Current+Units+of+Study+in+Math


 * Moving towards 4th quarter! Dakota STEP test is around the corner.**
 * Our classes are moving on to another strand of standards. I have set a goal to have the material covered in this area, so students will be able to create videos showing them teaching about a specific standard. Our school has a flip video camera that I would like to have the students utilize during their teaching unit! To teach is to remember!**

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=﻿ 6th grade - Red Jalapenos = 1

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Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem. **For example, 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.) 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? =====

Question:
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?

Question: How many 3/4-cup servings are in 2/3 of a cup of yogurt?

Question: How wide is a rectangular strip of land with length 3/4 mi and area 1/2 square mi?

Question: What does (a/b) ÷ (c/d) = ad/bc mean?

1. TEXTing p. 2. [] Have fun figuring out the fraction to find Grammy! 3. [] fractions and all the operations :) 4. [] This is really good with simple division of fractions. :) 5. [] This is a site that reminds us how to add fractions that have unlike denominators.

2

Compute fluently with multi-digit numbers and find common factors and multiples.
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to 100 and 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. For example, express 36 + 8 as 4 (9 + 2). Apply and extend previous understandings of numbers to the system of rational numbers.===

3 **Apply and extend previous understandings of numbers to the system of rational numbers. ** === 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, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of 0 in each situation. ++++++++ ===

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  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. =====  o 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.  o Understand signs of numbers 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.  o 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.  Understand ordering and absolute value of rational numbers.  o Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. //For example, interpret –3 > –7 as a statement that –3 is located to the right of –7 on a number line oriented from left to right.//  o Write, interpret, and explain statements of order for rational numbers in real-world contexts. //For example, write –3 oC > –7 oC to express the fact that –3 oC is warmer than –7 oC.// <span style="background: white; line-height: 16pt; margin: 0in 0in 10pt; tabstops: list 1.0in; text-indent: -0.25in;"> o <span style="color: #3b3b3a; font-family: 'Helvetica','sans-serif'; font-size: 13pt;">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 real-world situation. //For example, for an account balance of –30 dollars, write |–30| = 30 to describe the size of the debt in dollars.// <span style="background: white; line-height: 16pt; margin: 0in 0in 10pt; tabstops: list 1.0in; text-indent: -0.25in;"> o <span style="color: #3b3b3a; font-family: 'Helvetica','sans-serif'; font-size: 13pt;">Distinguish comparisons of absolute value from statements about order. //For example, recognize that an account balance less than –30 dollars represents a debt greater than 30 dollars.// <span style="background: white; line-height: 16pt; margin: 0in 0in 10pt; tabstops: list .5in; text-indent: -0.25in;"><span style="color: #3b3b3a; font-family: 'Helvetica','sans-serif'; font-size: 13pt;"> 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.

=** 7th grade - The Green Machine **=

Use random sampling to draw inferences about a population.
1. TEXTing p. 301 "Wildlife Sampling" p. 345 "Statistics to Predict" 2. []
 * Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce representative samples and support valid inferences.

//1. TEXTing p.// 2. []
 * Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. //For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be.//

Draw informal comparative inferences about two populations.
[] Inter-math dictionary: statistics with box and whisker plot on the same page to help us display data for two populations
 * Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. //For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable.//
 * Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. //For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourth-grade science book.//

Investigate chance processes and develop, use, and evaluate probability models.

 * Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.
 * Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-run relative frequency, and predict the approximate relative frequency given the probability. //For example, when rolling a number cube 600 times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.//
 * Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the agreement is not good, explain possible sources of the discrepancy.
 * Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. //For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.//
 * Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. //For example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-end down. Do the outcomes for the spinning penny appear to be equally likely based on the observed frequencies?//
 * Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
 * 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.
 * Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.
 * Design and use a simulation to generate frequencies for compound events. //For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?//

CHAPTER __ STUDY GUIDE AND QUIZZING

=﻿ 8th grade - Blue Diamonds =

Understand and apply the Pythagorean Theorem.

 * Explain a proof of the Pythagorean Theorem and its converse.

1. Related TEXTing p. 132-136 about the Pyth. Theorem and its converse

2. []

3. [] 1. Related TEXTing p. 137-140 about applying the Pythagorean Theorem p. 141 Lab about graphing irrational numbers 2. [] (if you can find a better website, I will take yours and put it here) :) 3. 1. Related TEXTing p. 142-145 about this theorem and the coordinate plane 2. []
 * Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
 * Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

CHAPTER 3 STUDY GUIDE AND QUIZZING

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

 * Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.

Investigate patterns of association in bivariate data.

 * Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association.
 * Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear
 * association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line.
 * Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height.
 * Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?