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The National Science Foundation funded A Video Research Report of the Children’s Math Worlds Research Project to show the levels of learning possible by children from backgrounds of poverty who experience good teaching. The classroom videos were taken in four public schools, three high-poverty urban schools with some to most students speaking a native language other than English and a suburban school with immigrants from many countries. The classrooms you will see were built by the continuing efforts of many dedicated teachers, students, parents, school administrators, and members of the Children’s Math Worlds research team. Language and ideas of students, teachers, and parents were woven into the curriculum as it was revised each year. The project had a strong emphasis on children explaining their thinking and on using math drawings developed in the project to support student thinking and explaining. None of our teachers had learned math in this way, so they were all brave pioneers in learning how to create such classrooms. All classrooms are complicated places, and no teaching segment can be perfect. We can all have ideas about how to change things the next time. I am enormously proud of and grateful to these teachers for being willing to share their classrooms so that everyone can see what students can do if we support them in their thinking. The Teaching Progressions show in more detail the learning progressions students experienced to reach the points shown on these Classroom Videos.

Classroom Videos

A - Classroom Components

B - Math Explanations

C - Longer Classroom

Teaching Examples

D - Kindergarten

E - G1 Single-Digit

Addition and Subtraction

F - G3 Single-Digit

Multiplication and Division

G - Place Value and Multidigit

Addition and Subtraction

H - G3 & G5 Fractions and Ratios

I - Teacher Interviews Grade 1

J - Teacher Interviews

Grades 2 and 3

G Place Value and Multidigit Addition and Subtraction shows first and second graders using dime, nickel, and penny strips to practice counting to 2-digit numbers and second graders comparing numbers and finding all eight related equations for 25 + 75 = 100. Second graders explain the Children’s Math Worlds methods for adding 2-digit and 3-digit numbers and for subtracting 3-digit numbers and relate the written methods to math drawings. Fourth graders explain three different written subtraction methods for 7-digit numbers. [32 minutes]

Part 1 G1 Dimes and Pennies shows Quick Practice with first graders showing values of a dime, nickel, and penny with fingers, and then counting by tens and fives and ones while flashing fingers to show the value of the increasing counts. The class then shows values of coin problems and of dime strips and pennies by counting by tens while flashing ten fingers, freezing, then counting by ones and flashing one finger each time. [4:20 minutes]

Part 2 Place Value Routine shows two second-grade Student Leaders each choosing a 2-digit number, making it with dime and nickel strips and single pennies, and the class counts by tens, fives, and ones to find the number. The same numbers are made and counted on a meter stick showing decimeters and centimeters (tens and ones). Students then say which number is more and which is less. [3:15 minutes]

Part 3 G2 8 Related Equations shows two second-grade Student Leaders leading a Quick Practice eliciting from the class and then writing the 8 related addition or subtraction equations from a Math Mountain: 25 + 75 = 100, 100 = 25 + 75, 75 + 25 = 100, 100 = 75 + 25, 100 – 25 = 75, 75 = 100 – 25, 100 – 75 = 25, 25 = 100 – 75. [5 minutes]

Part 4 G2 4 Methods for 67 + 86 shows second graders in a Spanish-speaking class explaining in English four Children’s Math Worlds addition methods: New Groups Below, New Groups Above, Show Subtotals from the left, and Show Subtotals from the right. The teacher supports students to use hundreds, tens, and ones language when they are explaining. [10:30 minutes]

Part 5 G2 Explaining 580 + 276 shows a second grader explaining his math drawing that shows the hundreds, tens, and ones in 580 + 276 and then explaining his written addition method beside the drawing. [1:35 minutes]

Part 6 G2 Explaining 600 – 247 shows a second grader explaining her math drawing of hundreds, tens, and ones and how she used it to solve 600 – 247 by ungrouping 1 hundred and then 1 ten to get enough to subtract the tens and the ones. She related her steps in the drawing to her steps in her written method. [1 minute]

Part 7 G3 Explaining 700 – 374 shows a third grader making up a word problem for 700 – 374 and then a girl explaining her math drawing and her written method and answering two questions from classmates. [2:30 minutes]

Part 8 G4 Explaining 7-Digit Subtraction shows three fourth graders using and then explaining different methods to ungroup 5,472,639 – 2,375,841 (ungrouping left to right, ungrouping right to left, ungrouping left to right without writing the first ungrouping step) and to subtract (left to right or right to left). Students discuss why they got the same answer. [13 minutes]

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G Place Value and Multidigit Addition and Subtraction shows first and second graders using dime, nickel, and penny strips to practice counting to 2-digit numbers and second graders comparing numbers and finding all eight related equations for 25 + 75 = 100. Second graders explain the Children’s Math Worlds methods for adding 2-digit and 3-digit numbers and for subtracting 3-digit numbers and relate the written methods to math drawings. Fourth graders explain three different written subtraction methods for 7-digit numbers. [32 minutes]

Part 1 G1 Dimes and Pennies shows Quick Practice with first graders showing values of a dime, nickel, and penny with fingers, and then counting by tens and fives and ones while flashing fingers to show the value of the increasing counts. The class then shows values of coin problems and of dime strips and pennies by counting by tens while flashing ten fingers, freezing, then counting by ones and flashing one finger each time. [4:20 minutes]

Part 2 Place Value Routine shows two second-grade Student Leaders each choosing a 2-digit number, making it with dime and nickel strips and single pennies, and the class counts by tens, fives, and ones to find the number. The same numbers are made and counted on a meter stick showing decimeters and centimeters (tens and ones). Students then say which number is more and which is less. [3:15 minutes]

Part 3 G2 8 Related Equations shows two second-grade Student Leaders leading a Quick Practice eliciting from the class and then writing the 8 related addition or subtraction equations from a Math Mountain: 25 + 75 = 100, 100 = 25 + 75, 75 + 25 = 100, 100 = 75 + 25, 100 – 25 = 75, 75 = 100 – 25, 100 – 75 = 25, 25 = 100 – 75. [5 minutes]

Part 4 G2 4 Methods for 67 + 86 shows second graders in a Spanish-speaking class explaining in English four Children’s Math Worlds addition methods: New Groups Below, New Groups Above, Show Subtotals from the left, and Show Subtotals from the right. The teacher supports students to use hundreds, tens, and ones language when they are explaining. [10:30 minutes]

Part 5 G2 Explaining 580 + 276 shows a second grader explaining his math drawing that shows the hundreds, tens, and ones in 580 + 276 and then explaining his written addition method beside the drawing. [1:35 minutes]

Part 6 G2 Explaining 600 – 247 shows a second grader explaining her math drawing of hundreds, tens, and ones and how she used it to solve 600 – 247 by ungrouping 1 hundred and then 1 ten to get enough to subtract the tens and the ones. She related her steps in the drawing to her steps in her written method. [1 minute]

Part 7 G3 Explaining 700 – 374 shows a third grader making up a word problem for 700 – 374 and then a girl explaining her math drawing and her written method and answering two questions from classmates. [2:30 minutes]

Part 8 G4 Explaining 7-Digit Subtraction shows three fourth graders using and then explaining different methods to ungroup 5,472,639 – 2,375,841 (ungrouping left to right, ungrouping right to left, ungrouping left to right without writing the first ungrouping step) and to subtract (left to right or right to left). Students discuss why they got the same answer. [13 minutes]

G Place Value and Multidigit Addition and Subtraction shows first and second graders using dime, nickel, and penny strips to practice counting to 2-digit numbers and second graders comparing numbers and finding all eight related equations for 25 + 75 = 100. Second graders explain the Children’s Math Worlds methods for adding 2-digit and 3-digit numbers and for subtracting 3-digit numbers and relate the written methods to math drawings. Fourth graders explain three different written subtraction methods for 7-digit numbers. [32 minutes]

Part 1 G1 Dimes and Pennies shows Quick Practice with first graders showing values of a dime, nickel, and penny with fingers, and then counting by tens and fives and ones while flashing fingers to show the value of the increasing counts. The class then shows values of coin problems and of dime strips and pennies by counting by tens while flashing ten fingers, freezing, then counting by ones and flashing one finger each time. [4:20 minutes]

Part 2 Place Value Routine shows two second-grade Student Leaders each choosing a 2-digit number, making it with dime and nickel strips and single pennies, and the class counts by tens, fives, and ones to find the number. The same numbers are made and counted on a meter stick showing decimeters and centimeters (tens and ones). Students then say which number is more and which is less. [3:15 minutes]

Part 3 G2 8 Related Equations shows two second-grade Student Leaders leading a Quick Practice eliciting from the class and then writing the 8 related addition or subtraction equations from a Math Mountain: 25 + 75 = 100, 100 = 25 + 75, 75 + 25 = 100, 100 = 75 + 25, 100 – 25 = 75, 75 = 100 – 25, 100 – 75 = 25, 25 = 100 – 75. [5 minutes]

Part 4 G2 4 Methods for 67 + 86 shows second graders in a Spanish-speaking class explaining in English four Children’s Math Worlds addition methods: New Groups Below, New Groups Above, Show Subtotals from the left, and Show Subtotals from the right. The teacher supports students to use hundreds, tens, and ones language when they are explaining. [10:30 minutes]

Part 5 G2 Explaining 580 + 276 shows a second grader explaining his math drawing that shows the hundreds, tens, and ones in 580 + 276 and then explaining his written addition method beside the drawing. [1:35 minutes]

Part 6 G2 Explaining 600 – 247 shows a second grader explaining her math drawing of hundreds, tens, and ones and how she used it to solve 600 – 247 by ungrouping 1 hundred and then 1 ten to get enough to subtract the tens and the ones. She related her steps in the drawing to her steps in her written method. [1 minute]

Part 7 G3 Explaining 700 – 374 shows a third grader making up a word problem for 700 – 374 and then a girl explaining her math drawing and her written method and answering two questions from classmates. [2:30 minutes]

Part 8 G4 Explaining 7-Digit Subtraction shows three fourth graders using and then explaining different methods to ungroup 5,472,639 – 2,375,841 (ungrouping left to right, ungrouping right to left, ungrouping left to right without writing the first ungrouping step) and to subtract (left to right or right to left). Students discuss why they got the same answer. [13 minutes]

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

Part 7

Part 8