# Mathematical translations

This lesson develops knowledge of algebraic expressions and their verbal equivalents. Students will establish a foundation for future Algebra I tasks by identifying mathematical symbols and expressions through group work and individual tasks. This lesson contains modifications for the novice high English Language Learner (ELL).

**A lesson plan for grades 6–12 English Language Development and Mathematics**

## Learning outcomes

Students will:

- gain knowledge of the relationship between verbal expressions and mathematical symbols.
- use manipulatives to translate mathematical expressions.
- translate the mathematical expressions into the verbal expressions, and vice versa.

## Teacher planning

### Time required for lesson

1 hour

### Materials/resources

- Soft drink bottle lids OR posterboard cut into two-inch diameter circles with the numbers and math operators written on them.
- Adhesive dots to place on the lids with the digits 0–9 and math operators (+, -, x, =) written on them. Be aware that the letter “x” can be confused with the multiplication operator.
- Permanent markers.
- Transparency of the chart What does it mean?.
- A list of algebraic expressions chosen by the teacher for the students to mathematically translate.
- A copy of the classwork worksheet and homework worksheet for each student.

### Technology resources

Overhead projector (optional)

## Pre-activities

Show the class a chart of the symbols and words for addition, subtraction, multiplication, division, and equality. As a class, ask the students for different synonyms for words on the chart.

The students will complete the chart during the class discussion, and then they can use the chart to help them throughout the lesson and homework assignment.

## Activities

### Part 1: Oral

- Put the students into pairs or groups of three.
- Read an example equation to the class and as a group try to translate the equation using the number disks (bottle lids). Attached to this lesson is a page of examples for the teacher to use.
- After everyone understands the task, read a different expression to the students.
- After reading the expression, have the students show the expression using their group’s manipulatives.
- Have one person from each group raise their hand when the group has an answer and the teacher can check for correctness.
- After a correct answer is found, have all of the groups correct their answer and discuss any questions that might arise.
- Continue giving expressions to the groups until you feel that they have an understanding of the translations.

### Part 2: Written

- Give each student a copy of the classwork worksheet.
- As a class, work through one example from each section. Have the students correct their work and answer any questions that arise.
- Have the students complete the worksheets in their groups. The teacher should walk around and monitor the students’ work.
- Have one student from each group raise their hand when they have completed the worksheets. Check the students’ work and have them correct any mistakes.

### Part 3: Individual Assignment/Homework

Give each student a copy of the homework worksheet. Have the student complete the assignment by themselves and bring it to class the next day.

## Assessment

- Collect the students’ homework worksheet and grade it for accuracy.
- Assessment could also be included on the next chapter test.
- A self-quiz is available at the Glencoe website for students to assess themselves. Two of the five questions in the self-quiz involve mathematical translation.

## Supplemental information

If you are interested in obtaining new bottle lids to make your number disks, they can be purchased from the Smith Container Corporation. It is more cost-effective to order in bulk.

Contact Information for lids #76108: Mandy Woodard, Smith Container Corporation, 1327-A Wood Branch Drive, Charlotte, NC 28273. (704) 588-6770 Ext. 226

### Modifications

- Place an ELL student with a native English speaker who will be beneficial to the ELL student’s learning to work together in a group or place an intermediate or an advance ELL student with a novice student to work together in a group.
- After completing the mathematical expression chart, read the expressions aloud to the student.
- Decrease the number of questions to be answered on the homework assignment but remember to incorporate all the concepts for this lesson.

### Alternative assessments

- On the chapter test give students multiple choice questions or matching questions instead of short answer questions where spelling can be an issue.
- Allow students extended time on the test.
- Give the students an oral section of the test so they can verbally convey the answer instead of having to write the answer.

### Critical vocabulary

- Addition
- Subtraction
- Division
- Multiplication
- Exponents
- Equal
- Translation
- Algebraic expression

### Comments

This lesson plan was developed during the English Language Development Standard Course of Study lesson planning institutes hosted by the North Carolina Department of Public Instruction and LEARN NC, June and July, 2004. It includes specific strategies, instructional modifications, and alternative assessments, which make this lesson accessible to limited English proficient students. Please note that this lesson has been aligned with the goals and objectives of the North Carolina English Language Development standards.

- Common Core State Standards
- Mathematics (2010)
#### Grade 6

- Expressions & Equations
- 6.EE.6Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
- 6.EE.7Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

#### Grade 7

- 7.EE.1Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.
- 7.EE.4Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Solve word problems leading to equations of the form px + q = r and p(x...

- Expressions & Equations
#### High School: Algebra

- Creating Equations
- ALG.CE.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

- Creating Equations

## North Carolina curriculum alignment

### English Language Development (2005)

**Objective 0.03**: Record information on familiar topics and academic areas using graphic organizers.

**Objective 0.05**: Develop basic and academic vocabulary based on familiar topics (e.g., high-frequency words, Dolch words).

**Objective 0.06**: Respond to most questions on familiar academic topics spoken slowly and distinctly, using two-word and three-word responses, gestures, and other non-verbal communication.

**Objective 0.11**: Read and comprehend instructions and directions, common environmental print, and informational text.

**Objective 0.12**: Comprehend basic academic vocabulary through visuals and/or realia (authentic objects).

### Mathematics (2004)

#### Grade 7

**Goal 5**: Algebra - The learner will demonstrate an understanding of linear relations and fundamental algebraic concepts.**Objective 5.02**: Translate among different representations of algebraic expressions, equations and inequalities.

#### Grade 8

**Goal 5**: Algebra - The learner will understand and use linear relations and functions.**Objective 5.01**: Develop an understanding of function.- Translate among verbal, tabular, graphic, and algebraic representations of functions.
- Identify relations and functions as linear or nonlinear.
- Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
- Interpret and compare properties of linear functions from tables, graphs, or equations.

#### Grade 9–12 — Introductory Mathematics

**Goal 4**: Algebra - The learner will understand and use linear relations and functions.**Objective 4.01**: Develop an understanding of function.- Translate among verbal, tabular, graphic, and algebraic representations of functions.
- Identify relations and functions as linear or nonlinear.
- Find, identify, and interpret the slope (rate of change) and intercepts of a linear relation.
- Interpret and compare properties of linear functions from tables, graphs, or equations.