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Elden [556K]
3 years ago
8

Dear Garden Designer,

Mathematics
1 answer:
guapka [62]3 years ago
7 0

Answer:

Step-by-step explanation:MATHEMATICAL GOALS

This lesson unit is intended to help assess how well students are able to interpret and use scale

drawings to plan a garden layout. This involves using proportional reasoning and metric units.

COMMON CORE STATE STANDARDS

This lesson relates to the following Standards for Mathematical Practices in the Common Core State

Standards for Mathematics, with a particular emphasis on Practices 1, 3, 4, 5, and 6:

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

8. Look for and express regularity in repeated reasoning.

This lesson gives students the opportunity to apply their knowledge of the following Standards for

Mathematical Content in the Common Core State Standards for Mathematics:

7.G: Draw, construct, and describe geometrical figures and describe the relationships between

them.

Solve real-life and mathematical problems involving angle measure, area, surface area,

and volume.

7.EE: Solve real-life and mathematical problems using numerical and algebraic expressions and

equations.

7.RP: Analyze proportional relationships and use them to solve real-world and mathematical

problems.

INTRODUCTION

This lesson unit is structured in the following way:

• Before the lesson, students work individually on a task designed to reveal their current levels of

understanding. You review their responses and create questions to help them improve their work.

• At the start of the lesson, students reflect on their individual responses, before producing a

collaborative improved solution to the task. Then, in the same small groups students analyze

sample responses. They then discuss as a whole-class the methods they have seen and used.

• In a follow-up lesson, students reflect on their work. If time allows, an extension task is available.

MATERIALS REQUIRED

• Each student will need a copy of Design a Garden and Garden Plan, some blank paper, a miniwhiteboard, pen, and eraser, and the How Did You Work? questionnaire. The Garden Plan should

be copied at exactly 100% scale so the measurements are accurate. If this is not possible,

photocopy the rules on S-3, one rule per student, which should then match the Garden Plan

measurements. It will be useful to have spare copies of the Garden Plan.

• Each small group of students will need a new copy of the Garden Plan, the Assistants’ Methods, a

glue stick, felt-tipped pen, and a sheet of poster paper. For the optional extension Mandy’s Second

Email will be needed. Provide short rules, meter rules, string, protractors, scissors, glue, card,

plain paper, graph paper, and colored pencils for students who choose to use them.

TIME NEEDED

20 minutes before the lesson, a 110-minute lesson (or two 60-minute lessons), and 10 minutes in a

follow-up lesson. Actual timings will depend on the needs of your students.

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One number is 6 more than a second number, the sum of the two numbers is 330. what are the numbers?
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Let's have the first number, the larger number, be <em>x</em>.  We'll have the second, smaller number be <em>y</em>.

We know that x = y + 6, since x is 6 greater than y.

We also know that 330 = x + y.

Because x = y + 6, 330 = y + 6 + y, which simplifies to 330 = 2y + 6.

Now all we need to do is simplify the equation.  First, we subtract 6 from both sides:

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So we have 324 = 2y.  Then we divide both sides by 2 to get:

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Plug in y = 162 into the equation x = y + 6 to get:

x = 162 + 6

x = 168

Let's check to make sure our answer is right.  168 is 6 more than 162.  162 + 168 equals 330.  So our two numbers are 168 and 162.

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