## RAT: Scenario 1

Scenario: Holly teaching estimating Country: USA Grade (student age): Grade 4 (age 9-10) Contributed by: Tracy Weston, University of Alabama, USA Context –curricular, professional, other As is the case in the United States, North Carolina has state mandated goals and objectives for mathematics instruction at each grade level.  The North Carolina Standard Course of Study (NCSCOS) indicates that in grade 4 students are to “Develop number sense for rational numbers 0.01 through 99,999,” which includes “understanding of place value (hundredths through ten thousands)” and “make estimates of rational numbers.”  They also are required to “develop fluency with addition and subtraction of non-negative rational numbers with decimals through hundredths” including “estimating sums and differences.” This school used the EnVisions curriculum, as mandated by the district (local authority).  Students in this school…

## RAT: Scenario 2

Scenario: John teaching properties of 3-D shapes Country: UK Grade (student age): Year 9 (age 13-14) Contributed by: Anne Thwaites, University of Cambridge, UK Context – national, curricular, professional, other The National Curriculum for mathematics in England includes solutions of quadratic equations in Key Stage 4 (years 10-11, pupil age 14-16). These pupils were near the end of year 9 and John had been working on graphical representation of quadratic expressions in a previous lesson and then on ‘completing the square’ [i.e. expressing in an equivalent form ], as specified in the 16-18 pupil age curriculum. John was a graduate pre-service teacher, and the lesson took place in a school-based placement towards the end of his one-year teacher preparation. Scenario John was teaching in an open entry secondary school (pupil…

## RAT: Scenario 3

Scenario: Chloe teaching a mental arithmetic strategy Country: UK Grade (student age): Year 1/2 (age 5-7) Contributed by: Tim Rowland, University of Cambridge, UK Context – national, curricular, professional, other At the time when this lesson was recorded, mathematics in primary schools was prescribed by a National Numeracy Strategy and a related curriculum framework. In the early years, in keeping with Dutch RME principles, arithmetic emphasises children’s mental methods, and introduces a number of related strategies. The focus for this lesson is subtracting near-multiples of 10 (specifically, 9, 11, 19, 21) by subtracting 10 (or 20) and then adjusting by 1. Chloë was a graduate pre-service teacher, and the lesson took place in a school-based placement towards the end of her one-year teacher preparation. Scenario The objectives of the lesson…