6 4 6 Illustrative Mathematics Grade 6 Unit 4 Lesson 6 Morgan

The script introduces a math lesson focused on division of fractions using tape diagrams. It emphasizes the importance of visual representation to understand fractions and division, especially when dealing with tricky concepts. The instructor encourages students to persevere through the challenging material and offers reassurance that mathematical shortcuts exist, but for now, a focus on understanding the diagrams is key.

This paragraph delves into using tape diagrams to visualize the division of fractions. It explains the concept of dividing 10 by 2.5, represented as finding how many groups of 2.5 are in 10. The instructor demonstrates how to create a tape diagram with 10 segments and then divides them into groups of 2.5, resulting in four complete groups plus a remainder. This approach helps in understanding division as finding the number of groups within a whole.

The script continues with an exercise to complete a tape diagram for the division problem of 7 by 2. It illustrates the process of dividing 7 into groups of 2 and identifying the remainder, which in this case is not a whole group but a fraction of the group size. The instructor emphasizes the importance of understanding the group size and the remainder in relation to it, concluding that there are three and a half groups of 2 in 7.

This section discusses representing division problems as multiplication problems, using the example of one divided by two-thirds. The script describes how to rewrite the division problem as a multiplication problem to find an unknown multiplier. It also explains how to use a tape diagram to represent the problem, showing that one whole can be divided into two-thirds, resulting in one whole group of two-thirds and a half of the group size remaining.

The script presents a series of practice problems involving division with tape diagrams. It covers dividing one by three-fourths, three by two-thirds, and five by three-halves, providing a step-by-step guide on how to set up and solve these problems using tape diagrams. The goal is to find the number of groups of the divisor within the dividend, and the diagrams help visualize the whole groups and any leftover segments.

This paragraph extends the use of tape diagrams to real-world problems, such as determining how many 3/8-inch thick books can make a stack that is 6 inches tall. The script guides through the process of drawing a tape diagram for 6 inches and dividing it into 3/8 segments to find the number of groups. It concludes that there are 16 groups of 3/8 in 6 inches, showcasing the practical application of the concept.

The script explores using tape diagrams to divide weights, specifically how many groups of a half are in two and three-fourths of a pound. It demonstrates dividing the weight into halves and counting the groups, including the remainder. The result is five and a half groups, illustrating the process of dividing a mixed number into equal parts and understanding the concept of remainders in division.

This section uses a baker's example to illustrate division with fractions. The script explains how the baker used 2 kilograms of flour for batches that require two-fifths of a kilogram each. By drawing a tape diagram and dividing 2 kilograms into fifths, it shows that 5 batches can be made, which is verified by multiplying the number of batches by the flour required per batch, yielding the original amount of flour.

The script provides instructions for solving division problems with tape diagrams, specifically for dividing 3 by 1/4 and 3 by 3/5. It explains the process of drawing the diagrams, dividing the wholes into the appropriate fractions, and counting the number of groups that can be made. The examples result in 12 groups of 1/4 in 3 and 5 groups of 3/5 in 3, reinforcing the concept of division as finding groups within a whole.

This paragraph focuses on calculating the number of half-day segments in a week using a tape diagram. It explains dividing the 7 days of the week into half-day segments, resulting in 14 half-days. The script also touches on the concept of reciprocal multiplication as an alternative method to arrive at the same answer, providing a brief review of previous knowledge.

The script presents a statement made by Diego regarding the division of 1 by 5/6, which he claims equals 6/5. The instructor confirms the correctness of Diego's statement and explains that it can be visually represented using a tape diagram. The diagram would show one whole group of 5/6 and a remainder of 1/5, aligning with the concept of division and the use of reciprocals.

This section reviews questions that represent the concept of dividing by four-fifths. The script identifies which questions correctly illustrate this division, including the multiplication of four-fifths by an unknown to equal one, and the division of one by four-fifths to find an unknown. It confirms that certain options are correct and align with the division concept.

The final paragraph of the script involves mental calculations of percentages, such as 10% of 70, 25% of 160, 50% of 350, and others. The instructor demonstrates strategies for simplifying these calculations, such as halving the number and then further dividing by known fractions. The results are presented, showcasing the ability to perform quick percentage calculations mentally.