These short clips are the same videos many CMP3 teachers use to review key math concepts when they prepare to teach CMP3 lessons. Use these helpful videos to bolster your math knowledge as you help your student with homework. The video clips highlight important mathematical ideas and concepts in each CMP3 Unit in an easy-to-understand visual way.
Connecting Equations, Tables, and Graphs
There are many ways to represent relationships between two quantitative variables, such as equations, tables, and graphs. This video illustrates the relationships among these representations. It is important for students to move freely among the various representations. By the end of the Unit, students should feel very comfortable with tables and graphs and with some simple equations. Students should also have an appreciation of the advantages and disadvantages of each representation.
Prime Time
Prime Factorization of 100There are several methods for finding the prime factorization of a number. This video outlines the steps of the repeated division strategy, but students may also make a factor tree in order to find the prime factorization of a number. These two methods are equally valid, so students should use the one that makes the most sense to them.
Factor Pairs of 12The key to finding all the factors of a given number, n, is to examine systematically the whole numbers that are less than or equal to the square root of n. Students probably have little understanding of square roots at this stage. They are more likely to understand it as the point where the factors in the factor pairs reverse order so that the first factor is greater than the second. Students can also see where the factor pairs reverse order geometrically. This video shows how superimposing the rectangles for a number on top of each other reveals the symmetry of the factor pairs.
Comparing Bits and Pieces
Equivalence of Fractions: One Fourth Is Three TwelfthsPartitioning and then partitioning again is an important skill that contributes to understanding equivalent fractions. This property of equivalence is used to add and subtract fractions with different denominators. This video shows how one fourth is equivalent to three twelfths in the context of partitioning a chewy fruit worm.
Let's Be Rational
Discrete Model for Mixed Number MultiplicationStudents model multiplication of fractions in many different ways. They may use area models. They may also partition a number line or fraction strip in order to represent fractions. They may use discrete models to make sense of situations in which the quantities they are working with are separate objects, such as apples, oranges, or muffins. Discrete models can also represent mixed numbers. This video shows a discrete model for evaluating $2{\displaystyle {\displaystyle \genfrac{}{}{10%}{}{1}{2}}}\times 3{\displaystyle {\displaystyle \genfrac{}{}{10%}{}{1}{2}}}$.
Area Model for Mixed Number MultiplicationArea models are one strategy that students use for multiplying fractions. This video demonstrates an area model approach for multiplying mixed numbers.
Covering and Surrounding
Area of TrianglesIn Investigation 2, students use their knowledge about finding area and perimeter of a rectangle to find the area and perimeter of a triangle. If you surround a triangle with a rectangle in a particular way, there are two small triangles that are inside the rectangle and also outside the triangle (Triangles 1 and 4 in the video). When you draw in the height of the triangle, the two triangles formed (Triangles 2 and 3 in the video) are congruent to the other two triangles in the rectangle.
Decimal Ops
Decomposing a Decimal NumberThis video shows how decimals can be decomposed into sums of their digits’ values, which can then be converted to equivalent fractions. Students can use the fraction expansion and their knowledge of operations with fractions to develop algorithms for operations with decimals.
Using a Percent Bar to Make Sense of Percents Greater Than 100Students are introduced to a percent situation in which they are given the final total of a purchase: the price plus the tax. They start with a percentage greater than 100%. This video illustrates a method for finding the price before tax.
Variables and Patterns
Connecting Equations, Tables, and GraphsThere are many ways to represent relationships between two quantitative variables, such as equations, tables, and graphs. This video illustrates the relationships among these representations. It is important for students to move freely among the various representations. By the end of the Unit, students should feel very comfortable with tables and graphs and with some simple equations. Students should also have an appreciation of the advantages and disadvantages of each representation.
Histograms display the distribution of numerical data using intervals. The vertical axis is labeled with either number counts or percents. So, the height of the bar indicates the frequency of data values within an interval. Students can use histograms to group data into intervals. This allows them to see patterns in the data distribution and identify the overall shape of a distribution.
Because data are organized by intervals, the bars touch. This shows the continuous nature of the number line. There are conventions that determine where entries whose data values occur at the end points of an interval will be placed. This video shows how to construct a histogram, paying particular attention to where points on the borders of intervals belong.
Using an Ordered-Value Bar Graph to Find the Mean Absolute DeviationThe MAD (mean absolute deviation) relates the variability of a distribution to the mean. It determines whether or not the data values in the data set are close to the mean. The MAD is the average distance between each data value and the mean. This video shows how you can use an ordered-value bar graph to find the MAD.