12 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 Levels K–5 Build Math Success with High-Impact Intervention Strengthen outcomes for students struggling in math by targeting specific skill gaps with this supplemental, evidence-based intervention. Grounded in the Concrete-Representational-Abstract (CRA) method and built on proven strategies, Focused Instruction: Mathematics Intervention helps students develop conceptual understanding, procedural fluency, and problem-solving skills. With 30 standards-aligned lessons and scaffolded practice activities, the program offers flexibility through a consistent five-part lesson format. FOCUSED INSTRUCTION: MATHEMATICS INTERVENTION NEW! Teacher’s Guide Management Guide Student Guided Practice Book Name: _______________________________________________________ Date: _____________________ © | Teacher Created Materials 153356—Focused Instruction: Mathematics Student Book 23 Lesson 3 Rich Math Task Smudged Labels Directions: Read the task carefully. Then, solve. 1. Who do you think packaged the greatest number of candy bars? 2. Who do you think packaged the least number of candy bars? 3. Justify your reasoning. A factory produces candy bars. The factory manager keeps track of the number of candy bars packaged by each employee every day, but the printer smudged the numbers. Employee Number of Candy Bars Mr. Smith 20,5 Ms. Barkley 1 ,933 Mrs. McMahon 0,563 Mr. Carlton 19,450 Ms. Weston 19, 0 © | 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 © | Teacher Created Materials 154669—Mathematics Intervention: Teacher’s Guide 35 Part 1 Lesson 6 Subtract Multi-Digit Numbers Explore 10–15 min. 1. Distribute base-ten blocks, and have each student build a tower to represent the number 456. Give students time to share the features of their towers, including the types of base- ten blocks they used. Students can use any groupings of base-ten blocks that show 456 (e.g., 400 + 50 + 6 or 400 + 40 + 16). 2. Have students remove 20 from 456. Then, have them share how their towers have changed. Students may need to regroup to subtract (e.g., exchange a rod for 10 unit cubes). 3. Observe how students are removing, or subtracting, the base-ten blocks. Use these observations to support students as they learn multi-digit subtraction. Vocabulary: Ask students to listen for the words difference, minuend, subtrahend, and regroup during the lesson. Write the words where students can see them. Students use strategies to build vocabulary on the second day of instruction. Explain 10–15 min. 4. Follow the Subtract with Base-Ten Blocks routine (card 8). Have students actively follow along as you subtract 262 – 134 using base-ten blocks and Place Value Mats (page 201). Thousands Hundreds Tens Ones 5. Have students actively follow along as you use a pictorial model to subtract 127 – 88. Write the problem and draw base-ten blocks to show the minuend 127. 1 2 7 − 8 8 6. Say, “We always start in the ones place when we subtract, but I can’t subtract 8 from 7.” Regroup by crossing off or erasing 1 rod and replacing it with 10 unit cubes. 7. Say, “The value of 127 is still the same. If I combine 1 hundred, 1 ten, and 17 ones, I have 127.” Model subtracting 8 by crossing off or erasing 8 unit cubes. Say, “We have 1 hundred, 1 ten, and 9 ones, or 119, left.” 8. Subtract the tens. Say, “I need to subtract 8 tens, but there is only 1 ten.” Regroup by crossing off or erasing the flat and replacing it with 10 rods. Model subtracting 8 tens by crossing off or erasing 8 rods. 9. Say, “We are left with 3 rods and 9 unit cubes, or 39. This is the difference, or the answer to 127 – 88.” Guided Practice 10–15 min. 10. Write 618 – 355 where students can see it. Have them solve the problem using Place Value Mats and base-ten blocks or by creating pictorial models. Look for students who are not regrouping correctly and provide corrective feedback in the moment. 11. Demonstrate how to find the difference (263) using base-ten blocks and a pictorial model. Have student volunteers describe how they know when and when not to regroup. Lesson 6 Instruction slides available. 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 Instructional Routine Cards Visit tcmpub.com/FIM-cat INTERVENTION
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