In this unit, students begin to understand that they can measure length more precisely through using parts of units (specifically halves and fourths). They represent fractions on a number line and use measurement as a context for understanding fractions. In the final lessons, students will understand that the length of an object or distance stays the same regardless of how they align the ruler.
Key Concepts:
- Measurements get more precise when we use parts of units. Length measurements can be partitioned into any size increments. (restricted to halves and quarters in grade 3) (Lesson 1)
- The quantitative measurement of an object is invariant (a toothpick's length does not change, regardless of how we align it to a ruler; the weight of a book doesn't change if we put another object on the scale with it). (Lesson 5)
- Measures can be reported to the nearest whole inch, half inch, or quarter inch. (Lesson 6)
Prior Knowledge Needed:
- Measuring length to the nearest whole units; (Grade 2, Unit 2; 2.MD.1)
- Represent whole numbers as equal lengths on a number line; (Grade 2, Unit 3; 2.MD.6)
- Unit fractions result from partitioning a whole; (Grade 3, Unit 4; 3.NF.A.1, 2a)
- Non-unit fractions are made up of unit fractions with the same denominator; (Grade 3, Unit 4; NF.A.1, 2a)
Units on the Horizon:
- Understanding equivalent fractions (Grade 3, Unit 10)
- Comparing fractions (Grade 3, Unit 11)
- Using equivalency to add and subtract fractions with unlike denominators (Grade 4, Unit 3)
Lessons
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Lesson objective: Recognize invariance of fractional distances on a number line. Students bring prior knowledge of invariance of whole numbers on a ruler from 2.MD.D.9. This prior knowledge is extended to invariance of fractions on a number line and rul...
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Lesson objective: Measure fractional lengths on number lines and rulers. This lesson helps to build procedural skill with identifying unit fractions on a number line (and ruler). The partitioning of number lines and rulers is used here to introduce the ...
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Lesson objective: Measure and draw fractional lengths on number lines and rulers. This lesson helps to build procedural skill with identifying unit fractions on a number line (and ruler). The partitioning of number lines and rulers are used here to intr...
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Lesson objective: Relate fractional invariance to a real life scenario. This lesson provides an opportunity for students to apply their knowledge and understanding of the invariance of fractions to a mathematical situation. Students are asked to find st...
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Lesson objective: Measure objects with precision by partitioning into smaller parts. Students bring prior knowledge of measuring fractional lengths on number lines and rulers to wholes, halves, and fourths from 3.MD.B.4. This prior knowledge is extended...
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Lesson objective: Measure lengths on number lines and rulers with precision by partitioning into smaller pieces. This lesson helps to build procedural skill with measuring to the nearest half, fourth and eigth. The re-partitioning of intervals on a rule...
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Lesson objective: Estimate length by measuring objects to the nearest whole, half, or fourth inch. Students bring prior knowledge of measuring with precision to the nearest whole, half, and fourth inch from earlier in this unit. This prior knowledge is ...
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Lesson objective: Measure lengths to the nearest whole, half, or quarter inch. This lesson helps to build procedural skill with measuring to the nearest whole, half, and quarter inch. Rulers are used here because they highlight the idea of measuring to ...
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Lesson objective: Measure lengths and report distances to the nearest whole, half, or quarter. This lesson helps to build procedural skill with measuring to the nearest whole, half, and quarter inch as well as appoximating distances on a number line. Ru...
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Lesson objective: Locate fractions on a number line that is partitioned into a different denominator. This lesson provides an opportunity for students to apply their knowledge and understanding of locating fractions on a number line to a mathematical si...