Unit 3- Multiplication and Division With

Unit 3- Multiplication and Division with

FACTORS of 1, 0, 3, 4, 6, 9, 8,7, and Area Introduction

3rd GradeMath Plans- 2nd 9 weeks - 3rd week

Week Three - (Days 1-5) - x4 facts and review of other facts learned

Teacher Notes:There are great resources in the book Mastering the Basic Math Facts in multiplication and division by Susan O’Connell and John SanGiovanni. Email Cindy Doolittle if you need a copy. Several of the resources in the lesson come from this book.

Big Ideas on Multiplying by 4s

Students have already explored doubling when they investigated x2 facts. Multiplying by 4 is simply doubling the product of the x2 facts.
Our number system is a system of patterns. Noticing that multiples of 4 are always even numbers or realizing that multiples of 4 are also multiples of 2 (in fact, that they are every other multiple of 2) leads to interesting conversation and insights.
The order of the factors does not change the product (the commutative property). If students know the product of 3 x 4, then they also know the product of 4 x 3.

Day One–Start x 4 facts.

Materials:

Daily Spiral Review and Flipchart (Resource Box)
If You Hopped Like a Frog by David Schwartz (2000)
How Many Legs? recording sheet (Resource Box)
2 - 10 number cards (Resource Box)
Exploring Legs recording sheet (Resource Box)
x 4 fact cards (Resource Box)

In this lesson -1) Students will understand equal groups of as multiplication (x 4 facts only).

Daily Spiral Review: Complete Daily Spiral Review and Flipchart (Resource Box).

Activating Strategy:Use the book If You Hopped Like a Frog by David Schwartz (2000) to open up this lesson. See below before reading the book.

Before Reading the Book:

Ask students if they have ever thought about being an animal. Read the letter from the author at the beginning of the book in which the author talks about wishing he was a frog and other animals.
Have students turn to a partner and share an animal or insect they might like to be and why.

During Reading:

Read the story once to have fun with the animal to human comparisons. Then reread the story, this time asking students to think about the number of legs for the different animals and insects as you read.
Help students create a line plot on their paper as you create one on the board, labeling it with numbers 0 - 8 for the number of legs for each animal mentioned. (This is the first exposure to line plots for 3rd graders.) As each animal or insect is mentioned, ask students to share the number of legs and then place an X on the corresponding number on their line plot as you record it on your line plot.

This line plot shows the number of legs for the animals in the story.

X = 1 animal

X X

X X X

X X X X X

0 1 2 3 4 5 6 7 8

Ask students to turn and tell a partner what their line plot shows about the animal legs.

You might ask them to identify the fewest legs and the most legs that any animal or insect had in the story.
You might ask them which quantity of legs was mentioned most often.
You might explore which types of animals or insects had various quantities of legs (e.g., insects, spiders, humans, birds).

After Reading:

Have students identify the number of legs that most animals had in the story (4) and compare that number to the number of legs people have (2).
Begin posing questions about animal legs and people legs (i.e., How many legs would 6 people have? How many legs would 6 frogs have? Have students first predict the number of legs for 6 frogs and 6 humans.Have them turn and tell a partner their prediction and how they determined the prediction.
Then, ask students to draw a diagram for each situation and write a multiplication sentence to show the actual number of legs (e.g., 6 x 2 = 12 and 6 x 4 = 24).
With the class, make a list of the 4-legged animals from the story (e.g., frog, brachiosaurus, shrew, chameleon, bear).
Have students choose a 4-legged animal from the list.
Using the How Many Legs? recording sheet (Resource Box), have students select a number card from a deck of 2 - 10 number cards (Resource Box) and place that number on the Number of People or Animals line on the recording sheet. Students draw a diagram and write a multiplication equation to find the amount of legs for that quantity of people, and then do the same to find the amount of legs for that quantity of animals. Remind students that they do not need to draw animals, but might use circles, Xs, or tallies. Have students repeat the process by randomly picking another number card from the 2 - 10 deck to indicate a new quantity of humans and animals.
After students have determined the total number of legs for two different-sized animal/human groups, have them share their data as you record it on the board. Chart the x2 multiplication equations in one column and the x4 in another column, progressing in order from 2 - 10 animals or humans in a group.
As you record the data gathered by the class, have each student record the data on a paper folded into two columns or on the Exploring Legs recording sheet (Resource Box).
Have students turn to partners and compare the products of the multiplication equations. Jump-start their thinking with some questions like:

What do you notice about the data?
How are the x2 and x4 facts related?
How might this help you remember the x4 facts.

Summarizing Strategy:In their journals, have students write about their observations on the following -

How are the products of x2 facts similar to the products of x4 facts?
How might this help you remember x4 facts?

Homework: Have students practice their x 4 facts. There are x 4 fact cards if needed in the resource box (2 sizes).

Day Two –Continue practicing with x4 facts.

Materials:

Daily Spiral Review and Flipchart (Resource Box)
Song on the Multiplication Facts of 4 (Resource Box)
Multi Models (Resource Box)
Capture (Resource Box)
Fancy Fours (Resource Box)
Math Facts Column (Resource Box)
Envision Math Textbook Lesson 6-3 - optional

In this lesson -

1) Students will interpret the meaning of factors – the size of the group or the number of groups. Students may use a number bond (from Singapore Math).

2) Students will explore the commutative property with manipulatives.

Activating Strategies:

Open up with the Song on the Multiplication Facts of 4 (Resource Box).

Teaching Strategies: Explore the Commutative Property also if students are ready to go there.

Have students understand the relationship between repeated addition, counting groups in unit form, and multiplication equations. Give each student 20 counters. Ask them to use their counters to make equal groups of four. How many counters will you put in each group? Show with their fingers (4 fingers).

How many equal groups of four did you make? (5 equal groups of 4 counters equals 20 counters)

Write an addition sentence to show your groups Write 4 + 4 + 4 + 4 + 4 = 20.

How many fours did we add to make 20? (5 fours - Record 5 fours = 20)

5 x 4 is another way to write 4 + 4 + 4 + 4 + 4. Ask students which way they like to write it? (5 x 4 might be an easier way to write a long addition sentence - multiplication is a more efficient way of showing the total than repeated addition)

Sample teacher board:

Do more examples if needed.

Commutative Property if students are ready. Do students see that 5 x 4 and 4 x 5 are the same answer?

5 x 4 = 20 4 x 5 = 20

Classwork - Have students pick from some of the following games:

Multi Models (Resource Box)
Capture (Resource Box)
Fancy Fours (Resource Box)

SummarizingStrategy:In your journal, answer the following question - Moses said that he knows that 5 x 10 is the same as 10 x 5.Jullia disagrees. Who is correct and how do you know?

Homework:

Assign Math Facts Column (Resource Box). Also have students practice at home their 4 facts (Resource Box). There are x 4 fact cards if needed in the Resource Box. If a student has mastered their 4mult. facts, then allow them to practice the 4 division facts.
Envision Math Textbook Lesson 6-3 - optional

Day Three–Continue practicing with x 4 facts.

Materials:

Daily Spiral Review and Flipchart (Resource Box)
4s Multiplication Go Fish x Facts (Resource Box) - did not run-off
Fact Fish (Resource Box)
Target 40 and Spinner (Resource Box)
Envision Math Textbook Lesson 6-3 – optional if not previously used

In this lesson -1) Students will understand equal groups of as multiplication (x 4 facts only).

Daily Spiral Review: Complete Daily Spiral Review and Flipchart (Resource Box).

Activating Strategy:Go to this site and select x 4 to practice as a class. If students have been successful with multiplying their 4 facts, go to the division site.

Multiplication-

Division-

Classwork - Remember to review all facts learned.

Have students play any of the following games:

4s Multiplication Go Fish x Facts (Resource Box) - did not run-off
Fact Fish (Resource Box)
Target 40 and Spinner (Resource Box)

Homework:

Have students practice at home their 4 facts (Resource Box). There are x 4 fact cards if needed in the Resource Box. If a student has mastered their 4mult. facts, then allow them to practice the 4 division facts.
Envision Math Textbook Lesson 6-3 – optional if not previously used

Day Four – Continue practicing with x 4 facts.

Materials:

Daily Spiral Review and Flipchart (Resource Box)
4s Sprint (Resource Box)
Memory Basketball (Resource Box)
Multiplication Facts Activity (Resource Box)

In this lesson -1) Students will understand equal groups of as multiplication (x 4 facts only).

Daily Spiral Review: Complete Daily Spiral Review and Flipchart (Resource Box).

Activating Strategy: Give students 4s Sprint (Resource Box) to start building up speed.

Classwork - Have students play any of the following games:

Memory Basketball (Resource Box)
Multiplication Facts Activity (Resource Box)

Homework:Teacher Choice and have students practice at home their 4 facts (Resource Box). There are x 4 fact cards if needed in the Resource Box. If a student has mastered their 4mult.facts, then allow them to practice the 4 division facts.

Day Five –Assess knowledge of x 4 facts

Materials:

Daily Spiral Review and Flipchart (Resource Box)
Multiplication Practice 2, 3, 4, 5 Flipchart (Resource Box)
Quiz 4 (Resource Box)
x 4 Fact Check (Resource Box) - one is multiplication only and the other one has x and ÷ facts
x 4 Fact Check (Resource Box) - multiplication only
x 4 Fact Check - Mixed Review (Resource Box) - this one assesses all facts learned (Best one if students are ready)

In this lesson -1) Teachers will monitor their students' progress toward automaticity of facts.

Daily Spiral Review: Complete Weekly Assessment and Flipchart (Resource Box).

Classwork - Use this time to repeat any of the activities for review. Also use Multiplication Practice 2, 3, 4, 5, Flipchart (Resource Box) for review.

Monitor Progress - Monitoring students' progress toward automaticity requires ongoing and varied techniques for assessing fact mastery and tracking each student's progress. Tracking progress allows teachers to celebrate students' mastery, identify concerns, and design appropriate interventions to address those concerns.

Teachers may give any of the following to monitor progress of x 4 facts:

Quiz 4 (Resource Box)
x 4 Fact Check (Resource Box) - one is multiplication only and the other one has x and ÷ facts
x 4 Fact Check (Resource Box) - multiplication only
x 4 Fact Check - Mixed Review (Resource Box) -Best one if students are ready

Remember to use the math fact automaticity interview if needed. Students need to be recording their practice times at home on the My Fact Log.

Homework:

Have students practice at home their facts (Resource Box). Fluency must be demonstrated by the end of 3rd grade.