**learning skilLS**

Visual Memory

Sustained Attention

Emotional Control

**instructional strategy**

**Memory Math Game**

Use memory math games to teach mental math skills

_________

**LEARNING PREFERENCE**S

**academic skill**

**Grade 4 – 6**

Use mental math strategies to multiply and divide whole numbers by 10 and 100, 0.1 and .01 an calculate percentages of 1%, 5%, 10%, 15%, 25%, 50%

Grade | Curriculum Focus | |||||

4 | Use mental math strategies to multiply whole numbers by 10, 100, and 1000 | |||||

4 | Use mental math strategies to divide whole numbers by 10 and 100. | |||||

5 | Use mental math to multiply whole numbers by 0.1 and 0.01 and estimate sums and differences of decimal numbers up to hundredthsdescription | |||||

6 | Use mental to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50% |

## Lesson Objective, Goal and Success Criteria

- Learn how to multiply whole numbers by 10, 100, 1000, 0.1 and 0.01 using mental math strategies.
- Learn how to divide whole numbers accurately, by 10 and 100, using mental math strategies.
- Acquire a deeper understanding about speed not necessarily being the goal when using mental math. The value is in portability, flexibility, and deeper understanding.
- Learn how to calculate percentages of 1%, 5%, 10%, 15%, 25%, 50% using mental math

Understand and apply mental math strategies consistently and accurately when multiplying and dividing whole numbers by 10 and 100.
Understand and apply mental math strategies when calculating percentages of 1%, 5%, 10%, 15%, 25%, 50%

- Correctly and consistently solve problems involving multiplying numbers by 10, 100, 1000, 0.1 and 0.01, dividing numbers by 10 and 100 and calculating percentage of 1%, 5%, 10%, 15%, 25%, 50%
- Explain which strategies were used to obtain the final answer.

## UDL Instruction

1.The students are assembled in groups of 3 or 4 (teacher chosen groups, or student chosen, depending on need and class dynamics). Each group is seated at a separate table and given a calculator, a sheet of questions (small group questions worksheet) and a package of 10-20 sticky notes to be shared among the group.
2. The teacher gives a quick review of the concept being taught.

3.The student groups then solve the small group questions of each concept (in supplementary worksheets) using a calculator. The group is trying to identify patterns in the answers or strategies they can use to solve these problems when they don’t have a calculator. The groups write as many patterns as they can think of using one sticky note for each strategy. The goal is to come up with as many strategies as possible within each group. Each group member has a different role for each question (uses calculator, records answer on worksheet, writes pattern on sticky notes) and these roles should be rotated after every 1 or 2 questions so everyone has a chance to participate in a different role.
4. Each group then places their sticky notes on a board at the front of the class. In a large class group discussion, the students share some of their answers and their strategies and observations (ie. number of spots moved for 10s and 100s, answers are always smaller or larger numbers than what you started etc).
The teacher guides students to find similar patterns discovered among each group and then as a group come up with a short description of each concept to write on the board.

Multiplication of whole numbers by 10, 100, 100: What “multiplication/multiplying” means, and which calculator symbol represents multiplication? What are whole numbers and decimals? |

Dividing whole numbers by 10 and 100: What “division/dividing” means, and which calculator symbol represents division? What are whole numbers and decimals? |

Multiply whole numbers by 0.1 and 0.01: What “multiplication/multiplying” means, and which calculator symbol represents multiplication? What are whole numbers and decimals? |

Calculating percentages of 1%, 5%, 10%, 15%, 25%, 50% What “percentage” means, and which calculator symbol represents percentage? What are whole numbers and percentages? |

**Sample Definition of Concepts:**

**Multiplying by 10-**add one zero to end of the number**Multiplying by 100-**add two zeros to the end of the number**Multiplying by 1000-**add three zeros to the end of the number**Dividing by 10-**the decimal moves left one spot**Dividing by 100-**the decimal moves left two spots.**Multiplying by 0.1-**the decimal moves left one spot**Multiplying by 0.01-**the decimal moves left two spots**Calculating percentages by 5%-**calculate 10% first then divide number in half**Calculate percentages by 15%-**calculate 10% first then 5% and add together totals**Calculate percentages by 25%-**divide number by 4

## Differentiated Instruction

The students return to their initial groups to play a game of

On the remaining 3 blank squares, use mental math only (no calculators), to compute the problems below:

**Two Truths and a Lie concentration.**Each student in each group gets 6 pre-cut blank square papers (see supplemental materials) so if there are 3 people in the group, then the group should have 18 squares all together. Each student completes the following steps (which are written on the board and also repeated out loud by the teacher) one step at a time:**Multiplying by 10, 100 or 1000:**

- On the first 3 squares, write one whole number from 10 up to 99,999 on each square. 3 of the 6 squares should have only one number each on them.

**Example:**35 | 6481 | 459 |

Multiplying by 10, 100 and 1000Square #1: Multiply by 10 or 100 and put answer on the square- this will be the first truthSquare #2: Multiply by 100 or 1000 and put answer on the square- this will be the second truthSquare #3: First multiply by 1000 and then add 1 or 2 more zeros. Your answer will NOT be multiplied by 10, 100 or 1000 so it will be a wrong answer- it will be the lie. |

**Example of completed 6 squares:**35 | 6481 | 459 |

Truth (multiply by 10) 350 | Truth (multiply by 1000) 6,481,000 | Lie (not multiplied by 10, 100, 1000) 4,590,000 |

**Dividing by 10 and 100:**

- On the first 3 squares, write one whole number from 10 up to 99,999 on each square. 3 of the 6 squares should have only one number each on them.

**Example:**35 | 6481 | 459 |

Dividing by 10 and 100Square #1: Divide by 10 and put answer on the square- this will be the first truthSquare #2: Divide by 100 or 1000 and put answer on the square- this will be the second truthSquare #3: Move the decimal 3 places to the left. Your answer will NOT be divided by 10 or 100 so it will be a wrong answer- it will be the lie. |

**Example of completed 6 squares:**35 | 6481 | 459 |

Truth (divided by 100) .35 | Truth (divided by 10) 648.1 | Lie (not divided by 10 or 100) .459 |

**Multiplying by 0.1 and 0.01:**

- On the first 3 squares, write one whole number from 10 up to 99,999 on each square. 3 of the 6 squares should have only one number each on them.

**Example:**35 | 6481 | 459 |

Multiplying by 0.1 and 0.01Square #1: Multiply by 0.1 and put answer on the square- this will be the first truthSquare #2: Multiply by 0.01and put answer on the square- this will be the second truthSquare #3: Move the decimal 3 places to the left. Your answer will NOT be multiplied by 0.1 or 0.01, so it will be a wrong answer- it will be the lie |

**Example of completed 6 squares:**35 | 6481 | 459 |

Truth (multiply by 0.1) 3.5 | Truth (multiply by 0.01) 64.81 | Lie (not multiplied by 0.1 or 0.01) .459 |

**Calculating percentages by 5%, 15%, 25%, 50%**

**Example:**40 | 6400 | 480 |

Calculating percentages by 5%, 15%, 25%, 50%Square #1: Multiply by 5% or 15% and put answer on the square- this will be the first truthSquare #2: Multiply by 25% or 50% and put answer on the square- this will be the second truthSquare #3: Multiply by 20% (sum of 10% + 10%). Your answer will NOT be multiplied 5%, 15%, 25% or 50% so it will be a wrong answer- it will be the lie |

**Example of completed 6 squares:**40 | 6400 | 480 |

Truth (multiply by 15%) 6 | Truth (multiply by 25%) 1600 | Lie (not multiplied by 5%,15%,25%,50%) 960 |

**Teacher Tip:**The teacher should circulate and support as needed students who are really struggling. It is okay if students get more than one answer incorrect (or have more than one lie) as the solutions will be discussed at the end. Students may also need clarification that they are writing three numbers and then one answer for each number on a separate square. The group members place all squares face down and mix them up well.The groups or the teacher can decide the group’s playing order. The group then plays a “concentration/matching game”, where each student in the group takes a turn in order trying to match the whole number squares with their matching correct response squares.- Multiplied by 10, 100, or 1000
- Divided by 10 or 100
- Multiplied by 0.1 or 0.01
- Multiplied by 5%, 15%, 25% or 50%

## Measurement of Success

**Small Group Activity:**

- Each group puts away the remaining unmatched squares. Then each student in each group with the most number of matched squares turns their squares face up with the matched numbers laying beside each other.
- Each group of students now move to the table on their left. They review the matched squares facing up on the table which belong to the student with the most matches. If they see any matches that are incorrect, they put a stroke through both squares of the match. The teacher checks each table to ensure the crossed off squares are really incorrect answers.
- The student from all the groups who has the most matched squares (excluding those squares which are crossed off as incorrect) is the winner of the full class activity.

**Full Class Discussion:**The class comes together as a group. The teacher collects any matched squares that were marked off as incorrect (if any) and asks the class to explain why these matches are incorrect. Common errors may be missing zeroes, moving the decimal too far, or in the wrong direction.

**Individual Activity:**The teacher then passes out to each student a set of 10 questions (in supplementary material) from the individual activity for the students to complete a short timed activity. The set of questions can be handed out based on ability and grade level. Students will have 1 minute to answer the questions as quickly as possible. To minimize any anxiety for this timed activity, encourage students to try their best and let them know they may not have time to finish all the questions and that is okay. These sheets can be collected by the teacher to review at a later time to determine the student’s current ability level.The amount of questions answered correctly will be a strong indicator of success, since the activity was timed. The “strict timing” will encourage using mental math, or even “guessing”, rather than “working out the answer the long way”. With class goals and class composition/student needs, the teacher may underemphasize (or even eliminate) the time goal. Consistent error patterns may emerge (moving the decimal too far, or not far enough, adding zeroes, etc).

## Materials, References and Resources

**Calculators-**resources already in classroom

**Pre-cut blank paper squares**– supplementary materials

Fogerty, Mignon. (2013). 5 Tips for Faster Mental Division
5 Tips for Faster Mental Division (Part 1) – Quick and Dirty Tips
Khan Academy. (2019). Multiplying and Dividing by 10, 100, and 1000

**Multiply and Divide by 10, 100, and 1000- The Maths Guy**

**Dividing Decimals by 10, 100, and 1000- Let’s Do Math**