Students solve multi-step problems involving measurement conversions, line plots, and fraction operations, including addition and subtraction of fractions with unlike denominators. They also explain patterns when multiplying and dividing by powers of 10 and interpret multiplication as scaling, by comparing products with factors.
Unit Narrative
In this unit, students deepen their understanding of place-value relationships of numbers in base ten, unit conversion, operations on fractions with unlike denominators, and multiplicative comparison. The work here builds on several important ideas from grade 4.
In grade 4, students learned the value of each digit in a whole number is 10 times the value of the same digit in a place to its right. Here, they extend that insight to include decimals to the thousandths. Students recognize that the value of each digit in a place (including decimal places) is the value of the same digit in the place to its left.
This idea is highlighted as students perform measurement conversions in metric units.
Previously, students learned to convert from a larger unit to a smaller unit. Here, they learn to convert from a smaller unit to a larger unit. They observe how the digits shift when multiplied or divided by a power of 10 and learn to use exponential notation for powers of 10 to represent large numbers.
L
mL
5
6.3
0.95
800,000
65
Next, students turn their attention to fractions. In earlier grades, students made sense of equivalent fractions, added and subtracted fractions with the same denominator, and added tenths and hundredths. In this unit, they add and subtract fractions with different denominators. They see that the key is to find a common denominator and analyze different techniques for doing so.
Students then solve problems that involve measurement data (in halves, fourths, and eighths) that are displayed on line plots.
In the final section, students reason about the size of a product of fractions and the sizes of the factors. This work builds on the multiplicative comparison work in grade 4, in which students compared a whole number as “_____ times as many (or as much) as” another whole number. Here, students reason about products of a whole number and a fraction, without finding the value of each product. They use diagrams and expressions to support their reasoning.
Write , , or in each blank to make true statements.
