# Start Training

## Visuals

- 10 digits 0-1-2
- One, 1, Uni, Unit, 17 words
- Two, 2, count by
- Count to 20 and back to 0
- Fract - Break - Fraction - 7 words
- 20 exchange - half and fourth
- Fract 20: 1 -2- 5- 10
- 572 Septillion
- 769 Quintillion
- Numbers in the News - COVID-19
- News - $2.2 T $1200 A, $500 C
- 893 P Quadrillions in the News

## Inspiration

A burning desire to climb. Missing limbs? No problem.## Methods

- Math Therapy Overview
- Base-10 - understand through experience
- Describe and reason with language - words and symbols
- Count into easily recognizable patterns
- Model numbers with place value chart and money
- Student teaches others about new discoveries

## Materials

- Language-enhanced Place Value Chart by Dyscalculia.org
- Resource Folder
- China marker (grease pencil) or dry-erase markers in green, blue, purple, black, orange, silver, brown.
- COINS ~ 15 each: dimes, pennies; 6 quarters; 3 fifty-cent pieces; 25 nickels
- Realistic Money Set - 10 each: $1, $2, $5, $10, $20, $50, $100, $500, $1k, $10k,$100k, $500k.
- Camera

## Base Ten

**DIGITS**

- 10 fingers
- 10 digits
- 0-1-2-3-4-5-6-7-8-9

**Place Value Parking Lot **

- 1 digit per spot
- Counting $ in dice patterns of 5.

**Fraction**

- anything that is
,**some**, of the desired amount.**but not all** - $2 out of $5 needed for lunch , is 2/5, two-fifths
- $13 out of $15 needed for a T-shirt is 13/15, thirteen-fifteenths
- $13 out of $50 needed for a fancy sweatshirt, IS 13/50, thirteen-fiftieths
- $12 out of $100 needed for a birthday, is 12/100, twelve-hundredths.
- Fractions mean nothing without context. You always need to say what the fraction means.
- Example: $ dollars, points, cups...

## Sample Lesson

**Count$1 bills** and record digits on place value chart.

When reach 10, *notice that 10 has 2 digits* that *cannot* park in the 0nes' parking space.

Place finger on ones' place and write 1**0**, ending the 1**0** in the ones' place because that's the unit we are recording the amount of (*one* dollar bills).

Note ways to make $10:

- As 10
**ones**. (*1 x 10 = 10*) - Or as 1
**ten**. (*10 x 1 = 10*)

Add 3 more *ones*.

Record 3 in *ones place*.

Notice ways to make $13:

- 13
*ones**(1 x 13 = 13*) - one
*ten*and 3*ones*(*1 x 10 + 3 = 13*)

Trade 10 *ones* for a $10.

Record the number of $10s in the *tens'* parking spot.

Add 3 more $**1**0s to $10, and change the number in the *tens'* place to **4. ***(10 + 30 = 40)*

Add another $10, and change digit in tens' place to 5. (*40 + 10 = 50*)

Trad five $10s for a $50 bill. Notice that $50 is still a 5 in the tens' spot.

**Talk about ways to pay $53. **

- 53
*one*dollar bills - 5
*ten*dollar bills and 3*ones* - a $50 bill and three $1s

Add 2 more tens, and revise digit to 7. (*50 + 20 = 70*)

**Discuss ways to pay $73:**

- 73 one dollar bills
- Seven $10s and three $1s
- One $50, two $10s, three $1s

**Misspeaks:** A student will occasionally say what they do not mean (ex. 700 for 70).

**Guidance ** Tell the student that misspeaking is a common brain glitch that you shouldn't be embarrassed about, *but should anticipate,* so you must double-check and triple-check, to avoid mistakes.

**Always be sure of your unit **(what you're talking about - tens, ones, cups, inches, teaspoons or tablespoons...). Take your time to be sure.

**Update Standard Notation as you work:**

Add 3 more tens and update the chart. Erase the 7 in the tens' place, and put a finger in the tens' place and write 10 tens, ending 1**0** in the tens' spot.

Read: 10 tens, is 1 hundred.(*10 x 10 = 100*)

All together, read number as 103. One hundred three.

Ways to make 103:

- 103 one dollar bills
*(1 x 103)* - 10 ten dollar bills and 3 ones
*(10 x 10 + 1 x 3 = 103)*- one $50 and five $10s and three $1s
*(50 x 1 + 10 x 5 + 1 x 3 = 103)*

- one $50 and five $10s and three $1s
- two $50s and three $1s
*(50 x 2 + 1 x 3 = 103)* - 1 hundred bill and three $1s
*(100 x 1 + 1 x 3 = 103)*

Add one more ten and read, 113. One thirteen. One hundred and thirteen. *(103 + 10 = 113)*

**Ways to make $113:**

(1) 113 ones $1s *(1 x 113 = 113)*

(2) 1 hundred, 1 ten, three $1s* (100 + 10 + 1 x 3 = 113)*

(3) two $50s, one $10, three $1s *(50 x 2 + 10 + 1 x 3 = 113) *

(4) eleven $10s, three $1s *(10 x 11 + 1 x 3 = 113)*

**Teach 4 people** and make up a story.

**Birthday Money - A story to practice adding using the PV chart.**

"**I** opened one birthday card and it had five $1s in it, so I write the digit 5 in the one's parking place. **T**hen I opened another card and it had six $1s inside, so all together, I have eleven $1s, so I erase the 5 and record 11 ones, which is the same as 1 ten and 1 one. **T**hen, the next card I opened, had a $10 inside. So I now erase the 1, and put a 2 in the ten's spot. I have $21 so far. **T**he next card, from Grandma, had a $50 in it - that is 5 more tens. 2 + 5 tens is 7 tens. I erase the 2 and write 7 in the tens' parking spot. That's $71, all together. **N**ext, I open a card from my Grandpa and it contains a $50 and a $20. That's $70 more. So, I have to erase the 7 in the tens' spot, and write 7 + 7 = 14 tens, so I write 14 in the tens place and read the number (141) as, "one hundred forty-one dollars. **I** will deposit it in the bank. **W**hen I withdraw it, I can tell them not to give me one hundred and forty-one ones, or 14 tens and one $1. I'm telling them I want two $50s and two $20s and a $1."

**Film: **Take a video of the student teaching how to count and record using the place value chart, money, patterns, digits, and different ways to say and make the same amount.

**Independence:** Encourage the student to explain what they see and do. Wean students from looking to others for prompting and answers. Give students time to formulate their thoughts and explain what to do and why.

**Experience makes confidence!**

## Fluency

**Use Numbers in the News to Build Math Fluency**

- identify the UNIT
- identify the key numbers
- encode the number on the place value chart
- write the number in standard notation
- write it with the digits and place: ex. 3 hundred
- words spoken
- words written
- model with money
- expanded notation
- International System prefix
- SI symbol
- power of ten (scientific notation)
- prime factorization

## Scope & Sequence I

You are going to play with money to become fluent in the language of mathematics. The more ways you can explain an idea, the more fluent you are in the language.

Throughout the exercises, you are going to be using many different ways to SHOW and DESCRIBE and WRITE about what you have done.

*The student is learning skip counting, fact families, multiplication facts, addition facts, number composition and decomposition, standard notation, equations, basic operations, patterns, relationships, visual-spatial and verbal reasoning, unit conversion, equivalency, and the language of mathematics - verbal, operational, and symbolic.*

Start with $1 bills.

Count them out into patterns of 5 in a serial fashion, "1, 2, 3, 4, 5..."

Stop and record the amount counted on the place value chart in the ONES PLACE.

Now, write what you just did in SYMBOLIC FORM on the board:

1 + 1 + 1 + 1 + 1 = 5

### 1 x 5 = 5

### 5 x 1 = 5

Keep counting $1s until you reach 9.

Stop and write the 9 in the ONE's COLUMN of the place value chart.

Update the equations on the board:

** 1** + **1** + 1 + 1 + **1** + **1** + 1 + 1 + **1** = **9**

5 + 4 = 9

### 1 x 9 = 9

### 1 x 5 + 1 x 4 = 9

### 9 ÷ 1 = 9

Now add a tenth $1 so you have 2 complete sets of 5 on the table.

How will you update the chart to show that you have 10 ones, if you can only place * 1 digit* in a place value parking space?

You put your finger on the Ones' Place and write the number 10, so that the number 1**0** *ends* in the Ones' Place.

Now describe what you have:

I have 1 set of 10.

I have 10 ONES.

I can trade my ten ONES in for a $10. and then I have 1 TEN and 0 ONES.

Now update the equations:

1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 10

### 1 x 10 = 10

5 + 5 = 10

### 5 x 2 = 10

### 10 ÷ 1 = 10

### 10 ÷ 2 = 5

3 + 2 + 3 + 2 = 10

### 3 x 2 + 2 x 2 = 10

4 + 1 + 4 + 1 = 10

### 4 x 2 + 1 x 2 = 10

### Count-by Sequence:

$**1**; $**2**; $**3** ($2+$1); $**4** ($2+$2); $**5**; $**6** ($5+$1); $**7 **($5+$2); $**8** ($5+$2+; $1); $**9** ($5+$2+$2); $**10**; $**11** ($10+$1); $**12** ($10+$2);* $ 13 ($10+$2+$1); $14 ($10+$2+$2)*; $

**15**($10+$5);

*$*; $

**16**($10+$5+$1); $**17**($10+$5+$2); $**18**($10+$5+$2+$1); $**19**($10+$5+$2+$2)**20**; $

**25**($20+$5);

*$*$

**30**($20+$10); $**35**($20+$10+$5);**50**; $100; $

**150**($100+$50); $

**1,000**; $

**10,000**; $

**100,000**; $

**500,000**; $

**1M**; $

**10M**; $

**100M**; $

**1G**; $

**10G**; $

**100G**; $

**1T**; $

**10T**; $

**100T**; $

**1P**; $

**10P**; $

**100P**