Solving One-Step Inequalities

Explicit Instruction/Teacher modeling

• Write this one-step inequality on the whiteboard:X +3≥11. Ask students to point out what distinguishes inequalities from equations (students should note that equations use equal signs and inequalities use symbols like ≥ , ≤, >, and <).
• State that solving one-step inequalities is similar to solving one-step equations since you can use inverse operations to isolate the variable in both. Note that there are some key differences when solving one-step inequalities, and you will point these out using a few examples.
• 返回您在白板上写的一步添加不等式（x +3≥11）。询问学生如何使用反操作来解决此问题（学生应该说他们将从不平等的两侧减去3）。在白板上显示此步骤，以获取不等式的解决方案（x≥8）。
• 提醒学生，您可以在数字行上将解决方案设置为此不等式。在白板上，在中心写下一个数字线。提醒学生查看不等式符号以确定如何绘制不等式（对于x≥8，您应该在8上添加一个封闭的圆圈，并在数字行上的8个右侧遮荫）。
• 在董事会上写下此一步减法不平等：y − 5 < −1. Have students discuss how to solve this inequality with a partner. Actively monitor student discussions. Then call one student up to the whiteboard to correctly solve this inequality. With the class, talk through how you would graph the solution (y < 4) on a number line (add an open circle on 4 and shade everything to the left of 4).
• Write this one-step multiplication inequality on the board:−3n ≤ 18. Ask students how they would solve this inequality using inverse operations (divide both sides of the inequality by −3). Tell students that any time you divide a multiplication or division inequality by a negative number, you need to flip the inequality sign. So, for this example, the solution is n ≥ −6.
• 简要说明为什么在乘以或除以负数时将不平等标志翻转。让学生考虑示例x> 3.向学生询问一种解决这种不平等的解决方案（例如4> 3）。告诉学生，如果您将不平等的两面乘以-1，则不平等将不再是正确的（-4不大于-3）。因此，您需要翻转不平等标志，以使不平等现实。更一般而言，任何大数量都会使x> 3和-x <-3 true。
• Write this one-step division inequality on the board:g÷2> -10. Ask students how they would solve this inequality using inverse operations (multiply both sides of the inequality by 2). Point out that since you’re not dividing by a negative number in this example, you don’t need to flip the inequality sign. So, the solution is g > −20.

Guided Practice

• 向学生分发解决一步不平等的工作表。
• Instruct students to read through the examples on the worksheet as a refresher before they begin working on the practice problems.
• 让每个学生与伴侣一起工作以完成练习问题。鼓励学生在解决和绘制不平等现象时与伴侣进行措施。

Independent working time

• Have students play the Treasure Diving: One-Step Addition and Subtraction Inequalities game and the Treasure Diving: One-Step Multiplication and Division Inequalities game. Students should complete these games independently using a computer (or tablet).