Math Level 6.1 - 6.2
UNIT 1 - NUMBER SYSTEM FLUENCY
STANDARDS:
MGSE6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, including reasoning strategies such as using visual fraction models and equations to represent the problem. For example:
MGSE6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
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.
MGSE6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, including reasoning strategies such as 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 many 3/4-cup servings are in 2/3 of a cup of yogurt?
- How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?
- Three pizzas are cut so each person at the table receives ¼ pizza. How many people are at the table?
- Create a story context for (2/3)÷(3/4) and use a visual fraction model to show the quotient;
- Use the relationship between multiplication and division to explain that (2/3)÷(3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc)
MGSE6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
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.
BIG IDEAS:
- A ratio is a number that relates two quantities or measures within a given situation in a multiplicative relationship (in contrast to a difference or additive relationship).The relationships and rules that govern whole numbers, govern all rational numbers.
- Making explicit the type of relationships that exist between two values will minimize confusion between multiplicative and additive situations.
- Ratios can express comparisons of a part to whole, (a/b with b ≠ 0), for example, the ratio of the number of boys in a class to the number of students in the class.
- The ratio of the length to the width of a rectangle is a part-to-part relationship.
- Understand that fractions are also part-whole ratios, meaning fractions are also ratios. Percentages are ratios and are sometimes used to express ratios.
- Both part-to-whole and part-to-part ratios compare two measures of the same type of thing. A ratio can also be a rate.
- A rate is a comparison of the measures of two different things or quantities; the measuring unit is different for each value. For example if 4 similar vans carry 36 passengers, then the comparison of 4 vans to 36 passengers is a ratio.
- All rates of speed are ratios that compare distance to time, such as driving at 45 miles per hour or jogging at 7 minutes per mile.
- Ratios use division to represent relations between two quantities.
ESSENTIAL QUESTIONS FOR THIS UNIT:
Why would it be useful to know the greatest common factor of a set of numbers?
Why would it be useful to know the least common multiple of a set of numbers?
How can the distributive property help me with computation?
Why does the process of invert and multiply work when dividing fractions?
When I divide one number by another number, do I always get a quotient smaller than my original number?
When I divide a fraction by a fraction what do the dividend, quotient and divisor represent?
What kind of models can I use to show solutions to word problems involving fractions?
Which strategies are helpful when dividing multi-digit numbers?
Which strategies are helpful when performing operations on multi-digit decimals?
Why would it be useful to know the greatest common factor of a set of numbers?
Why would it be useful to know the least common multiple of a set of numbers?
How can the distributive property help me with computation?
Why does the process of invert and multiply work when dividing fractions?
When I divide one number by another number, do I always get a quotient smaller than my original number?
When I divide a fraction by a fraction what do the dividend, quotient and divisor represent?
What kind of models can I use to show solutions to word problems involving fractions?
Which strategies are helpful when dividing multi-digit numbers?
Which strategies are helpful when performing operations on multi-digit decimals?
In this unit students will:
- Find the greatest common factor of two whole numbers less than or equal to 100.Find the least common multiple of two whole numbers less than or equal to 12.
- 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 factor.
- Interpret and compute quotients of fractions.
- Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem.
- Fluently divide multi-digit numbers using the standard algorithm.
- Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
UNIT 2 - Rate, Ratio, and Proportional Reasoning Using Equivalent Fractions
STANDARDS:
MGSE6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
MGSE6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.
MGSE6.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.
MGSE6.RP.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MGSE6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MGSE6.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.
MGSE6.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?
MGSE6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
MGSE6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0 (b not equal to zero), and use rate language in the context of a ratio relationship.
MGSE6.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.
MGSE6.RP.3a Make tables of equivalent ratios relating quantities with whole number measurements, find missing values in tables, and plot the pairs of values on the coordinate plane. Use tables to compare ratios.
MGSE6.RP.3b Solve unit rate problems including those involving unit pricing and constant speed.
MGSE6.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.
MGSE6.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?
In this unit, students will:
- gain a deeper understanding of proportional reasoning through instruction and practice
- develop and use multiplicative thinking
- develop a sense of proportional reasoning
- develop the understanding that ratio is a comparison of two numbers or quantities
- find percents using the same processes for solving rates and proportions
- solve real-life problems involving measurement units that need to be converted
UNIT 3 - EXPRESSIONS
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.
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.
BIG IDEAS:
- Variables can be used as unique unknown values or as quantities that vary.
- Exponential notation is a way to express repeated products of the same number.
- Algebraic expressions may be used to represent and generalize mathematical problems and real life situations.
- Properties of numbers can be used to simplify and evaluate expressions.
- Algebraic properties can be used to create equivalent expressions.
- Two equivalent expressions form an equation.
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?
Unit 4 - One Step Equations and Inequalities
STANDARDS:
MGSE.6.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.
MGSE.6.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 (where your domain may be limited i.e. Time will not be negative). 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 nonnegative 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.
MGSE.6.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 a 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.
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); give 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 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?
Unit 5 - Area and Volume
STANDARDS:
MGSE6.G.1 Find area of right triangles, other triangles, quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
MGSE6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths (1/2 u), and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = (length) x (width) x (height) and V= (area of base) x (height) to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
MGSE6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Useful Tutorial Videos:
SURFACE AREA - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/basic-geometry-surface-area/v/finding-surface-area-using-net
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/basic-geometry-surface-area/e/find-surface-area-by-adding-areas-of-faces
VOLUME - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/v/volume-of-a-rectangular-prism-or-box-examples
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/e/volume_1
VOLUME WORD PROBLEMS - https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-additional-topics-math/v/sat-math-s1-harder
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-with-fractions/e/volume-word-problems-with-fractions
- https://www.khanacademy.org/math/pre-algebra/pre-algebra-measurement/pre-algebra-volume-rectangular/e/volume_2
More to THINK About...https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/v/how-volume-changes-from-changing-dimensions
SURFACE AREA - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/basic-geometry-surface-area/v/finding-surface-area-using-net
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/basic-geometry-surface-area/e/find-surface-area-by-adding-areas-of-faces
VOLUME - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/v/volume-of-a-rectangular-prism-or-box-examples
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/e/volume_1
VOLUME WORD PROBLEMS - https://www.khanacademy.org/test-prep/sat/sat-math-practice/new-sat-additional-topics-math/v/sat-math-s1-harder
practice - https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-with-fractions/e/volume-word-problems-with-fractions
- https://www.khanacademy.org/math/pre-algebra/pre-algebra-measurement/pre-algebra-volume-rectangular/e/volume_2
More to THINK About...https://www.khanacademy.org/math/basic-geo/basic-geo-volume-sa/volume-rect-prism/v/how-volume-changes-from-changing-dimensions
UNIT 6 - Statistics
STANDARDS:
MGSE6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
MGSE6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
MGSE6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
MGSE6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
MGSE6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range). d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
MGSE6.SP.1. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
MGSE6.SP.2. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.
MGSE6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
MGSE6.SP.4. Display numerical data in plots on a number line, including dot plots, histograms, and box plots.
MGSE6.SP.5 Summarize numerical data sets in relation to their context, such as by: a. Reporting the number of observations. b. Describing the nature of the attribute under investigation, including how it was measured and its units of measurement. c. Giving quantitative measures of center (median and/or mean) and variability (interquartile range). d. Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data was gathered.
In this unit students will:
- Analyze data from many different sources such as organized lists, box-plots, bar graphs, histograms and dot plots.
- Understand that responses to statistical questions may vary.
- Understand that data can be described by a single number.
- Determine quantitative measures of center (median and/or mean).
- Determine quantitative measures of variability (interquartile range and range).
UNIT 7 - Rational Explorations: Numbers and their Opposites
MGSE6.NS.5 Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (e.g., temperature above/below zero, elevation above/below sea level, debits/credits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation.
MGSE6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
MGSE6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., −(−3) = 3, and that 0 is its own opposite. MGSE6.NS.6b Understand signs of number in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
MGSE6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
MGSE6.NS.7 Understand ordering and absolute value of rational numbers.
MGSE6NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
MGSE6.NS.7b Write, interpret, and explain statements of order for rational numbers in realworld contexts.
MGSE6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation.
MGSE6.NS.7d Distinguish comparisons of absolute value from statements about order.
MGSE6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
MGSE6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply those techniques in the context of solving real-world mathematical problems.
MGSE6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.
MGSE6.NS.6a Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., −(−3) = 3, and that 0 is its own opposite. MGSE6.NS.6b Understand signs of number in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
MGSE6.NS.6c Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.
MGSE6.NS.7 Understand ordering and absolute value of rational numbers.
MGSE6NS.7a Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram.
MGSE6.NS.7b Write, interpret, and explain statements of order for rational numbers in realworld contexts.
MGSE6.NS.7c Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a realworld situation.
MGSE6.NS.7d Distinguish comparisons of absolute value from statements about order.
MGSE6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of the coordinate plane. Include use of coordinates and absolute value to find distances between points with the same first coordinate or the same second coordinate.
MGSE6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply those techniques in the context of solving real-world mathematical problems.
ESSENTIAL QUESTIONS:
- When are negative numbers used and why are they important?
- Why is it useful for me to know the absolute value of a number?
- When is graphing on the coordinate plane helpful?
- How do I use positive and negative numbers in everyday life?
- Where do I place positive and negative rational numbers on the number line?
- How do I use positive and negative numbers to represent quantities in real-world contexts?
- What are opposites, and how are opposites shown on a number line?
- How do statements of inequality help me place numbers on a number line?
- How can I use coordinates to find the distances between points?
- How can I use number lines to find the distances between points?
- How can I use absolute value to find the lengths of the sides of polygons on the coordinate plane?