Students are continuing to practice using visualizations to identify quantities in word problems, and to assist thier understanding of the relationships between quantities. Students benefit from visualizing a situation in a personal way, and understanding the parts of their diagram represented by an equation. Is it the total? the size of the group? the number of groups?
This week, students are challenged to draw diagrams and write equations to represent simple division situations. Some students draw concrete diagrams; others draw abstract ones. Any diagrammatic representation is fine as long as it enables students to make sense of the relationship between the number of groups, the size of a group, and a total amount. We will continue to use equivalent ratios to solve a variety of problems.
FRACTIONS In this unit, students will thinking about the relationships between the numbers in a division equation. They see that they can estimate the size of the quotient by reasoning about the relative sizes of the divisor and the dividend. First, they explore concrete situations. For example, they estimate how many thinner and thicker objects are needed to make a stack of a given height, and how many segments of a certain size make a particular length.
In grade 4, students began converting units of measurements by multiplying. The work in grade 5 expanded to include conversion by dividing, but was still restricted to units within the same measurement system. In this lesson, students progress to converting units that may be in different systems of measurement, using ratio reasoning and recently-learned strategies such as double number lines, tables, and multiplication or division of unit rates.
Sorry, this post should have gone out Monday morning.
Students have completed their work on using pictures, double number lines and tables to find equivalent ratios and solve ratio problems. Happy to report that everyone rocked the end of the unit assessment, so we have started Unit Rates and Percentages!
We began by reviewing measurement concepts, like length, area, volume, and capacity. Students are using what they know about ratios and rates to reason about measurements in different units of measurement such as pounds and kilograms. In earlier grades, students converted yards to feet using the fact that 1 yard is 3 feet, and kilometers to meters using the fact that 1 kilometer is 1,000 meters. Now in grade 6, students convert units that do not always use whole numbers.