ILLINOIS TEACH & TALK

Continue to build on students’ understanding and application of writing and solving one-step equations from a problem situation to multi-step problem situations. This is also the context for students to practice using rational numbers including: integers, and positive and negative fractions and decimals.

As students analyze a situation, they need to identify what operation should be completed first, then the values for that computation. Each set of the needed operation and values is determined in order. Finally an equation matching the order of operations is written. For example, Bonnie goes out to eat and buys a meal that costs $12.50 that includes a tax of $.75. She only wants to leave a tip based on the cost of the food. In this situation, students need to realize that the tax must be subtracted from the total cost before being multiplied by the percent of tip and then added back to obtain the final cost. C = (12.50 - .75)(1 + T) + .75 = 11.75(1 +T) + .75 where C = cost and T = tip.

Provide multiple opportunities for students to work with multi-step problem situations that have multiple solutions and therefore can be represented by an inequality. Students need to be aware that values can satisfy an inequality but not be appropriate for the situation, therefore limiting the solutions for that particular problem.

Explanations and Examples

7.EE.3  Students solve contextual problems using rational numbers. Students convert between fractions, decimals, and percents as needed to solve the problem. Students use estimation to justify the reasonableness of answers.

Estimation strategies for calculations with fractions and decimals extend from students’ work with whole number operations. Estimation strategies include, but are not limited to:

• front-end estimation with adjusting (using the highest place value and estimating from the front end making adjustments to the estimate by taking into account the remaining amounts),

• clustering around an average (when the values are close together an average value is selected and multiplied by the number of values to determine an estimate),

• rounding and adjusting (students round down or round up and then adjust their estimate depending on how much the rounding affected the original values),

• using friendly or compatible numbers such as factors (students seek to fit numbers together  - i.e., rounding to factors and grouping numbers together that have round sums like 100 or 1000), and

• using benchmark numbers that are easy to compute (student’s select close whole numbers for fractions or decimals to determine an estimate).