11 FOCUSED INSTRUCTION: MATHEMATICS INTERVENTION Name:__________________________________ Date:__________________ Benchmark Preassessment Lessons 28–29 © | Teacher Created Materials 153404—Mathematics Intervention: Assessment Guide 43 Directions: Solve each problem. 55. Which statement about the image is true? a b c A Ray b and ray c appear to be perpendicular. B Line a and ray b appear to be parallel. C Line a and ray b appear to be perpendicular. D Line a and ray c appear to be parallel. 56. Which polygon has exactly 1 pair of parallel sides? A B C D 57. A right angle is shown. Which angles are obtuse angles? A B C D 58. A triangle is shown. Which statement about this shape is true? A This is an obtuse triangle because it has 1 obtuse angle. B This is an acute triangle because it has 2 acute angles. C This is an obtuse triangle because it has 3 obtuse angles. D This is a right triangle because it has 1 right angle. Assessment Guide Management Guide © | Teacher Created Materials 153386—Mathematics Intervention: Management Guide 11 11 Research and Best Practices Concrete, Representational, Abstract The Concrete-Representational-Abstract (CRA) instructional sequence is a well-established, research-based, evidence-based approach to teaching mathematical concepts and procedures . It is particularly effective for struggling learners and for students with learning disabilities, but it can be beneficial for all learners . This instructional methodology has been studied across grade levels and student ability levels . The CRA method involves three stages: concrete, representational, and abstract . Each stage builds upon the previous one to enhance students’ conceptual understanding and procedural fluency in mathematics . It is important to note that in documentation and research CRA may also be referred to as Concrete-Pictorial-Abstract (CPA) or Concrete– Semi-concrete–Abstract (CSA) . Mathematics education researchers and authors may be more likely to use the CSA terminology as all three stages are representations . Regardless of the nomenclature, the evidence is consistent . Concrete In the concrete stage, students engage with physical objects to model mathematical concepts . This hands-on approach allows students to manipulate objects, making abstract ideas more tangible and comprehensible . For example, to learn addition, students might use counters or base-ten blocks to physically combine groups and count the total . Using concrete materials helps students form solid foundations for the mathematical concepts being taught . This stage is often skipped due to time constraints, misconceptions about its necessity, and lack of resources or training . Even students in intermediate and secondary grades find success with higher-level abstract mathematics using manipulatives . Concrete manipulatives allow students to physically engage with mathematical concepts, which helps them form a solid conceptual framework . Representational The representational stage, also known as the semi-concrete or pictorial stage, involves transitioning from physical objects to visual representations . In this stage, students use drawings, models, or diagrams to represent the concrete objects they previously manipulated . This step helps bridge the gap between the tangible and the abstract by allowing students to visualize mathematical concepts without relying on physical objects . For instance, students might draw tally marks or number lines to represent the addition process . By explicitly including the representational stage, educators can highlight the importance of this intermediate step in helping students transition from hands-on manipulation to abstract thinking . It makes the learning process more gradual and less abrupt, thereby helping students understand and internalize mathematical concepts more effectively . It also supports the transfer of knowledge, providing accessible strategies for situations where manipulatives are not available . It allows students to visualize mathematical concepts without the immediate need to use physical objects . This visualization step is crucial for students to develop the ability to think abstractly, which is essential for higher-level mathematics . Concrete Representational Abstract Game Cards 154610_154611_FMI_GameCards_L4.indd 86 154610_154611_FMI_GameCards_L4.indd 86 11/18/24 2:58 PM 11/18/24 2:58 PM 154654—Mathematics Intervention: Games Booklett © | Teacher Created Materials 10 Game Variation 3 to 4 Players Fishing for Fractions Skill: Match fractions to their visual representations. Materials: Fraction Cards How to Win: The player who collects the most cards wins. How to Play 1. Shuffle the Fraction Cards from the card deck. Deal 4 cards to each player. Place the rest of the cards face down in a draw pile in the center of the playing space. 2. The oldest player goes first. 3. On your turn, ask if anyone has a card that matches one of the fractions in your hand. For example, “Does anyone have 1 10 ?” • If another player has the fraction, they must give it to you. Then, lay the matching cards in front of you and take another turn. • If the other players do not have the fraction, you must fish for a fraction by picking up the top card in the draw pile. The player to your right goes next. 4. When all cards are matched, count your collected cards. The player with the most cards wins! Does anyone have 3 5? Games Booklet INSIDE EVERY KIT • 1 Teacher’s Guide with 30 standards-based lessons • 1 Student Guided Practice Book • 1 Assessment Guide • 1 Management Guide • Instructional Routine Cards • Dice and Timers • 1 Games Booklet and Game Cards to practice and apply foundational math skills INTERVENTION
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2026-2027 New York City Full Line Catalog
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