# 8.4: Algebra

- Page ID
- 74327

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## Recommendation 1: Use Solved Problems to Engage Learners

### Discuss Solved Problems and Their Structure

### Pick Problems That Reflect the Lesson Goal

### Questions to lead discussion

### Common issues and solutions

## Recommendation #2: Use the Structure of Equations

### Imprecise vs. precise mathematical language

Imprecise language |
Precise mathematical language |

Take out the x. | |

Move the 5 over. | Subtract 5 from both sides of the equation. |

Use the distributive property. | |

Solve an expression. | |

A is apples. | |

Plug in the 2. | Substitute 2 for x. |

To simplify, flip it and multiply. | To simplify, multiply both sides by the reciprocal. |

To divide a fraction, invert and multiply. | To divide fractions, multiply by the reciprocal. |

Do the opposite to each side. | |

The numbers cancel out. | |

Plug it into the expression. | Evaluate the expression. |

### Use reflexive questioning

### Using diagrams to denote the underlying structure

### Common issues and solutions

## Recommendation #3: Intentionally Choose Specific Strategies

Conventional method | Alternative method |

Question 3a + 9b – 7a + 2b – 8a (if a = 6 and b = 8) | |

Levi’s restaurant bill, including tax, but before tip, was $23.00. If he wanted to leave a 12.5% tip, how much money should he leave in total? | |

10% of $23.00 is $2.30, and one quarter of $2.30 is $0.56, which totals $2.86, so the total bill with tip would be $23.00 + $2.86 or $25.86. | |

Solve for x: 5(x + 1) = 25 | |

Solve for x: 8(x – 5) = 2(x – 5) + 12 | |

Solve for x: 3(x – 5) + 3x + 12 = 2(4x + 1) + 3x + 10 | |