District Blueprint - Intermediate Math 1
A steering committee of representatives from most schools in Alpine School District creating the following blueprint as a recommended sequence for the content in the new Utah Core. These resources will help you transition from the old core to the new core standards.
The following is a brief outline of the District Blueprint for Intermediate Math 1.
To download the full blueprint (including examples) click here.
To download the full blueprint (including examples) click here.
1- Rational Numbers Unit
The first four learning objectives should be taught throughout the Rational Numbers Unit
7.NS.1.b.3 I can interpret sums of rational numbers using contextual situations.
7.NS.2.a.2 I can interpret products of rational numbers using contextual situations.
7.NS.2.b.3 I can interpret quotients of rational numbers using contextual situations.
7.NS.3 I can solve contextual situations and mathematical problems involving the four operations with rational numbers. (When working with complex fractions use the same rules as simple fractions.)
7.NS.1.c.2 I can show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in contextual situations.
7.NS.1.b.1 I can understand that p + q is a number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
7.NS.1.b.2 I can show that a number and its opposite have a sum of 0 (additive inverses)
7.NS.1.c.1 I can understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
7.NS.2.b.1 I can understand that integers can be divided, and every quotient of integers (with non-zero divisor) is a rational number.
7.NS.2.c I can apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2.b.2 I can understand that if p and q are integers, then –(p/q) = (–p)/q = p/(–q).
7.NS.1.d I can apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2.a.1 I can understand the properties used to multiply fractions extend to all rational numbers, with a particular emphasis on the distributive property and signed numbers.
7.NS.2.d.1 I can convert a rational number to a decimal using long division;
7.NS.2.d.2 I can understand that the decimal form of a rational number terminates in 0s or eventually repeats.
Note: Operations with integers are NOT included in any previous grade level.
7.NS.1.a I can describe rational numbers in a contextual situation.
7.NS.1.b.3 I can interpret sums of rational numbers using contextual situations.
7.NS.2.a.2 I can interpret products of rational numbers using contextual situations.
7.NS.2.b.3 I can interpret quotients of rational numbers using contextual situations.
7.NS.3 I can solve contextual situations and mathematical problems involving the four operations with rational numbers. (When working with complex fractions use the same rules as simple fractions.)
7.NS.1.c.2 I can show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in contextual situations.
7.NS.1.b.1 I can understand that p + q is a number located a distance |q| from p, in the positive or negative direction depending on whether q is positive or negative.
7.NS.1.b.2 I can show that a number and its opposite have a sum of 0 (additive inverses)
7.NS.1.c.1 I can understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q).
7.NS.2.b.1 I can understand that integers can be divided, and every quotient of integers (with non-zero divisor) is a rational number.
7.NS.2.c I can apply properties of operations as strategies to multiply and divide rational numbers.
7.NS.2.b.2 I can understand that if p and q are integers, then –(p/q) = (–p)/q = p/(–q).
7.NS.1.d I can apply properties of operations as strategies to add and subtract rational numbers. 7.NS.2.a.1 I can understand the properties used to multiply fractions extend to all rational numbers, with a particular emphasis on the distributive property and signed numbers.
7.NS.2.d.1 I can convert a rational number to a decimal using long division;
7.NS.2.d.2 I can understand that the decimal form of a rational number terminates in 0s or eventually repeats.
Note: Operations with integers are NOT included in any previous grade level.
7.NS.1.a I can describe rational numbers in a contextual situation.
2- Proportional Reasoning Unit
The first two learning objectives should be taught throughout the Proportional Reasoning Unit
7.RP.3 I can use proportional reasoning to solve multistep ratio and percent problems.
7.RP.2.c I can represent proportional relationships by equations.
7.SP.1.c I understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.2.b I can generate multiple samples of the same size from the same population to gauge the variation in estimates or predictions of the parameter.
Note: Parameter is the true value of the population’s unknown characteristic. A statistic is calculated from the sample and is only an estimate of the population’s parameter.
7.SP.1.b I understand that the generalizations made are only valid if the sample is representative of the population.
7.SP.2.a I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest (the desired information).
7.SP.1.a I understand that information can be gathered about a population from a sample of the population.
7.RP.2.b I can determine the constant of proportionality (unit rate) from a variety of representations (tables, graphs, equations, diagrams, and verbal descriptions).
7.RP.2.d.1 I can explain the meaning of the x-value and y-value on the graph of a proportional relationship in terms of the contextual situation.
7.RP.2.a I can determine whether 2 quantities are proportional
7.RP.2.d.2 I can explain why r is the unit rate when the graph passes through the points (0,0) and (1,r).
7.RP.1 I can compute unit rates associated with ratios of complex fractions such as: lengths, areas, and other quantities given in like or different units.
7.G.1 I can solve problems involving scale drawings of geometric figures
7.RP.3 I can use proportional reasoning to solve multistep ratio and percent problems.
7.RP.2.c I can represent proportional relationships by equations.
7.SP.1.c I understand that random sampling tends to produce representative samples and support valid inferences.
7.SP.2.b I can generate multiple samples of the same size from the same population to gauge the variation in estimates or predictions of the parameter.
Note: Parameter is the true value of the population’s unknown characteristic. A statistic is calculated from the sample and is only an estimate of the population’s parameter.
7.SP.1.b I understand that the generalizations made are only valid if the sample is representative of the population.
7.SP.2.a I can use data from a random sample to draw inferences about a population with an unknown characteristic of interest (the desired information).
7.SP.1.a I understand that information can be gathered about a population from a sample of the population.
7.RP.2.b I can determine the constant of proportionality (unit rate) from a variety of representations (tables, graphs, equations, diagrams, and verbal descriptions).
7.RP.2.d.1 I can explain the meaning of the x-value and y-value on the graph of a proportional relationship in terms of the contextual situation.
7.RP.2.a I can determine whether 2 quantities are proportional
7.RP.2.d.2 I can explain why r is the unit rate when the graph passes through the points (0,0) and (1,r).
7.RP.1 I can compute unit rates associated with ratios of complex fractions such as: lengths, areas, and other quantities given in like or different units.
7.G.1 I can solve problems involving scale drawings of geometric figures
3- Statistics and Probability Unit
7.SP.8.c I can design and use a simulation to generate frequencies for compound events.
7.SP.8.b I can create representations (organized lists, tables and tree diagrams) of sample spaces for compound events.
7.SP.7.a I can develop a uniform probability model (all outcomes equally likely) and use it to determine the likelihood of a given event.
7.SP.5 I can understand the probability of a chance event is the likelihood of the event occurring and is expressed as a number between 0 and 1
7.SP.8.b.1 I can identify the outcomes for a given event.
7.SP.8.a I can understand that just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
7.SP.6.a I can approximate the probability of an event by collecting data and observing its long-run relative frequency.
7.SP.4 I can use measures of center (mean and median) and variability (interquartile range, mean absolute deviation) from random samples to make informal comparative inferences about two populations.
7.SP.6.b I can predict the approximate relative frequency given the theoretical probability.
7.SP.7.b I can create a probability model, eg. bar graph, circle graph, (which may not be uniform) by observing frequencies in data generated from an experiment.
7.SP.3 I can use visual representations (box & whisker plots, dot plots, etc.) to compare the centers(mean and median) and variability (interquartile range, mean absolute deviation) of two data sets (This standard builds on 6.SP.5 where mean absolute deviation is introduced.).
Note – How to find the Mean Absolute Deviation from a data set.
The Mean Absolute Deviation is calculated in three simple steps.
1) Determine the Mean: Add all numbers and divide by the count
example: the weights of the following three people, denoted by letters are
A - 56 Kgs B - 78 Kgs C - 90 Kgs
Mean = (56+78+90)/3= 74.6
2) Determine deviation of each variable from the Mean
i.e 56-74.6 = -18.67
78-74.6= 3.33
90-74.6 =15.33
3) Find the average of the absolute values of the deviations. i.e eliminate the negative aspect
Thus the Mean Absolute Deviation is (18.67 +3.33+15.33)/3 =12.44
Alternatively, you can use the excel formula =AVEDEV(56,78,90) to obtain the result.
Note: For a detailed example please see pages 22-24 of Arizona’s Grade 7 explanation of the Common Core.
Click here for Arizona explanation
7.SP.8.b I can create representations (organized lists, tables and tree diagrams) of sample spaces for compound events.
7.SP.7.a I can develop a uniform probability model (all outcomes equally likely) and use it to determine the likelihood of a given event.
7.SP.5 I can understand the probability of a chance event is the likelihood of the event occurring and is expressed as a number between 0 and 1
7.SP.8.b.1 I can identify the outcomes for a given event.
7.SP.8.a I can understand that just as with simple events, the probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.
7.SP.6.a I can approximate the probability of an event by collecting data and observing its long-run relative frequency.
7.SP.4 I can use measures of center (mean and median) and variability (interquartile range, mean absolute deviation) from random samples to make informal comparative inferences about two populations.
7.SP.6.b I can predict the approximate relative frequency given the theoretical probability.
7.SP.7.b I can create a probability model, eg. bar graph, circle graph, (which may not be uniform) by observing frequencies in data generated from an experiment.
7.SP.3 I can use visual representations (box & whisker plots, dot plots, etc.) to compare the centers(mean and median) and variability (interquartile range, mean absolute deviation) of two data sets (This standard builds on 6.SP.5 where mean absolute deviation is introduced.).
Note – How to find the Mean Absolute Deviation from a data set.
The Mean Absolute Deviation is calculated in three simple steps.
1) Determine the Mean: Add all numbers and divide by the count
example: the weights of the following three people, denoted by letters are
A - 56 Kgs B - 78 Kgs C - 90 Kgs
Mean = (56+78+90)/3= 74.6
2) Determine deviation of each variable from the Mean
i.e 56-74.6 = -18.67
78-74.6= 3.33
90-74.6 =15.33
3) Find the average of the absolute values of the deviations. i.e eliminate the negative aspect
Thus the Mean Absolute Deviation is (18.67 +3.33+15.33)/3 =12.44
Alternatively, you can use the excel formula =AVEDEV(56,78,90) to obtain the result.
Note: For a detailed example please see pages 22-24 of Arizona’s Grade 7 explanation of the Common Core.
Click here for Arizona explanation
4- Geometry
7.G.3 I can describe cross sections of three-dimensional figures.
Click here for Web resource
7.G.2 I can draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions, focusing on triangles.
Alpine School District objective: Develop the idea of supplementary and complementary angles
7.G.1 I can solve problems involving scale drawings of geometric figures.
7.G.6 I can solve contextual situations and math problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
7.G.4.c I can visually demonstrate the relationship between area and circumference of a circle.
7.G.4.a I can recite the formulas for the area and circumference of a circle.
7.G.4.b I can solve problems involving area and circumference.
Click here for Web resource
7.G.2 I can draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions, focusing on triangles.
Alpine School District objective: Develop the idea of supplementary and complementary angles
7.G.1 I can solve problems involving scale drawings of geometric figures.
7.G.6 I can solve contextual situations and math problems involving area, volume, and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.
7.G.4.c I can visually demonstrate the relationship between area and circumference of a circle.
7.G.4.a I can recite the formulas for the area and circumference of a circle.
7.G.4.b I can solve problems involving area and circumference.
5- Solving Equations
7.EE.4.b.2 I can graph the solution set of an inequality and interpret it in the context of the problem.
7.EE.2 I can understand that rewriting an expression in different forms in a contextual situation can shed light on the problem and how the quantities in it are related.
7.EE.4.a.1 I can develop and solve simple equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers, for contextual situations
7.G.5 I can use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Note: The focus of this objective in the Solving Equations unit should be to find missing angles by solving an equation.
7.EE.3.b I can convert between numerical forms as appropriate and assess the reasonableness of answers using mental computation and estimation strategies.
7.EE.4.a.2 I can solve a contextual situation numerically or by solving an equation and compare the processes involved in each case.
7.EE.3.a I can solve multi-step contextual situations posed with positive and negative rational numbers in any form. (whole numbers, fractions, and decimals)
7.EE.4.b.1 I can develop and solve simple inequalities of the form px + q > r and px + q < r, where p, q, and r are specific rational numbers, for contextual situations.
7.EE.1 I can apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
7.EE.2 I can understand that rewriting an expression in different forms in a contextual situation can shed light on the problem and how the quantities in it are related.
7.EE.4.a.1 I can develop and solve simple equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers, for contextual situations
7.G.5 I can use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
Note: The focus of this objective in the Solving Equations unit should be to find missing angles by solving an equation.
7.EE.3.b I can convert between numerical forms as appropriate and assess the reasonableness of answers using mental computation and estimation strategies.
7.EE.4.a.2 I can solve a contextual situation numerically or by solving an equation and compare the processes involved in each case.
7.EE.3.a I can solve multi-step contextual situations posed with positive and negative rational numbers in any form. (whole numbers, fractions, and decimals)
7.EE.4.b.1 I can develop and solve simple inequalities of the form px + q > r and px + q < r, where p, q, and r are specific rational numbers, for contextual situations.
7.EE.1 I can apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.