1 of 69

Scaffolding EngageNY Mathematics for English Learners

Anita Bright, Ph.D.

Portland State University

Portland, Oregon

February 4, 2014

2 of 69

Our Agenda

Looking at a lesson
A few quick ways to scaffold INSTRUCTION
Questions?

Visit http://goo.gl/Visit http://goo.gl/Ua0fcf to access the electronic version of this document.

abright@pdx.edu

3 of 69

Let’s look at part of a lesson.

What do you notice that might be problematic for English learners?

What might you do to modify this lesson?

http://goo.gl/ http://goo.gl/Ua0fcf

abright@pdx.edu

4 of 69

Grade 6, Module 5, Lesson 11: � Volume with Fractional Edge Lengths and Unit Cubes

abright@pdx.edu

5 of 69

abright@pdx.edu

6 of 69

abright@pdx.edu

7 of 69

How many 1 in x 1 in x 1 in cubes will fit in the following prism?

Have students discuss their solution with a partner.

How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism?

How did you determine this number?

abright@pdx.edu

8 of 69

How many layers of 1 in by 1 in by 1 in cubes would fit inside the prism?
If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box?
How did you determine this number?
How is the number of cubes or dice related to the volume?
What other ways can you determine the volume of a rectangular prism?

abright@pdx.edu

9 of 69

Example 1 (5 minutes)

The same package in the opening exercise will be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box?

How many cubes could we fit across the length? The width? The height?

abright@pdx.edu

10 of 69

Now let’s look at how to improve it…

abright@pdx.edu

11 of 69

How many 1 in x 1 in x 1 in cubes will fit in the following prism?

Have students discuss their solution with a partner.

How many 1 in x 1 in x 1 in cubes would fit across the bottom of the rectangular prism?

How did you determine this number?

abright@pdx.edu

12 of 69

How many layers of 1 in x 1 in x 1 in cubes would fit inside the prism?
If each cube represents dice that need to be shipped, how many 1 in x 1 in x 1 in dice will fit in the box?
How did you determine this number?
How is the number of cubes or dice related to the volume?
What other ways can you determine the volume of a rectangular prism?

abright@pdx.edu

13 of 69

Example 1 (5 minutes)

The same package in the opening exercise will be used to ship miniature dice whose side lengths have been cut in half. The dice are ½ in x ½ in x ½ in cubes. How many dice of this size can fit in the box?

How many cubes could we fit across the length? The width? The height?

abright@pdx.edu

14 of 69

Let’s look at another example.

abright@pdx.edu

15 of 69

3. A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in.

a. How many small toys can be packed into the larger box for shipping?

abright@pdx.edu

16 of 69

Here’s a re-wording:

Original

A toy company is packaging its toys to be shipped. Some of the very small toys are placed inside a cube shaped box with side lengths of ½ in. These smaller boxes are then packed into a shipping box with dimensions of 12 in x 4 ½ in x 3 ½ in.

How many small toys can be packed into the larger box for shipping?

Scaffolded

A toy company puts small toys into boxes. The boxes are cubes with side length of ½ in.

These small boxes are put inside a bigger box with dimensions of 12 in. x 4 ½ in. x 3 ½ in.

How many toys can be put into the larger box?

abright@pdx.edu

17 of 69

Another note on this lesson

Words are used interchangeably:

Long/ length
High/ height (and sometimes deep/ depth)
Width/ wide

Some words are have multiple meanings (like volume).

These relationships between these words need to be taught!

abright@pdx.edu

18 of 69

How can teachers scaffold this curriculum?

abright@pdx.edu

19 of 69

Three* big ideas:

Reduce language load (to increase accessibility).

Use graphic organizers (to help students focus on the big ideas).

Provide support for speaking and writing (to enrich their academic register).

*More big ideas at the end!

abright@pdx.edu

20 of 69

Reduce the language load

Text is written in present tense and may be redundant for clarity.

Sentences are short with no or few clauses. (These may read awkwardly to fluent speakers of English.)

New sentences begin on a new line.

abright@pdx.edu

21 of 69

Contexts are familiar to students in school.

Names chosen for examples are simple and phonetic and should not be similar to content (including names like Ray and Mark).

Pictures/ visuals/ illustrations are used to make content clearer.

abright@pdx.edu

22 of 69

Words with multiple meanings that might be confusing are not used (ie, a garden plot and the request to plot points on a coordinate plane).

Language is internally consistent (if practice problems ask students to solve, the assessments should use the same term). If language is not internally consistent, then different terms are highlighted and taught (add, plus, sum, combine, all mean the same thing).

abright@pdx.edu

23 of 69

A Standard Example (Lesson 8.1, p. 12)

Suppose a colony of bacteria doubles in size every 8 hours for a few days under tight laboratory conditions. If the initial size is 𝐵, what is the size of the colony after 2 days?

�

A Modified Example

A group of objects doubles every 8 hours.

Today there are B objects in the group.

How many objects are in the group after 2 days?

(There are 24 hours in one day.)

abright@pdx.edu

24 of 69

A Standard Example (Lesson 8.1, p. 12)

A rectangular area of land is being sold off in smaller pieces. The total area of the land is 𝟐^𝟏𝟓 square miles. The pieces being sold are 𝟖^𝟑square miles in size. How many smaller pieces of land can be sold at the stated size? Compute the actual number of pieces.

�

Modified Example

Kim has a farm in the shape of a rectangle.

The area of Kim’s farm is 𝟐^𝟏𝟓 square miles.

Kim divides her farm into pieces that are each 𝟖^𝟑square miles in size.

How many pieces does Kim make?

abright@pdx.edu

25 of 69

Provide side-by-side texts.

Look at how useful this is! (Google translate will even provide a read-aloud.)

(Note: This is best for students who are already highly LITERATE in their first language. Do not assume this is the case with all students.)

abright@pdx.edu

26 of 69

abright@pdx.edu

27 of 69

Provide step-by-step instructions in student-friendly language & use visuals.

From a lesson on translating one-step word problems to algebraic equations.

Directions:�a) Define a variable for each problem.

b) Write an equation to represent the information.

c) Be sure the equation requires the use of one inverse operation to find the solution!

d) Show a check for each solution.

abright@pdx.edu

28 of 69

abright@pdx.edu

29 of 69

2. Provide graphic organizers.

Non-verbal displays of relationships
A way to visually organize thinking

abright@pdx.edu

30 of 69

abright@pdx.edu

31 of 69

abright@pdx.edu

32 of 69

Similarities and differences

abright@pdx.edu

33 of 69

Graphic organizer

abright@pdx.edu

34 of 69

Frayer model

abright@pdx.edu

35 of 69

Foldables

These don’t have to be from a template. Anything can work!

abright@pdx.edu

36 of 69

Have students identify similarities and differences.

Venn diagrams
T-charts

abright@pdx.edu

37 of 69

Similarities and Differences

abright@pdx.edu

Concept: Conic Sections

parabola

hyperbola

circle

ellipse

38 of 69

Similarities and Differences

abright@pdx.edu

Concept: ____________

39 of 69

Similarities and Differences�

abright@pdx.edu

Concept: Which does not

belong?

(Can you think of another term that would fit?)

acute

parallel

obtuse

right

40 of 69

3. Provide support for speaking and writing

Each day needs structured opportunities for students to speak and write in English.

abright@pdx.edu

41 of 69

Give concrete guidelines for speaking, reading, writing or listening.

“Turn to your neighbor and explain…”

Write the day’s objective on the board and have students read it along with you. Point to each word as you read aloud.

Provide sentence frames for anyone who may benefit.

(“I know the area of parallelogram B is larger/ smaller ______ than the area of parallelogram A because _____.”)

(More advanced students might be ready for some transition language like this: http://writing2.richmond.edu/writing/wweb/trans1.http://writing2.richmond.edu/writing/wweb/trans1.html)

abright@pdx.edu

42 of 69

Sentence frames (perhaps with word banks) can support student explanations.

Visit this link for some elementary examples from Justin Johnson.

See also page 24 of this fabulous document from Kate Kinsella.

abright@pdx.edu

43 of 69

“The volume of my prism is ___units cubed. I found this by ______.
“My idea is similar to _____’s because ____.”

abright@pdx.edu

44 of 69

“I know the answer is a fraction because_____”

Word bank:

Added

Less than one

Combined

Whole number

Equal

abright@pdx.edu

45 of 69

Have students chorally repeat key vocabulary or phrases.

Have students chorally repeat the key term in creative ways.
(“The word is pronounced hypotenuse. Again, hypotenuse. Repeat after me: hypotenuse. Whisper it: hypotenuse. This side of the room only: hypotenuse. Everyone wearing jeans, hypotenuse.” )
Why? It lowers the affective filter since there are multiple voices speaking at once. It promotes fluency. It provides and accurate auditory imprint.

abright@pdx.edu

46 of 69

Be direct about language.

EXAMPLE OBJECTIVE FOR A LESSON: �
Identify perfect squares; determine square roots.

Discuss the word square. Ask students to describe what a square is: a shape with 4 equal sides and 4 right angles. Have students point out objects in the room that are squares.
Introduce expressions with the word square that students will use in this lesson – square number, perfect square, squared, square root.
Explain to students that the word square can be a noun or a verb. In the expression “the square of a number…”, square is a noun. In the expression “if we square the number…”, square is a verb.
Tell students that we will be using the word root in the mathematical expression square root. Ask students if they know any other uses of the word root (roots of trees or plants, family roots). Point out to students that in these cases, the word root relates to the beginning or foundation for something.

abright@pdx.edu

47 of 69

Use online resources for key vocabulary.

How about a cool dictionary?

Or what about Google translate?

abright@pdx.edu

48 of 69

Provide word banks.

These can provide appropriate and relevant vocabulary to use in speaking or writing about the content.
Adjacent

Complementary

Congruent

Equal

Supplementary

Vertical

abright@pdx.edu

49 of 69

Other rich ideas

abright@pdx.edu

50 of 69

Use manipulatives!

The more concrete and visual these ideas can be, the better!

Remember this thing? Use something from the classroom instead!

abright@pdx.edu

51 of 69

Connect to the real lives of students. Use concrete examples whenever possible.

Example: The same shape can have multiple names.
This is a picture of Dalia. She is:

A sister
A student
A cousin
A daughter
An accountant
A friend
A driver
A winner

All at the same time!
In the same way, this slide can be seen as a closed figure, a parallelogram, a rectangle, a polygon…

abright@pdx.edu

52 of 69

Show finished examples and provide a rubric for self-evaluation.

___ x 3 = ___

What factor can you use in this equation to make a product that is even and between 10 and 40? Show all possible solutions. Explain your strategy.

abright@pdx.edu

53 of 69

Name and notice

Look at this mathematical writing

Identify what qualities make this mathematical writing strong.

The Necessity of Language Instruction in Mathematics; Angela Alcantar, Sunshine Price, and Michelle Stroup English Language Acquisition Specialists, Salem-Keizer Public Schools. 2013.

abright@pdx.edu

54 of 69

abright@pdx.edu

55 of 69

Use quick, formative assessment to establish background knowledge

Teaching students how to find the mean and median? What do they need to know?
They must FIRST know how to:

Count
Put numbers in order from smallest to largest
Add
Divide

abright@pdx.edu

56 of 69

Incorporate interactive games.

These can explicitly include scripted speech.

“When I substitute 8 for the variable c, my equation is equal to 3.

abright@pdx.edu

57 of 69

Replace obscure words or contexts with things from a high-frequency word list.

Students learn English beginning with HIGH FREQUENCY words. Here’s one example of a list.

Try to choose SCHOOL contexts.

abright@pdx.edu

58 of 69

Allow students to show what they know in different ways.

abright@pdx.edu

59 of 69

CCSS.Math.Practice.MP4 Model with mathematics

In each of the 16 houses in the neighborhood, there were 2 dogs.

How many dogs total lived in the neighborhood?

Say it with pictures.

Say it with numbers.

Say it with words.

abright@pdx.edu

60 of 69

Say it with pictures.

abright@pdx.edu

@@

61 of 69

Say it with numbers.

how many dogs how many houses

2 x 16 = 32

Total number of dogs

62 of 69

Say it with words.

There were two dogs at each house and 16 houses so I counted by 2’s sixteen times. I used my fingers to help me keep track.

The Necessity of Language Instruction in Mathematics; Angela Alcantar, Sunshine Price, and Michelle Stroup English Language Acquisition Specialists, Salem-Keizer Public Schools. 2013.

abright@pdx.edu

63 of 69

Final things to keep in mind

abright@pdx.edu

64 of 69

Mathematics is not a universal language

MUCH of what we share with students is embedded in language that is specific.

Example: Think of the similarities and differences between the words OF and OFF.

Example: Hypotenuse is the longest side of a right triangle. EVERYONE learns the word hypotenuse; ELs need to learn the word LONGEST.

abright@pdx.edu

65 of 69

Fractions may be �especially challenging

The METRIC SYSTEM is used in pretty much the entire rest of the world.

abright@pdx.edu

66 of 69

We can’t assume literacy in L1.

Not all students have had access to ongoing formal education.

Students may have yet-undiagnosed learning differences.

abright@pdx.edu

67 of 69

Students learn casual language before academic language.

This means they may sound comfortable and fluent, but may need additional support in their writing and speaking in an academic register.

abright@pdx.edu

68 of 69

Communicating in a new language can be very stressful.

Above everything else, we need to prioritize the health and well-being of our students by ensuring our classrooms are safe and welcoming.

(Humiliation is not a desired instructional strategy.)

abright@pdx.edu

69 of 69

Thanks for your time!

http://goo.gl/Ua0fcf