## 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.

## 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

## 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

## 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.

## 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

*p*x + 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.