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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

H G3 & G5 Fractions and Ratios shows third and fifth graders finding and explaining equivalent fractions in different ways: using rows of the multiplication table to show many equivalent fractions and drawing fraction bars and/or fraction number lines. Fifth graders practice a unit fraction times a whole number and solve puzzles made from two intersecting rows and columns of a multiplication table. [19:40 minutes]

Part 1 G3 Equivalent Fractions shows third graders using rows cut from a multiplication table to see and explain many equivalent fractions as different multiples of the same simplest fraction. Students then make math drawings using fraction bars to show and explain why 2/7 = 6/21 and end by stating the general pattern: The smaller the denominator, the bigger the parts (the unit fractions). [10:30 minutes]

Part 2 G5 Equivalent Fractions shows a fifth grader explaining fraction bar and number line drawings to show that ½ = 3/6. The teacher then summarizes the opposite relation using the drawings: It takes three of the smaller 1/6ths to make the larger ½. [2:50 minutes]

Part 3 G5 Unit Fraction x Whole Number shows a Quick Practice in which two Student Leaders elicit answers to unit fraction x whole number problems such as 1/6 x 42. [0:42 minutes]

Part 4 G5 Multiplication Table Puzzles shows fifth graders dividing or multiplying to find the unknown number in puzzles made from intersections of two rows and two columns of a multiplication table. These puzzles show proportions and are part of the Children’s Math Worlds approach to ratio and proportion based on the multiplication table (see Math Expressions Grade 6 for the full approach). [5:35 minutes]

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H G3 & G5 Fractions and Ratios shows third and fifth graders finding and explaining equivalent fractions in different ways: using rows of the multiplication table to show many equivalent fractions and drawing fraction bars and/or fraction number lines. Fifth graders practice a unit fraction times a whole number and solve puzzles made from two intersecting rows and columns of a multiplication table. [19:40 minutes]

Part 1 G3 Equivalent Fractions shows third graders using rows cut from a multiplication table to see and explain many equivalent fractions as different multiples of the same simplest fraction. Students then make math drawings using fraction bars to show and explain why 2/7 = 6/21 and end by stating the general pattern: The smaller the denominator, the bigger the parts (the unit fractions). [10:30 minutes]

Part 2 G5 Equivalent Fractions shows a fifth grader explaining fraction bar and number line drawings to show that ½ = 3/6. The teacher then summarizes the opposite relation using the drawings: It takes three of the smaller 1/6ths to make the larger ½. [2:50 minutes]

Part 3 G5 Unit Fraction x Whole Number shows a Quick Practice in which two Student Leaders elicit answers to unit fraction x whole number problems such as 1/6 x 42. [0:42 minutes]

Part 4 G5 Multiplication Table Puzzles shows fifth graders dividing or multiplying to find the unknown number in puzzles made from intersections of two rows and two columns of a multiplication table. These puzzles show proportions and are part of the Children’s Math Worlds approach to ratio and proportion based on the multiplication table (see Math Expressions Grade 6 for the full approach). [5:35 minutes]

H G3 & G5 Fractions and Ratios shows third and fifth graders finding and explaining equivalent fractions in different ways: using rows of the multiplication table to show many equivalent fractions and drawing fraction bars and/or fraction number lines. Fifth graders practice a unit fraction times a whole number and solve puzzles made from two intersecting rows and columns of a multiplication table. [19:40 minutes]

Part 1 G3 Equivalent Fractions shows third graders using rows cut from a multiplication table to see and explain many equivalent fractions as different multiples of the same simplest fraction. Students then make math drawings using fraction bars to show and explain why 2/7 = 6/21 and end by stating the general pattern: The smaller the denominator, the bigger the parts (the unit fractions). [10:30 minutes]

Part 2 G5 Equivalent Fractions shows a fifth grader explaining fraction bar and number line drawings to show that ½ = 3/6. The teacher then summarizes the opposite relation using the drawings: It takes three of the smaller 1/6ths to make the larger ½. [2:50 minutes]

Part 3 G5 Unit Fraction x Whole Number shows a Quick Practice in which two Student Leaders elicit answers to unit fraction x whole number problems such as 1/6 x 42. [0:42 minutes]

Part 4 G5 Multiplication Table Puzzles shows fifth graders dividing or multiplying to find the unknown number in puzzles made from intersections of two rows and two columns of a multiplication table. These puzzles show proportions and are part of the Children’s Math Worlds approach to ratio and proportion based on the multiplication table (see Math Expressions Grade 6 for the full approach). [5:35 minutes]

Part 1

Part 2

Part 3

Part 4

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