During this unit, students will focus on problem solving in order to demonstrate fluency with addition and subtraction to 1000 and demonstrate fluency for multiplication and division within 100. Students will solve problems involving measurement and estimation of liquid volumes, and masses of objects. In addition, students will represent data using picture graphs and bar graphs and interpret the data to solve problems. In Grade 3 students draw picture graphs in which each picture represents more than one object, and they draw bar graphs in which the height of a given bar in tick marks must be multiplied by the scale factor in order to yield the number of objects in the given category.
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Students need to:
- Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
- Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with measurement scale) to represent the problem. (This unit extends students work in Unit 2 to include multiplication and division to solve problems involving measurement quantities). Note: Students are NOT responsible for doing conversions. However, the comparison between ml and l / g and kg may help students “reason” about volumes and masses.
- Fluently add and subtract within 1000 using strategies and algorithms based on the following: place value, properties of operations or the relationship between addition and subtraction. Note: A range of algorithms may be used.
- Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 x 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products of two one-digit numbers.
- Solve two-step problems involving the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.