mathematical sentence that contains an equal sign
• Independent variable: A variable that stands alone and isn't changed by the other variables you are trying to measure. For example, someone's age might be an independent variable.
• Inequality: A mathematical sentence that contains the symbols >, <, ≥, or ≤.
• Inverse Operation: A mathematical process that combines two or more numbers such that its product or sum equals the identity.
• Multiplication Property of Equality: States that when both sides of an equation are multiplied by the same number, the remaining expressions are still equal.
• Proportion: An equation which states that two ratios are equal.
• Solution: the set of all values which, when substituted for unknowns, make an equation true.
• Substitution: the process of replacing a variable in an expression with its actual value.
• Subtraction Property of Equality: States that when both sides of an equation have the same number subtracted from them, the remaining expressions are still equal.
• Term: A number, a variable, or a product of numbers and variables.
• Variable: A letter or symbol used to represent a number or quantities that vary.
6.1 Math standards that we will continue in January
The student will be able to reason about and solve one-variable equations and inequalities.
MGSE6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
MGSE6.EE.6 Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MGSE.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.
MGSE.6.EE.8 Write an inequality of the form x < c or x > c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x < c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Represent and analyze quantitative relationships between dependent and independent variables.
MGSE6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. b. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝑑 = 65𝑡 to represent the relationship between distance and time. Understand ratio concepts and use ratio reasoning to solve problems.
MGSE.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems utilizing strategies such as tables of equivalent ratios, tape diagrams (bar models), double number line diagrams, and/or equations.
MGSE.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MGSE.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MGSE.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); given a percent, solve problems involving finding the whole given a part and the part given the whole.
MGSE.6.RP.3d Given a conversion factor, use ratio reasoning to convert measurement units within one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities. For example, given 1 in. = 2.54 cm, how many centimeters are in 6 inches?
BIG IDEAS
• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
• Relate and compare different forms of representation for a relationship.
• Use values from specified sets to make an equation or inequality true.
• Develop an initial conceptual understanding of different uses of variables.
• Graphs can be used to represent all of the possible solutions to a given situation.
• Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
• Students will solve one-step equations.
ESSENTIAL QUESTIONS
• How is an equation like a balance? How can the idea of balance help me solve an equation?
• What strategies can I use to help me understand and represent real situations using proportions, equations and inequalities?
• How can I write, interpret and manipulate proportions, equations, and inequalities?
• How can I solve a proportion and an equation?
• How can I tell the difference between an expression, equation and an inequality?
• How are the solutions of equations and inequalities different?
• What does an equal sign mean mathematically?
• How can proportions be used to solve problems?
• How can proportional relationships be described using the equation y = kx?
• How can proportional relationships be represented using rules, tables, and graphs?
• How can the graph of y = kx be interpreted for different contexts?
• How does a change in one variable affect the other variable in a given situation?
• Which tells me more about the relationship I am investigating, a table, a graph or a formula?
MGSE6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
MGSE6.EE.6 Use variables to represent numbers and write expressions when solving a real world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
MGSE.6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all non-negative rational numbers.
MGSE.6.EE.8 Write an inequality of the form x < c or x > c to represent a constraint or condition in a real-world or mathematical problem. Recognize that inequalities of the form x < c or x < c have infinitely many solutions; represent solutions of such inequalities on number line diagrams. Represent and analyze quantitative relationships between dependent and independent variables.
MGSE6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another. a. Write an equation to express one quantity, the dependent variable, in terms of the other quantity, the independent variable. b. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation. For example, in a problem involving motion at constant speed, list and graph ordered pairs of distances and times, and write the equation 𝑑 = 65𝑡 to represent the relationship between distance and time. Understand ratio concepts and use ratio reasoning to solve problems.
MGSE.6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems utilizing strategies such as tables of equivalent ratios, tape diagrams (bar models), double number line diagrams, and/or equations.
MGSE.6.RP.3a Make tables of equivalent ratios relating quantities with whole-number measurements, find missing values in the tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MGSE.6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MGSE.6.RP.3c Find a percent of a quantity as a rate per 100 (e.g. 30% of a quantity means 30/100 times the quantity); given a percent, solve problems involving finding the whole given a part and the part given the whole.
MGSE.6.RP.3d Given a conversion factor, use ratio reasoning to convert measurement units within one system of measurement and between two systems of measurements (customary and metric); manipulate and transform units appropriately when multiplying or dividing quantities. For example, given 1 in. = 2.54 cm, how many centimeters are in 6 inches?
BIG IDEAS
• Represent, analyze, and generalize a variety of patterns with tables, graphs, words, and, when possible, symbolic rules.
• Relate and compare different forms of representation for a relationship.
• Use values from specified sets to make an equation or inequality true.
• Develop an initial conceptual understanding of different uses of variables.
• Graphs can be used to represent all of the possible solutions to a given situation.
• Many problems encountered in everyday life can be solved using proportions, equations or inequalities.
• Students will solve one-step equations.
ESSENTIAL QUESTIONS
• How is an equation like a balance? How can the idea of balance help me solve an equation?
• What strategies can I use to help me understand and represent real situations using proportions, equations and inequalities?
• How can I write, interpret and manipulate proportions, equations, and inequalities?
• How can I solve a proportion and an equation?
• How can I tell the difference between an expression, equation and an inequality?
• How are the solutions of equations and inequalities different?
• What does an equal sign mean mathematically?
• How can proportions be used to solve problems?
• How can proportional relationships be described using the equation y = kx?
• How can proportional relationships be represented using rules, tables, and graphs?
• How can the graph of y = kx be interpreted for different contexts?
• How does a change in one variable affect the other variable in a given situation?
• Which tells me more about the relationship I am investigating, a table, a graph or a formula?
Monday, December 18, 2017
Update for 12/19
Dear Parents,
Our Literacy tests are today as well as our final draft of the student's opinion pieces. Signed papers also go home today. We will have the PBIS celebration for those students who earned 120 points on Wednesday. Our Winter Centers will be on Thursday from 11:30-12:30. Please make sure your student is bringing a coat each day. Thanks for all of your support!
Jenny M-G
Our Literacy tests are today as well as our final draft of the student's opinion pieces. Signed papers also go home today. We will have the PBIS celebration for those students who earned 120 points on Wednesday. Our Winter Centers will be on Thursday from 11:30-12:30. Please make sure your student is bringing a coat each day. Thanks for all of your support!
Jenny M-G
Tuesday, December 12, 2017
Update for 12/12
Dear Parents,
I hope you survived the cold and that your kiddos enjoyed the snow like mine did! Our Science test on cells and microorganisms has been postponed until tomorrow, 12/13. In math, students will be making their test corrections on the 5.1 multiplying & dividing decimals and the 6.1 algebraic expressions tomorrow as well. Our narrative digital presentations that Mr. Funn from the Alliance Theater has been helping the students create will be on Friday, 12/15 from 11:30 to 12:30. Please come if you are able! Also, we will finish up our opinion piece final drafts next Monday, 12/18. Please let me know if you have any questions about the 5.1 and 6.1 rubrics I sent out on Remind. Thank you, as always, for your support!!
Jenny M-G
5.1 math resources:
I hope you survived the cold and that your kiddos enjoyed the snow like mine did! Our Science test on cells and microorganisms has been postponed until tomorrow, 12/13. In math, students will be making their test corrections on the 5.1 multiplying & dividing decimals and the 6.1 algebraic expressions tomorrow as well. Our narrative digital presentations that Mr. Funn from the Alliance Theater has been helping the students create will be on Friday, 12/15 from 11:30 to 12:30. Please come if you are able! Also, we will finish up our opinion piece final drafts next Monday, 12/18. Please let me know if you have any questions about the 5.1 and 6.1 rubrics I sent out on Remind. Thank you, as always, for your support!!
Jenny M-G
5.1 math resources:
|
MGSE.5.NF.2
Solve word problems involving
addition and subtraction of fractions, 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 + ½ = 3/7, by observing that 3/7 < ½.
Simplify
Fractions:
Improper
Fractions:
Area
Models & Algorithm w/ Fractions
Fraction Interactive board:
Word Problems
Practice:
Games:
http://www.sheppardsoftware.com/mathgames/fractions/mathman_fractions_add_uncommon.htm
6.1 math resources:
MGSE6.EE.5 Understand solving an equation or
inequality as a process of answering a question: which values from a specified
set, if any, make the equation or inequality true? Use substitution to
determine whether a given number in a specified set makes an equation or
inequality true. MGSE6.EE.6 Use variables to represent numbers and write
expressions when solving a real world or mathematical problem; understand that
a variable can represent an unknown number, or, depending on the purpose at
hand, any number in a specified set.
algebra-flash-cards/
6.1 math Inequality word problems
https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1-inequalities/v/real-world-situations-with-inequalities
6.1 math Plotting Inequalities
https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1-inequalities/v/plotting-inequalities-on-a-number-line
6.1 math Balancing inequalities
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-solving-equations/v/why-we-do-the-same-thing-to-both-sides-simple-equations
6.1 Inequality Relationships
https://www.khanacademy.org/math/algebra/one-variable-linear-equations/alg1-solving-equations/v/representing-a-relationship-with-a-simple-equation
Writing resource:
|
Sunday, December 3, 2017
Update for 12/3
Dear Parents,
This week in science we are moving into studying microorganisms such as bacteria, mold, and protists. Our cells and microorganisms test will be next Monday, 12/11. In writing, students will be working on their opinion essay regarding whether or not chocolate milk should be sold in school. In 5.1 math, we will be wrapping up our exploration of adding, subtracting, multiplying, and dividing. Our Unit 3 test will be this Friday, 12/8. In 6.1 math, we will also be wrapping up our algebra unit with our Unit 3 test this Friday, 12/8. Please make sure your student is reviewing the work on Remind.
Please let me know if you have any questions!
Jenny M-G
5.1 grade math standards:
MGSE5.NBT.2 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. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to the hundredths.
MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
BIG IDEAS • Students will understand that the placement of the decimal is determined by multiplying or dividing a number by 10 or a multiple of 10. • Students will understand that multiplication and division are inverse operations of each other. • Students will understand that rules for multiplication and division of whole numbers also apply to decimals.
ESSENTIAL QUESTIONS • How can we use exponents to represent powers of 10? • How does multiplying or dividing by a power of ten affect the product? • How can we use models to help us multiply and divide decimals? • How do the rules of multiplying whole numbers relate to multiplying decimals? • How are multiplication and division related? • How are factors and multiples related to multiplication and division?
6th grade math standards:
MGSE6.EE.1 Write and evaluate expressions involving whole-number exponents.
MGSE6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. MGSE6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5-y.
MGSE6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
MGSE6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉 = 𝑠3 and 𝐴 = 6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠 = 1 2.
MGSE6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. MGSE6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them.) For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
MGSE6.NS.4 Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100. a. Find the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factors. (GCF) Example: 36 + 8 = 4(9 + 2) b. Apply the least common multiple of two whole numbers less than or equal to 12 to solve real-world problems.
ESSENTIAL QUESTIONS • How are “standard form” and “exponential form” related? • What is the purpose of an exponent? • How are exponents used when evaluating expressions? • How is the order of operations used to evaluate expressions? • How are exponents useful in solving mathematical and real world problems? • How are properties of numbers helpful in evaluating expressions? • What strategies can I use to help me understand and represent real situations using algebraic expressions? • How are the properties (Identify, Associative and Commutative) used to evaluate, simplify and expand expressions? • How is the Distributive Property used to evaluate, simplify and expand expressions? • How can I tell if two expressions are equivalent?
This week in science we are moving into studying microorganisms such as bacteria, mold, and protists. Our cells and microorganisms test will be next Monday, 12/11. In writing, students will be working on their opinion essay regarding whether or not chocolate milk should be sold in school. In 5.1 math, we will be wrapping up our exploration of adding, subtracting, multiplying, and dividing. Our Unit 3 test will be this Friday, 12/8. In 6.1 math, we will also be wrapping up our algebra unit with our Unit 3 test this Friday, 12/8. Please make sure your student is reviewing the work on Remind.
Please let me know if you have any questions!
Jenny M-G
5.1 grade math standards:
MGSE5.NBT.2 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. Use whole-number exponents to denote powers of 10. Perform operations with multi-digit whole numbers and with decimals to the hundredths.
MGSE5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.
BIG IDEAS • Students will understand that the placement of the decimal is determined by multiplying or dividing a number by 10 or a multiple of 10. • Students will understand that multiplication and division are inverse operations of each other. • Students will understand that rules for multiplication and division of whole numbers also apply to decimals.
ESSENTIAL QUESTIONS • How can we use exponents to represent powers of 10? • How does multiplying or dividing by a power of ten affect the product? • How can we use models to help us multiply and divide decimals? • How do the rules of multiplying whole numbers relate to multiplying decimals? • How are multiplication and division related? • How are factors and multiples related to multiplication and division?
6th grade math standards:
MGSE6.EE.1 Write and evaluate expressions involving whole-number exponents.
MGSE6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers. MGSE6.EE.2a Write expressions that record operations with numbers and with letters standing for numbers. For example, express the calculation “Subtract y from 5” as 5-y.
MGSE6.EE.2b Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity. For example, describe the expression 2(8 + 7) as a product of two factors; view (8 + 7) as both a single entity and a sum of two terms.
MGSE6.EE.2c Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations). For example, use the formulas 𝑉 = 𝑠3 and 𝐴 = 6𝑠2 to find the volume and surface area of a cube with sides of length 𝑠 = 1 2.
MGSE6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6(4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y. MGSE6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them.) For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.
MGSE6.NS.4 Find the common multiples of two whole numbers less than or equal to 12 and the common factors of two whole numbers less than or equal to 100. a. Find the greatest common factor of 2 whole numbers and use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factors. (GCF) Example: 36 + 8 = 4(9 + 2) b. Apply the least common multiple of two whole numbers less than or equal to 12 to solve real-world problems.
ESSENTIAL QUESTIONS • How are “standard form” and “exponential form” related? • What is the purpose of an exponent? • How are exponents used when evaluating expressions? • How is the order of operations used to evaluate expressions? • How are exponents useful in solving mathematical and real world problems? • How are properties of numbers helpful in evaluating expressions? • What strategies can I use to help me understand and represent real situations using algebraic expressions? • How are the properties (Identify, Associative and Commutative) used to evaluate, simplify and expand expressions? • How is the Distributive Property used to evaluate, simplify and expand expressions? • How can I tell if two expressions are equivalent?
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