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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

F G3 Single-Digit Multiplication and Division shows third graders finding, explaining, and using patterns of 4 and of 9 to multiply and divide; they also write, share, and discuss word problems for three types of division situations. We also see fourth graders use comparison bars to represent and solve additive and multiplicative comparison problems. [57 minutes]

Part 1 G3 Count By 4s shows a teacher leading third graders in counting by 4s to multiply and divide and asking them to solve and explain examples. They multiply by stopping when their fingers show the known multiplier of 4 and the unknown product is the number they say, and they divide by stopping at the known product and looking at their fingers to see the unknown multiplier. [5 minutes]

Part 2 G3 Class Finds 9s Patterns shows third graders finding and explaining many patterns they see on the 120 board as they make groups of 9 and relate these groups to products of 9 = 10 – 1 (2 x 9 = 20 – 2 = 18, 3 x 9 = 30 – 3 = 27, etc.). [18 minutes].

Part 3 G3 Teacher Summarizes 9s Patterns shows the teacher summarizing the patterns children had found and described in Part 2. She then discusses why she values this activity for her students. [9:40 minutes]

Part 4 G3 Teaching Finger 9s shows the teacher building on the patterns students found relating 9s products to 10 – 1 products by developing and explaining how to show the tens and ones with fingers. She then shows and explains the Short-Cut Finger 9s that use the multiplier finger to separate the tens fingers from the ones fingers to show the product. [11:30 minutes]

Part 5 G3 Division Word Problems shows third graders sharing division word problems they made up for the different kinds of division situations: grouping, array, and multiplicative comparison. Each student explains how s/he solved the problem s/he wrote, and classmates ask questions. [8:30 minutes]

Part 6 G4 Comparison Problems shows fourth graders drawing comparison bars to compare amounts using addition/subtraction (more than/less than) and using multiplication/division (times as many as). [4:15 minutes]

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F G3 Single-Digit Multiplication and Division shows third graders finding, explaining, and using patterns of 4 and of 9 to multiply and divide; they also write, share, and discuss word problems for three types of division situations. We also see fourth graders use comparison bars to represent and solve additive and multiplicative comparison problems. [57 minutes]

Part 1 G3 Count By 4s shows a teacher leading third graders in counting by 4s to multiply and divide and asking them to solve and explain examples. They multiply by stopping when their fingers show the known multiplier of 4 and the unknown product is the number they say, and they divide by stopping at the known product and looking at their fingers to see the unknown multiplier. [5 minutes]

Part 2 G3 Class Finds 9s Patterns shows third graders finding and explaining many patterns they see on the 120 board as they make groups of 9 and relate these groups to products of 9 = 10 – 1 (2 x 9 = 20 – 2 = 18, 3 x 9 = 30 – 3 = 27, etc.). [18 minutes].

Part 3 G3 Teacher Summarizes 9s Patterns shows the teacher summarizing the patterns children had found and described in Part 2. She then discusses why she values this activity for her students. [9:40 minutes]

Part 4 G3 Teaching Finger 9s shows the teacher building on the patterns students found relating 9s products to 10 – 1 products by developing and explaining how to show the tens and ones with fingers. She then shows and explains the Short-Cut Finger 9s that use the multiplier finger to separate the tens fingers from the ones fingers to show the product. [11:30 minutes]

Part 5 G3 Division Word Problems shows third graders sharing division word problems they made up for the different kinds of division situations: grouping, array, and multiplicative comparison. Each student explains how s/he solved the problem s/he wrote, and classmates ask questions. [8:30 minutes]

Part 6 G4 Comparison Problems shows fourth graders drawing comparison bars to compare amounts using addition/subtraction (more than/less than) and using multiplication/division (times as many as). [4:15 minutes]

F G3 Single-Digit Multiplication and Division shows third graders finding, explaining, and using patterns of 4 and of 9 to multiply and divide; they also write, share, and discuss word problems for three types of division situations. We also see fourth graders use comparison bars to represent and solve additive and multiplicative comparison problems. [57 minutes]

Part 1 G3 Count By 4s shows a teacher leading third graders in counting by 4s to multiply and divide and asking them to solve and explain examples. They multiply by stopping when their fingers show the known multiplier of 4 and the unknown product is the number they say, and they divide by stopping at the known product and looking at their fingers to see the unknown multiplier. [5 minutes]

Part 2 G3 Class Finds 9s Patterns shows third graders finding and explaining many patterns they see on the 120 board as they make groups of 9 and relate these groups to products of 9 = 10 – 1 (2 x 9 = 20 – 2 = 18, 3 x 9 = 30 – 3 = 27, etc.). [18 minutes].

Part 3 G3 Teacher Summarizes 9s Patterns shows the teacher summarizing the patterns children had found and described in Part 2. She then discusses why she values this activity for her students. [9:40 minutes]

Part 4 G3 Teaching Finger 9s shows the teacher building on the patterns students found relating 9s products to 10 – 1 products by developing and explaining how to show the tens and ones with fingers. She then shows and explains the Short-Cut Finger 9s that use the multiplier finger to separate the tens fingers from the ones fingers to show the product. [11:30 minutes]

Part 5 G3 Division Word Problems shows third graders sharing division word problems they made up for the different kinds of division situations: grouping, array, and multiplicative comparison. Each student explains how s/he solved the problem s/he wrote, and classmates ask questions. [8:30 minutes]

Part 6 G4 Comparison Problems shows fourth graders drawing comparison bars to compare amounts using addition/subtraction (more than/less than) and using multiplication/division (times as many as). [4:15 minutes]

Part 1

Part 2

Part 3

Part 4

Part 5

Part 6

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